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dynare/matlab/get_identification_jacobians.m

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Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
function [E_y, dE_y, REDUCEDFORM, dREDUCEDFORM, DYNAMIC, dDYNAMIC, MOMENTS, dMOMENTS, dSPECTRUM, dMINIMAL, derivatives_info] = get_identification_jacobians(estim_params, M, oo, options, options_ident, indpmodel, indpstderr, indpcorr, indvobs)
% function [MEAN, dMEAN, REDUCEDFORM, dREDUCEDFORM, DYNAMIC, dDYNAMIC, MOMENTS, dMOMENTS, dSPECTRUM, dMINIMAL, derivatives_info] = get_identification_jacobians(estim_params, M, oo, options, options_ident, indpmodel, indpstderr, indpcorr, indvobs)
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% previously getJJ.m
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
% % Sets up the Jacobians needed for identification analysis
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% =========================================================================
% INPUTS
% estim_params: [structure] storing the estimation information
% M: [structure] storing the model information
% oo: [structure] storing the reduced-form solution results
% options: [structure] storing the options
% options_ident: [structure] storing the options for identification
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
% indpmodel: [modparam_nbr by 1] index of estimated parameters in M_.params;
% corresponds to model parameters (no stderr and no corr)
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% in estimated_params block; if estimated_params block is
% not available, then all model parameters are selected
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
% indpstderr: [stderrparam_nbr by 1] index of estimated standard errors,
% i.e. for all exogenous variables where "stderr" is given
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% in the estimated_params block; if estimated_params block
% is not available, then all stderr parameters are selected
% indpcorr: [corrparam_nbr by 2] matrix of estimated correlations,
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
% i.e. for all exogenous variables where "corr" is given
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% in the estimated_params block; if estimated_params block
% is not available, then no corr parameters are selected
% indvobs: [obs_nbr by 1] index of observed (VAROBS) variables
% -------------------------------------------------------------------------
% OUTPUTS
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
%
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
% MEAN [endo_nbr by 1], in DR order. Expectation of all model variables
% * order==1: corresponds to steady state
% * order==2: computed from pruned state space system (as in e.g. Andreasen, Fernandez-Villaverde, Rubio-Ramirez, 2018)
% dMEAN [endo_nbr by totparam_nbr], in DR Order, Jacobian (wrt all params) of MEAN
%
% REDUCEDFORM [rowredform_nbr by 1] in DR order. Steady state and reduced-form model solution matrices for all model variables
% * order==1: [Yss' vec(dghx)' vech(dghu*Sigma_e*dghu')']',
% where rowredform_nbr = endo_nbr+endo_nbr*nspred+endo_nbr*(endo_nbr+1)/2
% * order==2: [Yss' vec(dghx)' vech(dghu*Sigma_e*dghu')' vec(dghxx)' vec(dghxu)' vec(dghuu)' vec(dghs2)']',
% where rowredform_nbr = endo_nbr+endo_nbr*nspred+endo_nbr*(endo_nbr+1)/2+endo_nbr*nspred^2*endo_nbr*nspred*exo_nr+endo_nbr*exo_nbr^2+endo_nbr
% dREDUCEDFORM: [rowrf_nbr by totparam_nbr] in DR order, Jacobian (wrt all params) of REDUCEDFORM
% * order==1: corresponds to Iskrev (2010)'s J_2 matrix
% * order==2: corresponds to Mutschler (2015)'s J matrix
%
% DYNAMIC [rowdyn_nbr by 1] in declaration order. Steady state and dynamic model derivatives for all model variables
% * order==1: [ys' vec(g1)']', rowdyn_nbr=endo_nbr+length(g1)
% * order==2: [ys' vec(g1)' vec(g2)']', rowdyn_nbr=endo_nbr+length(g1)+length(g2)
% dDYNAMIC [rowdyn_nbr by modparam_nbr] in declaration order. Jacobian (wrt model parameters) of DYNAMIC
% * order==1: corresponds to Ratto and Iskrev (2011)'s J_\Gamma matrix (or LRE)
% * order==2: additionally includes derivatives of dynamic hessian
%
% MOMENTS: [obs_nbr+obs_nbr*(obs_nbr+1)/2+nlags*obs_nbr^2 by 1] in DR order. First two theoretical moments for VAROBS variables, i.e.
% [E[yobs]' vech(E[yobs*yobs'])' vec(E[yobs*yobs(-1)'])' ... vec(E[yobs*yobs(-nlag)'])']
% dMOMENTS: [obs_nbr+obs_nbr*(obs_nbr+1)/2+nlags*obs_nbr^2 by totparam_nbr] in DR order. Jacobian (wrt all params) of MOMENTS
% * order==1: corresponds to Iskrev (2010)'s J matrix
% * order==2: corresponds to Mutschler (2015)'s \bar{M}_2 matrix, i.e. theoretical moments from the pruned state space system
%
% dSPECTRUM: [totparam_nbr by totparam_nbr] in DR order. Gram matrix of Jacobian (wrt all params) of spectral density for VAROBS variables, where
% spectral density at frequency w: f(w) = (2*pi)^(-1)*H(exp(-i*w))*E[xi*xi']*ctranspose(H(exp(-i*w)) with H being the Transfer function
% dSPECTRUM = int_{-\pi}^\pi transpose(df(w)/dp')*(df(w)/dp') dw
% * order==1: corresponds to Qu and Tkachenko (2012)'s G matrix, where xi and H are computed from linear state space system
% * order==2: corresponds to Mutschler (2015)'s G_2 matrix, where xi and H are computed from pruned state space system
%
% dMINIMAL: [obs_nbr+minx^2+minx*exo_nbr+obs_nbr*minx+obs_nbr*exo_nbr+exo_nbr*(exo_nbr+1)/2 by totparam_nbr+minx^2+exo_nbr^2]
% Jacobian (wrt all params, and similarity_transformation_matrices (T and U)) of observational equivalent minimal ABCD system,
% corresponds to Komunjer and Ng (2011)'s Deltabar matrix, where
% MINIMAL = [vec(E[yobs]' vec(minA)' vec(minB)' vec(minC)' vec(minD)' vech(Sigma_e)']'
% * order==1: E[yobs] is equal to steady state
% * order==2: E[yobs] is computed from the pruned state space system (second-order accurate), as noted in section 5 of Komunjer and Ng (2011)
%
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
% derivatives_info [structure] for use in dsge_likelihood to compute Hessian analytically.
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
% Contains dA, dB, and d(B*Sigma_e*B'), where A and B are from Kalman filter. Only used at order==1.
%
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% -------------------------------------------------------------------------
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
% This function is called by
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% * identification_analysis.m
% -------------------------------------------------------------------------
% This function calls
% * commutation
% * get_minimal_state_representation
% * duplication
% * dyn_vech
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
% * get_perturbation_params_derivs (previously getH)
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% * get_all_parameters
% * fjaco
% * lyapunov_symm
% * identification_numerical_objective (previously thet2tau)
% * vec
% =========================================================================
% Copyright (C) 2010-2019 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
% =========================================================================
%get options
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
no_identification_moments = options_ident.no_identification_moments;
no_identification_minimal = options_ident.no_identification_minimal;
no_identification_spectrum = options_ident.no_identification_spectrum;
order = options_ident.order;
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
nlags = options_ident.ar;
useautocorr = options_ident.useautocorr;
grid_nbr = options_ident.grid_nbr;
kronflag = options_ident.analytic_derivation_mode;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
% set values
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
params0 = M.params; %values at which to evaluate dynamic, static and param_derivs files
Sigma_e0 = M.Sigma_e; %covariance matrix of exogenous shocks
Corr_e0 = M.Correlation_matrix; %correlation matrix of exogenous shocks
stderr_e0 = sqrt(diag(Sigma_e0)); %standard errors of exogenous shocks
para0 = get_all_parameters(estim_params, M); %get all selected parameters in estimated_params block, stderr and corr come first, then model parameters
if isempty(para0)
%if there is no estimated_params block, consider all stderr and all model parameters, but no corr parameters
para0 = [stderr_e0', params0'];
end
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
%get numbers/lengths of vectors
modparam_nbr = length(indpmodel);
stderrparam_nbr = length(indpstderr);
corrparam_nbr = size(indpcorr,1);
totparam_nbr = stderrparam_nbr + corrparam_nbr + modparam_nbr;
obs_nbr = length(indvobs);
exo_nbr = M.exo_nbr;
endo_nbr = M.endo_nbr;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
nspred = M.nspred;
nstatic = M.nstatic;
indvall = (1:endo_nbr)'; %index for all endogenous variables
d2flag = 0; % do not compute second parameter derivatives
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
% Get Jacobians (wrt selected params) of steady state, dynamic model derivatives and perturbation solution matrices for all endogenous variables
oo.dr.derivs = get_perturbation_params_derivs(M, options, estim_params, oo, indpmodel, indpstderr, indpcorr, d2flag);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
[I,~] = find(M.lead_lag_incidence'); %I is used to select nonzero columns of the Jacobian of endogenous variables in dynamic model files
yy0 = oo.dr.ys(I); %steady state of dynamic (endogenous and auxiliary variables) in lead_lag_incidence order
Yss = oo.dr.ys(oo.dr.order_var); % steady state in DR order
if order == 1
[~, g1 ] = feval([M.fname,'.dynamic'], yy0, oo.exo_steady_state', params0, oo.dr.ys, 1);
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
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%g1 is [endo_nbr by yy0ex0_nbr first derivative (wrt all dynamic variables) of dynamic model equations, i.e. df/dyy0ex0, rows are in declaration order, columns in lead_lag_incidence order
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
DYNAMIC = [Yss;
vec(g1(oo.dr.order_var,:))]; %add steady state and put rows of g1 in DR order
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
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dDYNAMIC = [oo.dr.derivs.dYss;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
reshape(oo.dr.derivs.dg1(oo.dr.order_var,:,:),size(oo.dr.derivs.dg1,1)*size(oo.dr.derivs.dg1,2),size(oo.dr.derivs.dg1,3)) ]; %reshape dg1 in DR order and add steady state
REDUCEDFORM = [Yss;
vec(oo.dr.ghx);
dyn_vech(oo.dr.ghu*Sigma_e0*transpose(oo.dr.ghu))]; %in DR order
dREDUCEDFORM = zeros(endo_nbr*nspred+endo_nbr*(endo_nbr+1)/2, totparam_nbr);
for j=1:totparam_nbr
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
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dREDUCEDFORM(:,j) = [vec(oo.dr.derivs.dghx(:,:,j));
dyn_vech(oo.dr.derivs.dOm(:,:,j))];
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
end
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
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dREDUCEDFORM = [ [zeros(endo_nbr, stderrparam_nbr+corrparam_nbr) oo.dr.derivs.dYss]; dREDUCEDFORM ]; % add steady state
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
elseif order == 2
[~, g1, g2 ] = feval([M.fname,'.dynamic'], yy0, oo.exo_steady_state', params0, oo.dr.ys, 1);
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
%g1 is [endo_nbr by yy0ex0_nbr first derivative (wrt all dynamic variables) of dynamic model equations, i.e. df/dyy0ex0, rows are in declaration order, columns in lead_lag_incidence order
%g2 is [endo_nbr by yy0ex0_nbr^2] second derivative (wrt all dynamic variables) of dynamic model equations, i.e. d(df/dyy0ex0)/dyy0ex0, rows are in declaration order, columns in lead_lag_incidence order
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
DYNAMIC = [Yss;
vec(g1(oo.dr.order_var,:));
vec(g2(oo.dr.order_var,:))]; %add steady state and put rows of g1 and g2 in DR order
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
dDYNAMIC = [oo.dr.derivs.dYss;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
reshape(oo.dr.derivs.dg1(oo.dr.order_var,:,:),size(oo.dr.derivs.dg1,1)*size(oo.dr.derivs.dg1,2),size(oo.dr.derivs.dg1,3)); %reshape dg1 in DR order
reshape(oo.dr.derivs.dg2(oo.dr.order_var,:),size(oo.dr.derivs.dg1,1)*size(oo.dr.derivs.dg1,2)^2,size(oo.dr.derivs.dg1,3))]; %reshape dg2 in DR order
REDUCEDFORM = [Yss;
vec(oo.dr.ghx);
dyn_vech(oo.dr.ghu*Sigma_e0*transpose(oo.dr.ghu));
vec(oo.dr.ghxx);
vec(oo.dr.ghxu);
vec(oo.dr.ghuu);
vec(oo.dr.ghs2)]; %in DR order
dREDUCEDFORM = zeros(endo_nbr*nspred+endo_nbr*(endo_nbr+1)/2+endo_nbr*nspred^2+endo_nbr*nspred*exo_nbr+endo_nbr*exo_nbr^2+endo_nbr, totparam_nbr);
for j=1:totparam_nbr
dREDUCEDFORM(:,j) = [vec(oo.dr.derivs.dghx(:,:,j));
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
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dyn_vech(oo.dr.derivs.dOm(:,:,j));
vec(oo.dr.derivs.dghxx(:,:,j));
vec(oo.dr.derivs.dghxu(:,:,j));
vec(oo.dr.derivs.dghuu(:,:,j));
vec(oo.dr.derivs.dghs2(:,j))];
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
end
dREDUCEDFORM = [ [zeros(endo_nbr, stderrparam_nbr+corrparam_nbr) oo.dr.derivs.dYss]; dREDUCEDFORM ]; % add steady state
elseif order == 3
[~, g1, g2, g3 ] = feval([M.fname,'.dynamic'], yy0, oo.exo_steady_state', params0, oo.dr.ys, 1);
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
%g1 is [endo_nbr by yy0ex0_nbr first derivative (wrt all dynamic variables) of dynamic model equations, i.e. df/dyy0ex0, rows are in declaration order, columns in lead_lag_incidence order
%g2 is [endo_nbr by yy0ex0_nbr^2] second derivative (wrt all dynamic variables) of dynamic model equations, i.e. d(df/dyy0ex0)/dyy0ex0, rows are in declaration order, columns in lead_lag_incidence order
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
DYNAMIC = [Yss;
vec(g1(oo.dr.order_var,:));
vec(g2(oo.dr.order_var,:));
vec(g3(oo.dr.order_var,:))]; %add steady state and put rows of g1 and g2 in DR order
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
dDYNAMIC = [oo.dr.derivs.dYss;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
reshape(oo.dr.derivs.dg1(oo.dr.order_var,:,:),size(oo.dr.derivs.dg1,1)*size(oo.dr.derivs.dg1,2),size(oo.dr.derivs.dg1,3)); %reshape dg1 in DR order
reshape(oo.dr.derivs.dg2(oo.dr.order_var,:),size(oo.dr.derivs.dg1,1)*size(oo.dr.derivs.dg1,2)^2,size(oo.dr.derivs.dg1,3));
reshape(oo.dr.derivs.dg2(oo.dr.order_var,:),size(oo.dr.derivs.dg1,1)*size(oo.dr.derivs.dg1,2)^2,size(oo.dr.derivs.dg1,3))]; %reshape dg3 in DR order
REDUCEDFORM = [Yss;
vec(oo.dr.ghx);
dyn_vech(oo.dr.ghu*Sigma_e0*transpose(oo.dr.ghu));
vec(oo.dr.ghxx); vec(oo.dr.ghxu); vec(oo.dr.ghuu); vec(oo.dr.ghs2);
vec(oo.dr.ghxxx); vec(oo.dr.ghxxu); vec(oo.dr.ghxuu); vec(oo.dr.ghuuu); vec(oo.dr.ghxss); vec(oo.dr.ghuss)]; %in DR order
dREDUCEDFORM = zeros(size(REDUCEDFORM,1)-endo_nbr, totparam_nbr);
for j=1:totparam_nbr
dREDUCEDFORM(:,j) = [vec(oo.dr.derivs.dghx(:,:,j));
dyn_vech(oo.dr.derivs.dOm(:,:,j));
vec(oo.dr.derivs.dghxx(:,:,j)); vec(oo.dr.derivs.dghxu(:,:,j)); vec(oo.dr.derivs.dghuu(:,:,j)); vec(oo.dr.derivs.dghs2(:,j))
vec(oo.dr.derivs.dghxxx(:,:,j)); vec(oo.dr.derivs.dghxxu(:,:,j)); vec(oo.dr.derivs.dghxuu(:,:,j)); vec(oo.dr.derivs.dghuuu(:,:,j)); vec(oo.dr.derivs.dghxss(:,:,j)); vec(oo.dr.derivs.dghuss(:,:,j))];
end
dREDUCEDFORM = [ [zeros(endo_nbr, stderrparam_nbr+corrparam_nbr) oo.dr.derivs.dYss]; dREDUCEDFORM ]; % add steady state
end
% Get (pruned) state space representation:
options.options_ident.indvobs = indvobs;
options.options_ident.indpmodel = indpmodel;
options.options_ident.indpstderr = indpstderr;
options.options_ident.indpcorr = indpcorr;
oo.dr = pruned_state_space_system(M, options, oo.dr);
Fixed bug regarding non-stationary variables in pruned moments
2019-12-20 12:26:38 +01:00
E_y = oo.dr.pruned.E_y; dE_y = oo.dr.pruned.dE_y;
A = oo.dr.pruned.A; dA = oo.dr.pruned.dA;
B = oo.dr.pruned.B; dB = oo.dr.pruned.dB;
C = oo.dr.pruned.C; dC = oo.dr.pruned.dC;
D = oo.dr.pruned.D; dD = oo.dr.pruned.dD;
c = oo.dr.pruned.c; dc = oo.dr.pruned.dc;
d = oo.dr.pruned.d; dd = oo.dr.pruned.dd;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
Varinov = oo.dr.pruned.Varinov; dVarinov = oo.dr.pruned.dVarinov;
Om_z = oo.dr.pruned.Om_z; dOm_z = oo.dr.pruned.dOm_z;
Om_y = oo.dr.pruned.Om_y; dOm_y = oo.dr.pruned.dOm_y;
%storage for Jacobians used in dsge_likelihood.m for analytical Gradient and Hession of likelihood (only at order=1)
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
derivatives_info = struct();
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
if order == 1
dT = zeros(endo_nbr,endo_nbr,totparam_nbr);
dT(:,(nstatic+1):(nstatic+nspred),:) = oo.dr.derivs.dghx;
derivatives_info.DT = dT;
derivatives_info.DOm = oo.dr.derivs.dOm;
derivatives_info.DYss = oo.dr.derivs.dYss;
end
%% Compute dMOMENTS
%Note that our state space system for computing second moments is the following:
% zhat = A*zhat(-1) + B*xi, where zhat = z - E(z)
% yhat = C*zhat(-1) + D*xi, where yhat = y - E(y)
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
if ~no_identification_moments
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
MOMENTS = identification_numerical_objective(para0, 1, estim_params, M, oo, options, indpmodel, indpstderr, indpcorr, indvobs, useautocorr, nlags, grid_nbr); %[outputflag=1]
MOMENTS = [E_y; MOMENTS];
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
if kronflag == -1
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
%numerical derivative of autocovariogram
dMOMENTS = fjaco(str2func('identification_numerical_objective'), para0, 1, estim_params, M, oo, options, indpmodel, indpstderr, indpcorr, indvobs, useautocorr, nlags, grid_nbr); %[outputflag=1]
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
M.params = params0; %make sure values are set back
M.Sigma_e = Sigma_e0; %make sure values are set back
M.Correlation_matrix = Corr_e0 ; %make sure values are set back
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dMOMENTS = [dE_y; dMOMENTS]; %add Jacobian of steady state of VAROBS variables
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
else
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dMOMENTS = zeros(obs_nbr + obs_nbr*(obs_nbr+1)/2 + nlags*obs_nbr^2 , totparam_nbr);
dMOMENTS(1:obs_nbr,:) = dE_y; %add Jacobian of first moments of VAROBS variables
% Denote Ezz0 = E[zhat*zhat'], then the following Lyapunov equation defines the autocovariagram: Ezz0 -A*Ezz0*A' = B*Sig_xi*B' = Om_z
Fixed bug regarding non-stationary variables in pruned moments
2019-12-20 12:26:38 +01:00
[Ezz0,u] = lyapunov_symm(A, Om_z, options.lyapunov_fixed_point_tol, options.qz_criterium, options.lyapunov_complex_threshold, 1, options.debug);
stationary_vars = (1:length(indvobs))';
if ~isempty(u)
x = abs(C*u);
stationary_vars = find(all(x < options.Schur_vec_tol,2));
end
Eyy0 = NaN*ones(obs_nbr,obs_nbr);
Eyy0(stationary_vars,stationary_vars) = C(stationary_vars,:)*Ezz0*C(stationary_vars,:)' + Om_y(stationary_vars,stationary_vars);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
%here method=1 is used, whereas all other calls of lyapunov_symm use method=2. The reason is that T and U are persistent, and input matrix A is the same, so using option 2 for all the rest of iterations spares a lot of computing time while not repeating Schur every time
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
indzeros = find(abs(Eyy0) < 1e-12); %find values that are numerical zero
Fixed bug regarding non-stationary variables in pruned moments
2019-12-20 12:26:38 +01:00
Eyy0(indzeros) = 0;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
if useautocorr
sdy = sqrt(diag(Eyy0)); %theoretical standard deviation
Fixed bug regarding non-stationary variables in pruned moments
2019-12-20 12:26:38 +01:00
sdy = sdy(stationary_vars);
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
sy = sdy*sdy'; %cross products of standard deviations
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
for jp = 1:totparam_nbr
if jp <= (stderrparam_nbr+corrparam_nbr)
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
%Note that for stderr and corr parameters, the derivatives of the system matrices are zero, i.e. dA=dB=dC=dD=0
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dEzz0 = lyapunov_symm(A,dOm_z(:,:,jp),options.lyapunov_fixed_point_tol,options.qz_criterium,options.lyapunov_complex_threshold,2,options.debug); %here method=2 is used to spare a lot of computing time while not repeating Schur every time
dEyy0 = C*dEzz0*C' + dOm_y(:,:,jp);
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
else %model parameters
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dEzz0 = lyapunov_symm(A,dOm_z(:,:,jp)+dA(:,:,jp)*Ezz0*A'+A*Ezz0*dA(:,:,jp)',options.lyapunov_fixed_point_tol,options.qz_criterium,options.lyapunov_complex_threshold,2,options.debug); %here method=2 is used to spare a lot of computing time while not repeating Schur every time
dEyy0 = dC(:,:,jp)*Ezz0*C' + C*dEzz0*C' + C*Ezz0*dC(:,:,jp)' + dOm_y(:,:,jp);
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
end
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
%indzeros = find(abs(dEyy0) < 1e-12);
%dEyy0(indzeros) = 0;
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
if useautocorr
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dsy = 1/2./sdy.*diag(dEyy0);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
dsy = dsy*sdy'+sdy*dsy';
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dEyy0corr = (dEyy0.*sy-dsy.*Eyy0)./(sy.*sy);
dEyy0corr = dEyy0corr-diag(diag(dEyy0corr))+diag(diag(dEyy0));
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
dMOMENTS(obs_nbr+1 : obs_nbr+obs_nbr*(obs_nbr+1)/2 , jp) = dyn_vech(dEyy0corr); %focus only on VAROBS variables
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
else
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dMOMENTS(obs_nbr+1 : obs_nbr+obs_nbr*(obs_nbr+1)/2 , jp) = dyn_vech(dEyy0); %focus only on VAROBS variables
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
Fixed bug regarding non-stationary variables in pruned moments
2019-12-20 12:26:38 +01:00
tmpEyyi = A*Ezz0*C(stationary_vars,:)' + B*Varinov*D(stationary_vars,:)';
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
%we could distinguish between stderr and corr params, but this has no real speed effect as we multipliy with zeros
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
dtmpEyyi = dA(:,:,jp)*Ezz0*C' + A*dEzz0*C' + A*Ezz0*dC(:,:,jp)' + dB(:,:,jp)*Varinov*D' + B*dVarinov(:,:,jp)*D' + B*Varinov*dD(:,:,jp)';
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
Ai = eye(size(A,1)); %this is A^0
dAi = zeros(size(A,1),size(A,1)); %this is d(A^0)
for i = 1:nlags
Fixed bug regarding non-stationary variables in pruned moments
2019-12-20 12:26:38 +01:00
Eyyi = C(stationary_vars,:)*Ai*tmpEyyi;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dEyyi = dC(:,:,jp)*Ai*tmpEyyi + C*dAi*tmpEyyi + C*Ai*dtmpEyyi;
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
if useautocorr
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dEyyi = (dEyyi.*sy-dsy.*Eyyi)./(sy.*sy);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dMOMENTS(obs_nbr + obs_nbr*(obs_nbr+1)/2 + (i-1)*obs_nbr^2 + 1 : obs_nbr + obs_nbr*(obs_nbr+1)/2 + i*obs_nbr^2, jp) = vec(dEyyi); %focus only on VAROBS variables
dAi = dAi*A + Ai*dA(:,:,jp); %note that this is d(A^(i-1))
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
Ai = Ai*A; %note that this is A^(i-1)
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
end
end
else
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
MOMENTS = [];
dMOMENTS = [];
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
%% Compute dSPECTRUM
%Note that our state space system for computing the spectrum is the following:
% zhat = A*zhat(-1) + B*xi, where zhat = z - E(z)
% yhat = C*zhat(-1) + D*xi, where yhat = y - E(y)
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
if ~no_identification_spectrum
%Some info on the spectral density: Dynare's state space system is given for states (z_{t} = A*z_{t-1} + B*u_{t}) and observables (y_{t} = C*z_{t-1} + D*u_{t})
%The spectral density for y_{t} can be computed using different methods, which are numerically equivalent
%See the following code example for the different ways;
% freqs = 2*pi*(-(grid_nbr/2):1:(grid_nbr/2))'/grid_nbr; %divides the interval [-pi;pi] into ngrid+1 points
% tpos = exp( sqrt(-1)*freqs); %positive Fourier frequencies
% tneg = exp(-sqrt(-1)*freqs); %negative Fourier frequencies
% IA = eye(size(A,1));
% IE = eye(M.exo_nbr);
% mathp_col1 = NaN(length(freqs),obs_nbr^2); mathp_col2 = mathp_col1; mathp_col3 = mathp_col1; mathp_col4 = mathp_col1;
% for ig = 1:length(freqs)
% %method 1: as in UnivariateSpectralDensity.m
% f_omega =(1/(2*pi))*( [(IA-A*tneg(ig))\B;IE]*M.Sigma_e*[B'/(IA-A'*tpos(ig)) IE]); % state variables
% g_omega1 = [C*tneg(ig) D]*f_omega*[C'*tpos(ig); D']; % selected variables
% %method 2: as in UnivariateSpectralDensity.m but simplified algebraically
% g_omega2 = (1/(2*pi))*( C*((tpos(ig)*IA-A)\(B*M.Sigma_e*B'))*((tneg(ig)*IA-A')\(C')) + D*M.Sigma_e*B'*((tneg(ig)*IA-A')\(C')) + C* ((tpos(ig)*IA-A)\(B*M.Sigma_e*D')) + D*M.Sigma_e*D' );
% %method 3: use transfer function note that ' is the complex conjugate transpose operator i.e. transpose(ffneg')==ffpos
% Transferfct = D+C*((tpos(ig)*IA-A)\B);
% g_omega3 = (1/(2*pi))*(Transferfct*M.Sigma_e*Transferfct');
% %method 4: kronecker products
% g_omega4 = (1/(2*pi))*( kron( D+C*((tneg(ig)^(-1)*IA-A)\B) , D+C*((tneg(ig)*IA-A)\B) )*M.Sigma_e(:));
% % store as matrix row
% mathp_col1(ig,:) = (g_omega1(:))'; mathp_col2(ig,:) = (g_omega2(:))'; mathp_col3(ig,:) = (g_omega3(:))'; mathp_col4(ig,:) = g_omega4;
% end
% disp([norm(mathp_col1 - mathp_col2); norm(mathp_col1 - mathp_col3); norm(mathp_col1 - mathp_col4); norm(mathp_col2 - mathp_col3); norm(mathp_col2 - mathp_col4); norm(mathp_col3 - mathp_col4);])
%In the following we focus on method 3
%Symmetry:
% Note that for the compuation of the G matrix we focus only on positive Fourier frequencies due to symmetry of the real part of the spectral density and, hence, the G matrix (which is real by construction).
% E.g. if grid_nbr=4, then we subdivide the intervall [-pi;pi] into [-3.1416;-1.5708;0;1.5708;3.1416], but focus only on [0;1.5708;3.1416] for the computation of the G matrix,
% keeping in mind that the frequencies [1.5708;3.1416] need to be added twice, whereas the 0 frequency is only added once.
freqs = (0 : pi/(grid_nbr/2):pi); % we focus only on positive frequencies
tpos = exp( sqrt(-1)*freqs); %positive Fourier frequencies
tneg = exp(-sqrt(-1)*freqs); %negative Fourier frequencies
IA = eye(size(A,1));
if kronflag == -1
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
%numerical derivative of spectral density
dOmega_tmp = fjaco(str2func('identification_numerical_objective'), para0, 2, estim_params, M, oo, options, indpmodel, indpstderr, indpcorr, indvobs, useautocorr, nlags, grid_nbr); %[outputflag=2]
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
M.params = params0; %make sure values are set back
M.Sigma_e = Sigma_e0; %make sure values are set back
M.Correlation_matrix = Corr_e0 ; %make sure values are set back
kk = 0;
for ig = 1:length(freqs)
kk = kk+1;
dOmega = dOmega_tmp(1 + (kk-1)*obs_nbr^2 : kk*obs_nbr^2,:);
if ig == 1 % add zero frequency once
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dSPECTRUM = dOmega'*dOmega;
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
else % due to symmetry to negative frequencies we can add positive frequencies twice
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dSPECTRUM = dSPECTRUM + 2*(dOmega'*dOmega);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
end
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
elseif kronflag == 1
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
%use Kronecker products
dA = reshape(dA,size(dA,1)*size(dA,2),size(dA,3));
dB = reshape(dB,size(dB,1)*size(dB,2),size(dB,3));
dC = reshape(dC,size(dC,1)*size(dC,2),size(dC,3));
dD = reshape(dD,size(dD,1)*size(dD,2),size(dD,3));
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dVarinov = reshape(dVarinov,size(dVarinov,1)*size(dVarinov,2),size(dVarinov,3));
K_obs_exo = commutation(obs_nbr,size(Varinov,1));
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
for ig=1:length(freqs)
z = tneg(ig);
zIminusA = (z*IA - A);
zIminusAinv = zIminusA\IA;
Transferfct = D + C*zIminusAinv*B; % Transfer function
dzIminusA = -dA;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dzIminusAinv = kron(-(transpose(zIminusA)\IA),zIminusAinv)*dzIminusA; %this takes long
dTransferfct = dD + DerivABCD(C,dC,zIminusAinv,dzIminusAinv,B,dB); %also long
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
dTransferfct_conjt = K_obs_exo*conj(dTransferfct);
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dOmega = (1/(2*pi))*DerivABCD(Transferfct,dTransferfct,Varinov,dVarinov,Transferfct',dTransferfct_conjt); %also long
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
if ig == 1 % add zero frequency once
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dSPECTRUM = dOmega'*dOmega;
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
else % due to symmetry to negative frequencies we can add positive frequencies twice
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dSPECTRUM = dSPECTRUM + 2*(dOmega'*dOmega);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
end
%put back into tensor notation
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dA = reshape(dA,size(A,1),size(A,2),totparam_nbr);
dB = reshape(dB,size(B,1),size(B,2),totparam_nbr);
dC = reshape(dC,size(C,1),size(C,2),totparam_nbr);
dD = reshape(dD,size(D,1),size(D,2),totparam_nbr);
dVarinov = reshape(dVarinov,size(Varinov,1),size(Varinov,2),totparam_nbr);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
elseif (kronflag==0) || (kronflag==-2)
for ig = 1:length(freqs)
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
IzminusA = tpos(ig)*IA - A;
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
invIzminusA = IzminusA\eye(size(A,1));
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
Transferfct = D + C*invIzminusA*B;
dOmega = zeros(obs_nbr^2,totparam_nbr);
for j = 1:totparam_nbr
if j <= stderrparam_nbr+corrparam_nbr %stderr and corr parameters: only dSig is nonzero
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dOmega_tmp = Transferfct*dVarinov(:,:,j)*Transferfct';
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
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else %model parameters
dinvIzminusA = -invIzminusA*(-dA(:,:,j))*invIzminusA;
dTransferfct = dD(:,:,j) + dC(:,:,j)*invIzminusA*B + C*dinvIzminusA*B + C*invIzminusA*dB(:,:,j);
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dOmega_tmp = dTransferfct*Varinov*Transferfct' + Transferfct*dVarinov(:,:,j)*Transferfct' + Transferfct*Varinov*dTransferfct';
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
dOmega(:,j) = (1/(2*pi))*dOmega_tmp(:);
end
if ig == 1 % add zero frequency once
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dSPECTRUM = dOmega'*dOmega;
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
else % due to symmetry to negative frequencies we can add positive frequencies twice
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dSPECTRUM = dSPECTRUM + 2*(dOmega'*dOmega);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
end
end
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% Normalize Matrix and add steady state Jacobian, note that G is real and symmetric by construction
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dSPECTRUM = 2*pi*dSPECTRUM./(2*length(freqs)-1) + dE_y'*dE_y;
dSPECTRUM = real(dSPECTRUM);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
else
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dSPECTRUM = [];
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
%% Compute dMINIMAL
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
if ~no_identification_minimal
if obs_nbr < exo_nbr
% Check whether criteria can be used
warning_KomunjerNg = 'WARNING: Komunjer and Ng (2011) failed:\n';
warning_KomunjerNg = [warning_KomunjerNg ' There are more shocks and measurement errors than observables, this is not implemented (yet).\n'];
warning_KomunjerNg = [warning_KomunjerNg ' Skip identification analysis based on minimal state space system.\n'];
fprintf(warning_KomunjerNg);
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dMINIMAL = [];
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
else
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
% Derive and check minimal state vector of first-order
[CheckCO,minnx,minA,minB,minC,minD,dminA,dminB,dminC,dminD] = get_minimal_state_representation(oo.dr.ghx(oo.dr.pruned.indx,:),... %A
oo.dr.ghu(oo.dr.pruned.indx,:),... %B
oo.dr.ghx(oo.dr.pruned.indy,:),... %C
oo.dr.ghu(oo.dr.pruned.indy,:),... %D
oo.dr.derivs.dghx(oo.dr.pruned.indx,:,:),... %dA
oo.dr.derivs.dghu(oo.dr.pruned.indx,:,:),... %dB
oo.dr.derivs.dghx(oo.dr.pruned.indy,:,:),... %dC
oo.dr.derivs.dghu(oo.dr.pruned.indy,:,:)); %dD
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
if CheckCO == 0
warning_KomunjerNg = 'WARNING: Komunjer and Ng (2011) failed:\n';
warning_KomunjerNg = [warning_KomunjerNg ' Conditions for minimality are not fullfilled:\n'];
warning_KomunjerNg = [warning_KomunjerNg ' Skip identification analysis based on minimal state space system.\n'];
fprintf(warning_KomunjerNg); %use sprintf to have line breaks
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dMINIMAL = [];
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
else
%reshape into Magnus-Neudecker Jacobians, i.e. dvec(X)/dp
dminA = reshape(dminA,size(dminA,1)*size(dminA,2),size(dminA,3));
dminB = reshape(dminB,size(dminB,1)*size(dminB,2),size(dminB,3));
dminC = reshape(dminC,size(dminC,1)*size(dminC,2),size(dminC,3));
dminD = reshape(dminD,size(dminD,1)*size(dminD,2),size(dminD,3));
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dvechSig = reshape(oo.dr.derivs.dSigma_e,exo_nbr*exo_nbr,totparam_nbr);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
indvechSig= find(tril(ones(exo_nbr,exo_nbr)));
dvechSig = dvechSig(indvechSig,:);
Inx = eye(minnx);
Inu = eye(exo_nbr);
[~,Enu] = duplication(exo_nbr);
KomunjerNg_DL = [dminA; dminB; dminC; dminD; dvechSig];
KomunjerNg_DT = [kron(transpose(minA),Inx) - kron(Inx,minA);
kron(transpose(minB),Inx);
-1*kron(Inx,minC);
zeros(obs_nbr*exo_nbr,minnx^2);
zeros(exo_nbr*(exo_nbr+1)/2,minnx^2)];
KomunjerNg_DU = [zeros(minnx^2,exo_nbr^2);
Global reindentation of MATLAB code (excluding submodules) Also convert to Unix end-of-lines, and remove trailing whitespaces.
2019-12-20 16:28:06 +01:00
kron(Inu,minB);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
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zeros(obs_nbr*minnx,exo_nbr^2);
kron(Inu,minD);
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
-2*Enu*kron(Sigma_e0,Inu)];
dMINIMAL = full([KomunjerNg_DL KomunjerNg_DT KomunjerNg_DU]);
%add Jacobian of steady state (here we also allow for higher-order perturbation, i.e. only the mean provides additional restrictions
dMINIMAL = [dE_y zeros(obs_nbr,minnx^2+exo_nbr^2); dMINIMAL];
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
end
else
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dMINIMAL = [];
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
function [dX] = DerivABCD(X1,dX1,X2,dX2,X3,dX3,X4,dX4)
% function [dX] = DerivABCD(X1,dX1,X2,dX2,X3,dX3,X4,dX4)
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% -------------------------------------------------------------------------
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
% Derivative of X(p)=X1(p)*X2(p)*X3(p)*X4(p) w.r.t to p
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% See Magnus and Neudecker (1999), p. 175
% -------------------------------------------------------------------------
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
% Inputs: Matrices X1,X2,X3,X4, and the corresponding derivatives w.r.t p.
% Output: Derivative of product of X1*X2*X3*X4 w.r.t. p
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% =========================================================================
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
nparam = size(dX1,2);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
% If one or more matrices are left out, they are set to zero
if nargin == 4
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
X3=speye(size(X2,2)); dX3=spalloc(numel(X3),nparam,0);
X4=speye(size(X3,2)); dX4=spalloc(numel(X4),nparam,0);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
elseif nargin == 6
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
X4=speye(size(X3,2)); dX4=spalloc(numel(X4),nparam,0);
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
dX = kron(transpose(X4)*transpose(X3)*transpose(X2),speye(size(X1,1)))*dX1...
+ kron(transpose(X4)*transpose(X3),X1)*dX2...
+ kron(transpose(X4),X1*X2)*dX3...
+ kron(speye(size(X4,2)),X1*X2*X3)*dX4;
Improvement of Identification Toolbox # Improvements * heavily commented (also auxiliary functions) and changed notation to make all the functions (hopefully) more readable and understandable, and hence, easier to debug * added identification criteria of Komunjer and Ng (2011, Econometrica) and Qu and Tkachenko (2012, Quantitative Economics) * tests can be turned of, i.e. nostrength disables identification strenght, noreducedform disables reduced form criteria, nomoments disables moment criteria, nospectrum disables spectrum criteria, nominimal disables minimal system criteria * all kronflags (analytic_derivation_mode) actually work in all functions * added functionality when there is correlation in Sigma_e and when one wants to consider corr parameters of exogenous shocks. Previously, (1) corr parameters were not allowed when calling identification and (2) when Sigma_e was not diagonal then the toolbox relied on numerical derviatives only (kronflag=-1). Now it is possible to handle both identification of corr parameters as well as correct analytical derivatives when Sigma_e is not diagonal with all possible kronflag values (-1|-2|0|1) * all plots and results are stored in the same folder named identification (previously there was another one with a capital I (Identification)) # Needed changes to preprocessor * add as field to options_ident: - tex (same as in options_) - nostrength (to turn off identification strength) - noreducedform (to turn off reduced form criteria) - nomoments (to turn off Iskrev's moment criteria) - nominimal (to turn off Komunjer and Ng's minimal system criteria) - nospectrum (to turn off Qu and Tkachenko's spectrum criteria) * add to options_ident: - normalize_jacobians (whether to normalize Jacobians or not) - grid_nbr (integer used to discretize the interval [-pi;pi] - tol_rank (tolerance level to compute ranks) - tol_deriv (tolerance level to select nonzero columns in derivatives) - tol_sv (tolerance level to select nonzero singular values) - ChecksViaSubsets (for debugging purposes, uses different function to find problematic parameter sets) - max_dim_subsets_groups (for debugging purposes, used for ChecksViaSubsets) # Further Suggestions * Rename getH.m into getParamsDerivReducedForm.m to make the purpose of this function evident * Rename getJJ.m into getIdentificationJacobians.m to make the purpose of this function evident * Rename thet2tau.m into IdentificationNumericalObjectiveFunction.m to make the purpose of this function evident * dYss, d2Yss, dg1 should also include derivatives wrt to stderr and corr parameters (even though these are just 0), as in other functions (getJJ, dynare_estimation) we always add these manually * I am pretty sure the current handling in getH.m of dYss and d2Yss is not correct in the case of nonstationary variables (if g2static is nonempty), I added a warning message, as I am not sure whether this is ever used * It would be straigthforward to also include stderr and corr parameters of measurement errors (these is not possible right now). Should I do this? * Computations of d2A and d2Om need to be checked, as the differences between computing these with analytically (kronflag=0|1) or numerically kronflag=-1|-2 is really large for the example model of AnSchorfheide. * I am not sure how to best normalize Qu and Tkachenko's G matrix. It looks (and in the Gaussian case actually is) very similar to the Ahess matrix. So I used the same normalization rule as for the Ahess matrix. See comments in identification_checks.m. Anyone has a better idea? Please also check the models in test/identification/cgg for differences. * parts that are unclear to me are marked by a [@wmutschl] tag * the run time of tests/identification/as2007.mod increases from 0h01m27s to 0h03m46s (as Qu and Tkachenko's G matrix takes a little while to compute). One could decrease prior_mc=250 to prior_mc=150. # New functions * commutation: Returns Magnus and Neudecker's commutation matrix that solves k*vec(X)=vec(X') * DerivABCD: Derivative of X(p)=A(p)*B(p)*C(p)*D(p) w.r.t to p as in Magnus and Neudecker (1999), p. 175 * DeriveMinimalState: Derives minimal state space system by checking observability and controllability of all possible combinations of variables * duplication: Duplication Matrix (and its Moore Penrose Inverse) as defined by Magnus and Neudecker (2002), p.49, Dp*vec(X) = X * identification_checks_via_subsets: finds problematic parameters in a bruteforce fashion: It computes the rank of the Jacobians for all possible parameter combinations, if the rank condition is not fullfilled, these parameter sets are flagged as non-identifiable. For debugging purposes only, as the current identification_checks.m (based on nullspace and multicorrelation coefficients) is much faster # Detailed changes in getH.m * functionality improvements - heavily commented (also auxiliary functions) and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - fixed function for all values of kronflag, i.e. kronflag=-2|-1|0|1. Previosuly, only kronflag=-2|0 were working, all other kronflags ran into errors (-1 was actually never called , but was dealt with in getJJ.m). I assume kronflag=-1|1 was used only for debugging issues, but still was not working. I fixed this now, the function now works out-of-the-box for all kronflag values. - I also outlined and documented what each kronflag does and point to the corresponding equations in Ratto and Iskrev (2012) or Iskrev (2010,Appendix A) - the function additionally outputs the Jacobians of B and Sig, which are needed for Qu and Tkachenko (2012) and Komunjer and Ng (2011)'s criteria - Moved computation of Jacobian of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into getJJ.m to have all Jacobians which are needed for identification in one place. That is, getH.m computes first and second parameter derivatives of (1) reduced-form solution, (2) steady state and (3) Jacobian of dynamic model, whereas getJJ computes and sets up all Jacobians which are used for identification purposes. Therefore, getH might be useful more generally for other purposes than identification. For instance, when doing a GMM estimation, we could use this function to compute analytically the gradient of the moments and provide this to the optimizer used in a GMM context. * output arguments - renamed `H` (Jacobian wrt parameters of tau=[ys;vec(A);vech(B * M_.Sigma_e * B')] into dTAU, (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `Hss` (Jacobian of steady state wrt model parameters only) into `dYss` (as H is very confusing here, see above) - renamed `H2ss` (Hessian wrt model parameters only of ys) into d2Yss (as H is very confusing, see above) - renamed `gp` into `dg1`, where g1 corresponds to the same variable as in dynamic model files. Note that in params_deriv files gp lacks the contribution of Jacobian wrt steady state and dg1 includes this using the implicit function theorem as outlined in Ratto and Iskrev (2012). Hence, dg1 denotes Jacobian wrt to parameters. It is useful and important to distinguish gp and dg1. - added `dB` (Jacobian wrt parameters of solution matrix B) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) - added `dSig` (Jacobian wrt parameters of M_.Sigma_e) needed for Qu and Tkachenko (2012) as well as Komunjer and Ng (2011) * input arguments - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - renamed `iv` (index of variables to consider) into `indvar` - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - included `indpcorr` a matrix of indices for corr parameters to be checked * misc - distinguished clearly between variables in DR or in declaration order without overwriting this in between - added which functions call getH.m - updated copyright to 2010-2019 # Detailed changes in getJJ.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - added functionality when Sigma_e is not diagonal and/or when one wants to consider corr parameters of exogenous shocks independent of the value of kronflag - tidied the function up, such that it sets up all Jacobians which are needed for identification, i.e. Iskrev's J matrix, Qu and Tkachenko (2012)'s G matrix, Komunjer and Ng (2011)'s D matrix, reduced-form solution (dTAU), linear rational expectation (i.e. Jacobian of steady state and dynamic model equations dLRE). - dTAU is now constructed in getJJ instead of in getH (see comment above in getH.m) - works for all kronflags, i.e. for numerical derivatives (-1 and -2) as well as for analytical derivatives based on kronecker products (1) or Sylvester Equations (0) - added functionality for stderr and corr parameters independent of the value of kronflag (previously this was only possible with numerical derivatives, now it works for all kronflags) - finds minimal state vector needed for Komunjer and Ng (2011)'s criteria (function `DeriveMinimalState.m`) - moved computations from kronflag=-1 (which were used in case of corr in shock block) into getH.m, so that getJJ now only sets up the Jacobians for LRE, Iskrev's J, Qu and Tkachenko's G and Komunjer and Ng's D, whereas getH computes the Jacobians (wrt parameters) of A, B, Sigma_e, Om, Yss and g1. This should simplify debugging as everything is now in one place and not in two * output arguments - renamed `JJ` into `J` - renamed `H` into `dTAU` (as H is very confusing, e.g. in other functions it is a Hessian, or Hss and H2ss is also just the steady state. Morevoer, tau is used in Iskrev(2010) for the steady state and reduced-form solution) - renamed `gp` into `dLRE`, as this corresponds to Jacobian of LRE=[Yss;vec(g1)] where g1 is the Jacobian of the dynamic model equations. - renamed `gam` into `MOMENTS` - added `G` for Qu and Tkachenko's Jacobian matrix G - added `D` for Komunjer and Ng's Jacobian matrix D - reordered output arguments * input arguments - added `options_ident` as input argument; hence, `kronflag`, `nlags` and `useautocorr` are removed from input arguments as these are available in options_ident - Renamed `M_` to `M`, `estim_params_` to `estim_params`, `options_` to `options` , `oo_` to `oo` to visualize that these are local and not global variables - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - renamed `mf` (index of VAROBS variables) into `indvobs` * misc - updated copyright to 2010-2019 - provided some comments on several ways to compute the spectral density matrix - added which functions call getJJ.m # Detailed changes in thet2tau.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - Added output option to compute spectral density matrix - Reorded and added some output option. - Instead of Om, `outputflag=0` computes B and Sigma_e, which are needed for Qu and Tkachenko as well as Komunjer and Ng. The Jacobian of Om is then computed in getJJ or getH from Jacobian of B and Sigma_e. Due to some testing with An and Schorfheide model this seems to be more accurate when I compare these with the analytical derivatives. The old behavior (computing Om directly) can be restored by setting `outputflag=-2`. - In total this function can now be used to compute numerically Jacobians of Yss, A, B, Sigma_e, Om, g1, autocovariogram and spectral density - Clearly distinguished (and commented) on the different outputs of this function. - Works for all types of parameters, ie. model, stderr and corr. - This function can now also be used when there is no estimated_params block. Previously, there was an error when there was no estimated_params block when calling `set_all_parameters` as this requires some information in `estim_params`. I fixed this by providing a temporary local estim_parms structure with the necessary information on model, stderr and corr parameters. In this way, this can be easily extended to also include stderr and corr parameters of measurement errors. * output arguments - renamed `tau` into `out`, as this function computes *very* different things (and not only tau) depending on an input flag * input arguments - renamed `flagmoments` into `outputflag` as this function does not only compute moments but many other things (see above) - renamed `indx` (index of model parameters to be checked) into `indpmodel`, the p makes it more clear that this is a parameter index - renamed `indexo` (index of stderr parameters) into `indpstderr`, the p makes it more clear that this is a parameter index - added `indpcorr` (index of corr parameters) - merged `mf` (index of observable variables) and `iv` (index of variables to consider) into a single index `indvar` as there is no need to distinguish between these two indices (they were never used in combination) - added `grid_nbr` (number of grid points to compute spectral density) - reordered input arguments * misc - added which functions call thet2tau - updated copyright to 2010-2019 # Detailed changes in identification_analysis.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - renamed `dg1` to `dLRE`, renamed `vecg1` to `lre`, renamed `H` to `dTAU` (see comments above) - added option `numzerotolderiv` with default `1.e-8` used for non-zero derivatives - added option `numzerotolrank` with default `1.e-10` used for rank computations - added theoretical identification analysis based on Komunjer and Ng (2011)'s method, i.e. steady state and observational equivalent spectral densities within a minimal system - added theoretical identification analysis based on Qu and Tkachenko (2012)'s method, i.e. steady state and spectral density - restructured the code slightly to combined chunks of code that belong together on the one hand, and on the other hand to differentiate between the different criteria - added call to new function `identification_checks_via_subsets.m` (see above for the definition of the functionality) to perform identification checks differently as find it more intuitive and (most likely) more precise. * input arguments - removed `bounds` and `dataset_` as input argument, because these are not needed - moved `name_tex` and `tittxt` into `options_ident` as these two inputs are only used in `ident_bruteforce.m` and already set in `dynare_identification.m` * output arguments - added `ide_spectrum` structure for Qu and Tkachenko's criteria based on the spectral density - added `ide_minimal` structure for Komunjer and Ng's criteria based on the minimal state space system - reordered output arguments * misc - added which functions call identification_analysis - updated copyright to 2010-2019 # Detailed changes in dynare_identification.m * functionality improvements - heavily commented and changed notation of several variables to make this function (hopefully) more readable and understandable, and hence, easier to debug - included more options (and default values) which can be set by the user, i.e. nostrength, nomoments, nominimal, nospectrum, tex, tol_rank, tol_deriv, tol_sv, grid_nbr, ChecksViaSubsets, max_dim_subsets_group - instead of turning warnings globally off, I specified the relevant warnings for matlab and octave, respectively, off - improved the warning messages slightly - restructured chunks of code with respect to different criteria * output arguments - renamed arguments: TAU to STO_TAU, GAM to STO_MOMENTS, LRE to STO_LRE, gp to STO_si_dLRE, H to STO_si_dTAU, JJ to STO_si_J - added arguments: STO_G and STO_D for the two new criteria * misc - added which functions call dynare_identification - updated copyright to 2010-2019 # Detailed changes in identification_checks.m * functionality improvements - added checks for Komunjer and Ng's D matrix. Note that the Jacobian D=[D_par D_rest], where D_par depends on the parameters and D_rest does not. So this is taken into account. - added checks for Qu and Tkachenko's G matrix. Note that the Jacobian G is a Gram matrix with dimension nparam x nparam, similar to Ahess. So this is taken into account. I am, however, not sure whether this is correct regarding the multicorrelation and pairwise correlation coefficients. Please double check. - the rank is now actually computed at the prespecified tolerance level (and not Matlab's default level), so this is in accordance to the further analysis of problematic parameter sets * output arguments - added the rank to output arguments which is later also displayed - replaced the J or JJ part in the variable names with X as this function is used for all sorts of Jacobians, not only Iskrev's J * input arguments - renamed hess_flag to output_flag (and clearly outlined what each value does) - added tol_rank and tol_sv as input arguments, such that the tolerance levels can be changed by the user and not preimplemented in this function - added param_nbr which is needed for Komunjer and Ng's D matrix * misc - updated copyright to 2010-2019 # Detailed changes in ident_bruteforce.m * functionality improvements - the output directory was set with a capital I, i.e. Identification, whereas in all other functions we rely on lower case i, i.e. identification. I changed this to lower-cases, so everything is now saved in the same folder. - changed displayed strings to be more precise with the corresponding papers and notation * input arguments - renamed `n` to `max_dim_cova_group` to name options the same across functions - renamed `pnames_TeX` to `name_tex` to name options the same across functions - added `tol_deriv` as tolerance level which can be changed by the user * misc - Added some comments - updated copyright to 2010-2019 # Detailed changes in disp_identification.m * functionality improvements - this function displays the same output for different Jacobians, hence I put the common code into a for loop. This should simplify changing the output that is printed to the console. Previously the code was simply repeated for the different criteria and only the strings changed. - some settings relevant for the computation are now printed as a summary to the console - the tolerance level, rank and required rank are always displayed on the command line to see how many problematic sets there are and which tolerance level was used - the function is also able to display problematic parameters computed by the new function `identification_checks_via_subsets.m` which is only used for debugging. * input arguments - added `idespectrum` structure for analysis based on Qu and Tkachenko - added `ideminimal` structure for analysis based on Komunjer and Ng - added `options_ident` to have all necessary settings in a structure * misc - Added some comments - Removed uncommented code that was not used as this was redundant and probably an artifact of the original programming?! - updated copyright to 2010-2019 # Detailed changes in dsge_likelihood.m * misc - adjusted call of getH due to changes of input and output arguments - updated copyright to 2010-2019 # Detailed changes in cosn.m * misc - commented functionality, input and output arguments of this function - updated copyright to 2010-2019
2019-03-20 16:44:54 +01:00
end %DerivABCD end
Finished identification order=1|2|3 Note that I still need to do a code clean up (provide some licenses for functions from other people) and to double check order=3. There is also much room for speed and memory improvement, but the code works fine for now. I will also provide more information to the merge request soon about the detailed changes for future reference.
2019-12-20 00:40:00 +01:00
end%main function end