329 lines
14 KiB
Matlab
329 lines
14 KiB
Matlab
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function [fval,info,exit_flag,grad,hess,SteadyState,trend_coeff,PHI_tilde,SIGMA_u_tilde,iXX,prior] = dsge_var_likelihood(xparam1,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,BoundsInfo,dr, endo_steady_state, exo_steady_state, exo_det_steady_state)
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% [fval,info,exit_flag,grad,hess,SteadyState,trend_coeff,PHI_tilde,SIGMA_u_tilde,iXX,prior] = dsge_var_likelihood(xparam1,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,BoundsInfo,dr, endo_steady_state, exo_steady_state, exo_det_steady_state)
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% Evaluates the posterior kernel of the BVAR-DSGE model.
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%
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% INPUTS
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% o xparam1 [double] Vector of model's parameters.
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% o gend [integer] Number of observations (without conditionning observations for the lags).
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% o dataset_ [dseries] object storing the dataset
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% o dataset_info [structure] storing informations about the sample.
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% o options_ [structure] describing the options
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% o M_ [structure] decribing the model
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% o estim_params_ [structure] characterizing parameters to be estimated
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% o bayestopt_ [structure] describing the priors
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% o BoundsInfo [structure] containing prior bounds
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% o dr [structure] Reduced form model.
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% o endo_steady_state [vector] steady state value for endogenous variables
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% o exo_steady_state [vector] steady state value for exogenous variables
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% o exo_det_steady_state [vector] steady state value for exogenous deterministic variables
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%
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% OUTPUTS
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% o fval [double] Value of the posterior kernel at xparam1.
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% o info [integer] Vector of informations about the penalty.
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% o exit_flag [integer] Zero if the function returns a penalty, one otherwise.
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% o grad [double] place holder for gradient of the likelihood
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% currently not supported by dsge_var
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% o hess [double] place holder for hessian matrix of the likelihood
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% currently not supported by dsge_var
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% o SteadyState [double] Steady state vector possibly recomputed
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% by call to dynare_resolve()
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% o trend_coeff [double] place holder for trend coefficients,
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% currently not supported by dsge_var
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% o PHI_tilde [double] Stacked BVAR-DSGE autoregressive matrices (at the mode associated to xparam1);
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% formula (28), DS (2004)
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% o SIGMA_u_tilde [double] Covariance matrix of the BVAR-DSGE (at the mode associated to xparam1),
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% formula (29), DS (2004)
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% o iXX [double] inv(lambda*T*Gamma_XX^*+ X'*X)
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% o prior [double] a matlab structure describing the dsge-var prior
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% - SIGMA_u_star: prior covariance matrix, formula (23), DS (2004)
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% - PHI_star: prior autoregressive matrices, formula (22), DS (2004)
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% - ArtificialSampleSize: number of artificial observations from the prior (T^* in DS (2004))
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% - DF = prior.ArtificialSampleSize - NumberOfParameters - NumberOfObservedVariables;
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% - iGXX_star: theoretical covariance of regressors ({\Gamma_{XX}^*}^{-1} in DS (2004))
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%
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% ALGORITHMS
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% Follows the computations outlined in Del Negro/Schorfheide (2004):
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% Priors from general equilibrium models for VARs, International Economic
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% Review, 45(2), pp. 643-673
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%
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% SPECIAL REQUIREMENTS
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% None.
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% Copyright © 2006-2023Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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% Initialize some of the output arguments.
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fval = [];
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exit_flag = 1;
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grad=[];
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hess=[];
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info = zeros(4,1);
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PHI_tilde = [];
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SIGMA_u_tilde = [];
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iXX = [];
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prior = [];
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trend_coeff=[];
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% Ensure that xparam1 is a column vector.
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% (Don't do the transformation if xparam1 is empty, otherwise it would become a
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% 0×1 matrix, which create issues with older MATLABs when comparing with [] in
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% check_bounds_and_definiteness_estimation)
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if ~isempty(xparam1)
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xparam1 = xparam1(:);
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end
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% Initialization of of the index for parameter dsge_prior_weight in M_.params.
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dsge_prior_weight_idx = strmatch('dsge_prior_weight', M_.param_names);
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% Get the number of estimated (dsge) parameters.
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nx = estim_params_.nvx + estim_params_.np;
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% Get the number of observed variables in the VAR model.
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NumberOfObservedVariables = dataset_.vobs;
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% Get the number of observations.
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NumberOfObservations = dataset_.nobs;
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% Get the number of lags in the VAR model.
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NumberOfLags = options_.dsge_varlag;
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% Get the number of parameters in the VAR model.
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NumberOfParameters = NumberOfObservedVariables*NumberOfLags ;
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if ~options_.noconstant
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NumberOfParameters = NumberOfParameters + 1;
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end
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% Get empirical second order moments for the observed variables.
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mYY= dataset_info.mYY;
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mYX= dataset_info.mYX;
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mXX= dataset_info.mXX;
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M_ = set_all_parameters(xparam1,estim_params_,M_);
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[fval,info,exit_flag,Q]=check_bounds_and_definiteness_estimation(xparam1, M_, estim_params_, BoundsInfo);
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if info(1)
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return
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end
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% Get the weight of the dsge prior.
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dsge_prior_weight = M_.params(dsge_prior_weight_idx);
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% Is the dsge prior proper?
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if dsge_prior_weight<(NumberOfParameters+NumberOfObservedVariables)/NumberOfObservations
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fval = Inf;
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exit_flag = 0;
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info(1) = 51;
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info(2)=dsge_prior_weight;
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info(3)=(NumberOfParameters+NumberOfObservedVariables)/dataset_.nobs;
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info(4)=abs(NumberOfObservations*dsge_prior_weight-(NumberOfParameters+NumberOfObservedVariables));
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return
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end
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%------------------------------------------------------------------------------
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% 2. call model setup & reduction program
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%------------------------------------------------------------------------------
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% Solve the Dsge model and get the matrices of the reduced form solution. T and R are the matrices of the
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% state equation
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[T,R,SteadyState,info] = dynare_resolve(M_,options_, dr, endo_steady_state, exo_steady_state, exo_det_steady_state,'restrict');
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% Return, with endogenous penalty when possible, if dynare_resolve issues an error code (defined in resol).
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if info(1)
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if info(1) == 3 || info(1) == 4 || info(1) == 5 || info(1)==6 ||info(1) == 19 ||...
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info(1) == 20 || info(1) == 21 || info(1) == 23 || info(1) == 26 || ...
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info(1) == 81 || info(1) == 84 || info(1) == 85
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%meaningful second entry of output that can be used
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fval = Inf;
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info(4) = info(2);
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exit_flag = 0;
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return
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else
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fval = Inf;
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info(4) = 0.1;
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exit_flag = 0;
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return
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end
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end
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% Define the mean/steady state vector.
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if ~options_.noconstant
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if options_.loglinear
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constant = transpose(log(SteadyState(bayestopt_.mfys)));
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else
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constant = transpose(SteadyState(bayestopt_.mfys));
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end
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else
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constant = zeros(1,NumberOfObservedVariables);
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end
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%------------------------------------------------------------------------------
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% 3. theoretical moments (second order)
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%------------------------------------------------------------------------------
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% Compute the theoretical second order moments
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tmp0 = lyapunov_symm(T,R*Q*R',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, [], options_.debug);
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mf = bayestopt_.mf1;
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% Get the non centered second order moments
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TheoreticalAutoCovarianceOfTheObservedVariables = zeros(NumberOfObservedVariables,NumberOfObservedVariables,NumberOfLags+1);
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TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1) = tmp0(mf,mf)+constant'*constant;
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for lag = 1:NumberOfLags
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tmp0 = T*tmp0;
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TheoreticalAutoCovarianceOfTheObservedVariables(:,:,lag+1) = tmp0(mf,mf) + constant'*constant;
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end
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% Build the theoretical "covariance" between Y and X
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GYX = zeros(NumberOfObservedVariables,NumberOfParameters);
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for i=1:NumberOfLags
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GYX(:,(i-1)*NumberOfObservedVariables+1:i*NumberOfObservedVariables) = TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1);
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end
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if ~options_.noconstant
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GYX(:,end) = constant';
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end
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% Build the theoretical "covariance" between X and X
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GXX = kron(eye(NumberOfLags), TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1));
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for i = 1:NumberOfLags-1
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tmp1 = diag(ones(NumberOfLags-i,1),i);
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tmp2 = diag(ones(NumberOfLags-i,1),-i);
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GXX = GXX + kron(tmp1,TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1));
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GXX = GXX + kron(tmp2,TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1)');
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end
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if ~options_.noconstant
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% Add one row and one column to GXX
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GXX = [GXX , kron(ones(NumberOfLags,1),constant') ; [ kron(ones(1,NumberOfLags),constant) , 1] ];
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end
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GYY = TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1);
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iGXX = inv(GXX);
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PHI_star = iGXX*transpose(GYX); %formula (22), DS (2004)
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SIGMA_u_star=GYY - GYX*PHI_star; %formula (23), DS (2004)
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[SIGMA_u_star_is_positive_definite, penalty] = ispd(SIGMA_u_star);
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if ~SIGMA_u_star_is_positive_definite
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fval = Inf;
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info(1) = 53;
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info(4) = penalty;
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exit_flag = 0;
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return
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end
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if ~isinf(dsge_prior_weight)% Evaluation of the likelihood of the dsge-var model when the dsge prior weight is finite.
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tmp0 = dsge_prior_weight*NumberOfObservations*TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1) + mYY ; %first term of square bracket in formula (29), DS (2004)
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tmp1 = dsge_prior_weight*NumberOfObservations*GYX + mYX; %first element of second term of square bracket in formula (29), DS (2004)
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tmp2 = inv(dsge_prior_weight*NumberOfObservations*GXX+mXX); %middle element of second term of square bracket in formula (29), DS (2004)
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SIGMA_u_tilde = tmp0 - tmp1*tmp2*tmp1'; %square bracket term in formula (29), DS (2004)
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clear('tmp0');
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[SIGMAu_is_positive_definite, penalty] = ispd(SIGMA_u_tilde);
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if ~SIGMAu_is_positive_definite
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fval = Inf;
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info(1) = 52;
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info(4) = penalty;
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exit_flag = 0;
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return
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end
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SIGMA_u_tilde = SIGMA_u_tilde / (NumberOfObservations*(1+dsge_prior_weight)); %prefactor of formula (29), DS (2004)
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PHI_tilde = tmp2*tmp1'; %formula (28), DS (2004)
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clear('tmp1');
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prodlng1 = sum(gammaln(.5*((1+dsge_prior_weight)*NumberOfObservations- ...
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NumberOfParameters ...
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+1-(1:NumberOfObservedVariables)'))); %last term in numerator of third line of (A.2), DS (2004)
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prodlng2 = sum(gammaln(.5*(dsge_prior_weight*NumberOfObservations- ...
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NumberOfParameters ...
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+1-(1:NumberOfObservedVariables)'))); %last term in denominator of third line of (A.2), DS (2004)
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%Compute minus log likelihood according to (A.2), DS (2004)
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lik = .5*NumberOfObservedVariables*log(det(dsge_prior_weight*NumberOfObservations*GXX+mXX)) ... %first term in numerator of second line of (A.2), DS (2004)
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+ .5*((dsge_prior_weight+1)*NumberOfObservations-NumberOfParameters)*log(det((dsge_prior_weight+1)*NumberOfObservations*SIGMA_u_tilde)) ... %second term in numerator of second line of (A.2), DS (2004)
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- .5*NumberOfObservedVariables*log(det(dsge_prior_weight*NumberOfObservations*GXX)) ... %first term in denominator of second line of (A.2), DS (2004)
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- .5*(dsge_prior_weight*NumberOfObservations-NumberOfParameters)*log(det(dsge_prior_weight*NumberOfObservations*SIGMA_u_star)) ... %second term in denominator of second line of (A.2), DS (2004)
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+ .5*NumberOfObservedVariables*NumberOfObservations*log(2*pi) ... %first term in numerator of third line of (A.2), DS (2004)
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- .5*log(2)*NumberOfObservedVariables*((dsge_prior_weight+1)*NumberOfObservations-NumberOfParameters) ... %second term in numerator of third line of (A.2), DS (2004)
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+ .5*log(2)*NumberOfObservedVariables*(dsge_prior_weight*NumberOfObservations-NumberOfParameters) ... %first term in denominator of third line of (A.2), DS (2004)
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- prodlng1 + prodlng2;
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else% Evaluation of the likelihood of the dsge-var model when the dsge prior weight is infinite.
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PHI_star = iGXX*transpose(GYX);
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%Compute minus log likelihood according to (33), DS (2004) (where the last term in the trace operator has been multiplied out)
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lik = NumberOfObservations * ( log(det(SIGMA_u_star)) + NumberOfObservedVariables*log(2*pi) + ...
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trace(inv(SIGMA_u_star)*(mYY - transpose(mYX*PHI_star) - mYX*PHI_star + transpose(PHI_star)*mXX*PHI_star)/NumberOfObservations));
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lik = .5*lik;% Minus likelihood
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SIGMA_u_tilde=SIGMA_u_star;
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PHI_tilde=PHI_star;
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end
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if isnan(lik)
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fval = Inf;
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info(1) = 45;
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info(4) = 0.1;
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exit_flag = 0;
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return
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end
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if imag(lik)~=0
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fval = Inf;
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info(1) = 46;
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info(4) = 0.1;
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exit_flag = 0;
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return
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end
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% Add the (logged) prior density for the dsge-parameters.
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lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
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fval = (lik-lnprior);
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if isnan(fval)
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fval = Inf;
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info(1) = 47;
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info(4) = 0.1;
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exit_flag = 0;
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return
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end
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if imag(fval)~=0
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fval = Inf;
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info(1) = 48;
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info(4) = 0.1;
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exit_flag = 0;
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return
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end
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if isinf(fval)~=0
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fval = Inf;
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info(1) = 50;
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info(4) = 0.1;
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exit_flag = 0;
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return
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end
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if (nargout >= 10)
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if isinf(dsge_prior_weight)
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iXX = iGXX;
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else
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iXX = tmp2;
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end
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end
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if (nargout==11)
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prior.SIGMA_u_star = SIGMA_u_star;
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prior.PHI_star = PHI_star;
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prior.ArtificialSampleSize = fix(dsge_prior_weight*NumberOfObservations);
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prior.DF = prior.ArtificialSampleSize - NumberOfParameters - NumberOfObservedVariables;
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prior.iGXX_star = iGXX;
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end
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