% DSGE model used in replication files of % An, Sungbae and Schorfheide, Frank, (2007), Bayesian Analysis of DSGE Models, Econometric Reviews, 26, issue 2-4, p. 113-172. % Adapted by Willi Mutschler (@wmutschl, willi@mutschler.eu) % ========================================================================= % Copyright © 2020-2021 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 . % ========================================================================= var c p R g y z INFL INT YGR; varexo e_r e_g e_z; parameters tau nu kap cyst psi1 psi2 rhor rhog rhoz rrst pist gamst; varobs INT YGR INFL; tau = 2; nu = 0.1; kap = 0.33; cyst = 0.85; psi1 = 1.5; psi2 = 0.125; rhor = 0.75; rhog = 0.95; rhoz = 0.9; rrst = 1; pist = 3.2; gamst = 0.55; model; #pist2 = exp(pist/400); #rrst2 = exp(rrst/400); #bet = 1/rrst2; #phi = tau*(1-nu)/nu/kap/pist2^2; #gst = 1/cyst; #cst = (1-nu)^(1/tau); #yst = cst*gst; #dy = y-y(-1); 1 = exp(-tau*c(+1)+tau*c+R-z(+1)-p(+1)); (1-nu)/nu/phi/(pist2^2)*(exp(tau*c)-1) = (exp(p)-1)*((1-1/2/nu)*exp(p)+1/2/nu) - bet*(exp(p(+1))-1)*exp(-tau*c(+1)+tau*c+y(+1)-y+p(+1)); exp(c-y) = exp(-g) - phi*pist2^2*gst/2*(exp(p)-1)^2; R = rhor*R(-1) + (1-rhor)*psi1*p + (1-rhor)*psi2*(dy+z) + e_r/100; g = rhog*g(-1) + e_g/100; z = rhoz*z(-1) + e_z/100; YGR = gamst+100*(dy+z); INFL = pist+400*p; INT = pist+rrst+4*gamst+400*R; end; steady_state_model; z = 0; p = 0; g = 0; R = 0; c = 0; y = 0; YGR = gamst; INFL = pist; INT = pist + rrst + 4*gamst; end; shocks; var e_r = 0.20^2; var e_g = 0.80^2; var e_z = 0.45^2; corr e_r,e_g = 0.2; end; @#if estimParams == 0 % Define only initial values without bounds estimated_params; %tau, 1.50; %kap, 0.15; psi1, 1.20; psi2, 0.50; rhor, 0.50; %rhog, 0.50; %rhoz, 0.50; %rrst, 1.20; %pist, 3.00; gamst, 0.75; stderr e_r, 0.30; stderr e_g, 0.30; stderr e_z, 0.30; corr e_r,e_g, 0.10; end; @#endif @#if estimParams == 1 % Define initial values and bounds estimated_params; %tau, 1.50, 1e-5, 10; %kap, 0.15, 1e-5, 10; psi1, 1.20, 1e-5, 10; psi2, 0.50, 1e-5, 10; rhor, 0.50, 1e-5, 0.99999; %rhog, 0.50, 1e-5, 0.99999; %rhoz, 0.50, 1e-5, 0.99999; %rrst, 1.20, 1e-5, 10; %pist, 3.00, 1e-5, 20; gamst, 0.75, -5, 5; stderr e_r, 0.30, 1e-8, 5; stderr e_g, 0.30, 1e-8, 5; stderr e_z, 0.30, 1e-8, 5; corr e_r,e_g, 0.10, -1, 1; end; @#endif @#if estimParams == 2 % Define prior distribution estimated_params; %tau, 1.50, 1e-5, 10, gamma_pdf, 2.00, 0.50; %kap, 0.15, 1e-5, 10, gamma_pdf, 0.33, 0.10; psi1, 1.20, 1e-5, 10, gamma_pdf, 1.50, 0.25; psi2, 0.50, 1e-5, 10, gamma_pdf, 0.125, 0.25; rhor, 0.50, 1e-5, 0.99999, beta_pdf, 0.50, 0.20; %rhog, 0.50, 1e-5, 0.99999, beta_pdf, 0.80, 0.10; %rhoz, 0.50, 1e-5, 0.99999, beta_pdf, 0.66, 0.15; %rrst, 1.20, 1e-5, 10, gamma_pdf, 0.50, 0.50; %pist, 3.00, 1e-5, 20, gamma_pdf, 7.00, 2.00; gamst, 0.75, -5, 5, normal_pdf, 0.40, 0.20; stderr e_r, 0.30, 1e-8, 5, inv_gamma_pdf, 0.50, 0.26; stderr e_g, 0.30, 1e-8, 5, inv_gamma_pdf, 1.25, 0.65; stderr e_z, 0.30, 1e-8, 5, inv_gamma_pdf, 0.63, 0.33; corr e_r,e_g, 0.10, -1, 1, uniform_pdf, , , -1, 1; end; @#endif % % Simulate data % stoch_simul(order=2,pruning,nodisplay,nomoments,periods=750,drop=500); % save('AnScho_MoM_data_2.mat', options_.varobs{:} ); % pause(1); %-------------------------------------------------------------------------- % Method of Moments Estimation %-------------------------------------------------------------------------- matched_moments; %first-order product moments YGR; YGR(-1); %redundant YGR(0)^1; %redundant YGR^1; %redundant YGR^1*INFL^0*INT^0; %redundant INFL(+2)^1; INT(-2); INT(2); %redundant %second-order contemporenous product moments YGR^2; YGR(-1)^2; %redundant YGR*YGR; %redundant YGR(1)*YGR(1); %redundant INFL*YGR; YGR*INFL; %redundant YGR(2)*INT(2); INT(2)*YGR(2); %redundant INT(2)^1*YGR(2)^1; %redundant YGR(2)^1*INT(2)^1; %redundant INFL(-2)^1*INFL(-2)^1; INFL(-1)*INT(-1); INT(0)^1*INT^1; INT(0)^1*INT^1*YGR(2)^0*INT(-2)^0*INFL^0; %redundant %second-order temporal product moments YGR*YGR(-1); YGR(3)*YGR(2); %redundant YGR(2)*YGR(3); %redundant YGR(-2)*YGR(-1); %redundant INT(3)^1*INT(-2)^1; YGR(5)^0*INFL*INFL(2)^1; YGR(5)^1*INFL(-3)^1; INFL(-3)^1*YGR(5)^1; %redundant INFL(3)*INT(2); @#ifdef Extended_Matched_Moments_Checks YGR^3; YGR(-3)^2*YGR(-3); %redundant YGR(-3)*YGR(-3)^2; %redundant YGR(0)^1*YGR(0)*YGR; %redundant INT(-2)^2*INFL(-1)^4; INFL(1)^4*INT(0)^2; %redundant INT(0)^2*INFL(1)^4; %redundant %YGR^2*INFL(-3)^4*INT(5)^6; %YGR^2*INT(5)^6*INFL(-3)^4;%redundant %INT(5)^6*YGR^2*INFL(-3)^4;%redundant @#endif end; M_.matched_moments_orig = M_.matched_moments; method_of_moments( % Necessary options mom_method = @{MoM_Method} % method of moments method; possible values: GMM|SMM , datafile = 'AnScho_MoM_data_2.mat' % name of filename with data % Options for both GMM and SMM % , bartlett_kernel_lag = 20 % bandwith in optimal weighting matrix , order = 2 % order of Taylor approximation in perturbation % , penalized_estimator % include deviation from prior mean as additional moment restriction and use prior precision as weight , pruning % use pruned state space system at higher-order , verbose % display and store intermediate estimation results , weighting_matrix = ['optimal'] % weighting matrix in moments distance objective function; possible values: OPTIMAL|IDENTITY_MATRIX|DIAGONAL|filename. Size of cell determines stages in iterated estimation, e.g. two state with ['DIAGONAL','OPTIMAL'] %, weighting_matrix_scaling_factor=1 % scaling of weighting matrix in objective function , se_tolx=1e-6 % step size for numerical computation of standard errors % Options for SMM , burnin=50 % number of periods dropped at beginning of simulation , bounded_shock_support % trim shocks in simulation to +- 2 stdev % , seed = 24051986 % seed used in simulations , simulation_multiple = 5 % multiple of the data length used for simulation % Options for GMM @#if MoM_Method == "GMM" , analytic_standard_errors % compute standard errors using analytical derivatives @#endif % General options % , dirname = 'MM' % directory in which to store estimation output % , graph_format = EPS % specify the file format(s) for graphs saved to disk % , nodisplay % do not display the graphs, but still save them to disk % , nograph % do not create graphs (which implies that they are not saved to the disk nor displayed) % , noprint % do not print stuff to console % , plot_priors = 1 % control plotting of priors % , prior_trunc = 1e-10 % probability of extreme values of the prior density that is ignored when computing bounds for the parameters % , TeX % print TeX tables and graphics % Data and model options % , first_obs = 501 % number of first observation % , logdata % if data is already in logs , nobs = 250 % number of observations % , prefilter=0 % demean each data series by its empirical mean and use centered moments % , xls_sheet = data % name/number of sheet with data in Excel % , xls_range = B2:D200 % range of data in Excel sheet % Optimization options that can be set by the user in the mod file, otherwise default values are provided % , huge_number=1e7 % value for replacing the infinite bounds on parameters by finite numbers. Used by some optimizers for numerical reasons @#ifdef NoEstim , mode_compute = 0 @#else , mode_compute = 13 % specifies the optimizer for minimization of moments distance , additional_optimizer_steps = [4] % vector of additional mode-finders run after mode_compute , mode_check % plot the target function for values around the computed minimum for each estimated parameter in turn @#endif % optim: a list of NAME and VALUE pairs to set options for the optimization routines. Available options depend on mode_compute, some exemplary common options: , optim = ('TolFun' , 1e-6 % termination tolerance on the function value, a positive scalar ,'TolX' , 1e-6 % termination tolerance on x, a positive scalar ,'MaxIter' , 3000 % maximum number of iterations allowed, a positive integer ,'MaxFunEvals' , 1D6 % maximum number of function evaluations allowed, a positive integer % ,'UseParallel' , 1 % when true (and supported by optimizer) solver estimates gradients in parallel (using Matlab/Octave's parallel toolbox) % ,'Jacobian' , 'off' % when 'off' gradient-based solvers approximate Jacobian using finite differences; for GMM we can also pass the analytical Jacobian to gradient-based solvers by setting this 'on' ) , silent_optimizer % run minimization of moments distance silently without displaying results or saving files in between % Numerical algorithms options % , aim_solver % Use AIM algorithm to compute perturbation approximation % , k_order_solver % use k_order_solver in higher order perturbation approximations % , dr=default % method used to compute the decision rule; possible values are DEFAULT, CYCLE_REDUCTION, LOGARITHMIC_REDUCTION % , dr_cycle_reduction_tol = 1e-7 % convergence criterion used in the cycle reduction algorithm % , dr_logarithmic_reduction_tol = 1e-12 % convergence criterion used in the logarithmic reduction algorithm % , dr_logarithmic_reduction_maxiter = 100 % maximum number of iterations used in the logarithmic reduction algorithm % , lyapunov = DEFAULT % algorithm used to solve lyapunov equations; possible values are DEFAULT, FIXED_POINT, DOUBLING, SQUARE_ROOT_SOLVER % , lyapunov_complex_threshold = 1e-15 % complex block threshold for the upper triangular matrix in symmetric Lyapunov equation solver % , lyapunov_fixed_point_tol = 1e-10 % convergence criterion used in the fixed point Lyapunov solver % , lyapunov_doubling_tol = 1e-16 % convergence criterion used in the doubling algorithm % , qz_criterium = 0.999999 % value used to split stable from unstable eigenvalues in reordering the Generalized Schur decomposition used for solving first order problems % , qz_zero_threshold = 1e-6 % value used to test if a generalized eigenvalue is 0/0 in the generalized Schur decomposition % , schur_vec_tol=1e-11 % tolerance level used to find nonstationary variables in Schur decomposition of the transition matrix % , mode_check_neighbourhood_size = 5 % width of the window (expressed in percentage deviation) around the computed minimum to be displayed on the diagnostic plots % , mode_check_symmetric_plots=1 % ensure that the check plots are symmetric around the minimum % , mode_check_number_of_points = 20 % number of points around the minimum where the target function is evaluated (for each parameter) );