290 lines
11 KiB
Modula-2
290 lines
11 KiB
Modula-2
/*
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* This file replicates the estimation of the cash in advance model (termed M1
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* in the paper) described in Frank Schorfheide (2000): "Loss function-based
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* evaluation of DSGE models", Journal of Applied Econometrics, 15(6), 645-670.
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*
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* The data are in file "fsdat_simul.m", and have been artificially generated.
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* They are therefore different from the original dataset used by Schorfheide.
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*
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* The prior distribution follows the one originally specified in Schorfheide's
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* paper, except for parameter rho. In the paper, the elicited beta prior for rho
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* implies an asymptote and corresponding prior mode at 0. It is generally
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* recommended to avoid this extreme type of prior. Some optimizers, for instance
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* mode_compute=12 (Mathworks' particleswarm algorithm) may find a posterior mode
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* with rho equal to zero. We lowered the value of the prior standard deviation
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* (changing .223 to .100) to remove the asymptote.
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*
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* The equations are taken from J. Nason and T. Cogley (1994): "Testing the
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* implications of long-run neutrality for monetary business cycle models",
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* Journal of Applied Econometrics, 9, S37-S70.
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* Note that there is an initial minus sign missing in equation (A1), p. S63.
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*
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* This implementation was originally written by Michel Juillard. Please note that the
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* following copyright notice only applies to this Dynare implementation of the
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* model.
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*/
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/*
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* Copyright © 2004-2017 Dynare 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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*/
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var m P c e W R k d n l gy_obs gp_obs y dA;
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varexo e_a e_m;
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parameters alp bet gam mst rho psi del;
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alp = 0.33;
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bet = 0.99;
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gam = 0.003;
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mst = 1.011;
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rho = 0.7;
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psi = 0.787;
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del = 0.02;
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model;
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dA = exp(gam+e_a);
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log(m) = (1-rho)*log(mst) + rho*log(m(-1))+e_m;
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-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c(+2)*P(+2)*m(+1))=0;
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W = l/n;
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-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
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R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
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1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
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c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
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P*c = m;
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m-1+d = l;
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e = exp(e_a);
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y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
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gy_obs = dA*y/y(-1);
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gp_obs = (P/P(-1))*m(-1)/dA;
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end;
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shocks;
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var e_a; stderr 0.014;
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var e_m; stderr 0.005;
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end;
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steady_state_model;
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dA = exp(gam);
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gst = 1/dA;
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m = mst;
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khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
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xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
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nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
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n = xist/(nust+xist);
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P = xist + nust;
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k = khst*n;
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l = psi*mst*n/( (1-psi)*(1-n) );
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c = mst/P;
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d = l - mst + 1;
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y = k^alp*n^(1-alp)*gst^alp;
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R = mst/bet;
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W = l/n;
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ist = y-c;
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q = 1 - d;
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e = 1;
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gp_obs = m/dA;
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gy_obs = dA;
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end;
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steady;
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check;
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estimated_params;
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alp, beta_pdf, 0.356, 0.02;
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bet, beta_pdf, 0.993, 0.002;
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gam, normal_pdf, 0.0085, 0.003;
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mst, normal_pdf, 1.0002, 0.007;
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rho, beta_pdf, 0.129, 0.100;
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psi, beta_pdf, 0.65, 0.05;
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del, beta_pdf, 0.01, 0.005;
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stderr e_a, inv_gamma_pdf, 0.035449, inf;
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stderr e_m, inv_gamma_pdf, 0.008862, inf;
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end;
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varobs gp_obs gy_obs;
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estimation(order=1,mode_compute=5,silent_optimizer, datafile='../fs2000/fsdat_simul.m', nobs=192, loglinear, mh_replic=20, mh_nblocks=1, mh_jscale=0.8,moments_varendo,
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conditional_variance_decomposition=[2,2000],consider_all_endogenous,sub_draws=2);
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stoch_simul(order=1,conditional_variance_decomposition=[2,2000],noprint,nograph);
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par=load([M_.fname filesep 'metropolis' filesep M_.fname '_posterior_draws1']);
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for par_iter=1:size(par.pdraws,1)
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M_=set_parameters_locally(M_,par.pdraws{par_iter,1});
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[info, oo_, options_, M_]=stoch_simul(M_, options_, oo_, var_list_);
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correlation(:,:,par_iter)=cell2mat(oo_.autocorr);
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covariance(:,:,par_iter)=oo_.var;
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conditional_variance_decomposition(:,:,:,par_iter)=oo_.conditional_variance_decomposition;
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variance_decomposition(:,:,par_iter)=oo_.variance_decomposition;
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end
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correlation=mean(correlation,3);
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nvars=M_.orig_endo_nbr;
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for var_iter_1=1:nvars
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for var_iter_2=1:nvars
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if max(abs(correlation(var_iter_1,var_iter_2:nvars:end)'-oo_.PosteriorTheoreticalMoments.dsge.correlation.Mean.(M_.endo_names{var_iter_1}).(M_.endo_names{var_iter_2})))>1e-8
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error('Correlations do not match')
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end
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end
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end
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covariance=mean(covariance,3);
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nvars=M_.orig_endo_nbr;
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for var_iter_1=1:nvars
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for var_iter_2=var_iter_1:nvars
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if max(abs(covariance(var_iter_1,var_iter_2)-oo_.PosteriorTheoreticalMoments.dsge.covariance.Mean.(M_.endo_names{var_iter_1}).(M_.endo_names{var_iter_2})))>1e-8
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error('Covariances do not match')
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end
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end
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end
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variance_decomposition=mean(variance_decomposition,3);
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nvars=M_.orig_endo_nbr;
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for var_iter_1=1:nvars
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for shock_iter=1:M_.exo_nbr
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if max(abs(variance_decomposition(var_iter_1,shock_iter)/100-oo_.PosteriorTheoreticalMoments.dsge.VarianceDecomposition.Mean.(M_.endo_names{var_iter_1}).(M_.exo_names{shock_iter})))>1e-8
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error('Variance decomposition does not match')
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end
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end
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end
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conditional_variance_decomposition=mean(conditional_variance_decomposition,4);
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nvars=M_.orig_endo_nbr;
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horizon_size=size(conditional_variance_decomposition,2);
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for var_iter_1=1:nvars
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for shock_iter=1:M_.exo_nbr
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for horizon_iter=1:horizon_size
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if max(abs(conditional_variance_decomposition(var_iter_1,horizon_iter,shock_iter)-oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition.Mean.(M_.endo_names{var_iter_1}).(M_.exo_names{shock_iter})(horizon_iter)))>1e-8
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error('Conditional Variance decomposition does not match')
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end
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end
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end
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end
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// case with measurement error
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estimated_params(overwrite);
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alp, beta_pdf, 0.356, 0.02;
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bet, beta_pdf, 0.993, 0.002;
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gam, normal_pdf, 0.0085, 0.003;
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mst, normal_pdf, 1.0002, 0.007;
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rho, beta_pdf, 0.129, 0.100;
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psi, beta_pdf, 0.65, 0.05;
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del, beta_pdf, 0.01, 0.005;
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stderr e_a, inv_gamma_pdf, 0.035449, inf;
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stderr e_m, inv_gamma_pdf, 0.008862, inf;
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stderr gp_obs, inv_gamma_pdf, 0.003, inf;
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end;
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estimation(order=1,mode_compute=5,silent_optimizer, datafile='../fs2000/fsdat_simul.m', nobs=192, loglinear, mh_replic=20, mh_nblocks=1, mh_jscale=0.8,moments_varendo,
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conditional_variance_decomposition=[2,2000],consider_all_endogenous,sub_draws=2);
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stoch_simul(order=1,conditional_variance_decomposition=[2,2000],noprint,nograph);
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par=load([M_.fname filesep 'metropolis' filesep M_.fname '_posterior_draws1']);
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for par_iter=1:size(par.pdraws,1)
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M_=set_parameters_locally(M_,par.pdraws{par_iter,1});
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[info, oo_, options_, M_]=stoch_simul(M_, options_, oo_, var_list_);
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correlation(:,:,par_iter)=cell2mat(oo_.autocorr);
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covariance(:,:,par_iter)=oo_.var;
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conditional_variance_decomposition(:,:,:,par_iter)=oo_.conditional_variance_decomposition;
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conditional_variance_decomposition_ME(:,:,:,par_iter)=oo_.conditional_variance_decomposition_ME;
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variance_decomposition(:,:,par_iter)=oo_.variance_decomposition;
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variance_decomposition_ME(:,:,par_iter)=oo_.variance_decomposition_ME;
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[~,obs_order]=sort(options_.varobs_id);
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end
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correlation=mean(correlation,3);
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nvars=M_.orig_endo_nbr;
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for var_iter_1=1:nvars
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for var_iter_2=1:nvars
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if max(abs(correlation(var_iter_1,var_iter_2:nvars:end)'-oo_.PosteriorTheoreticalMoments.dsge.correlation.Mean.(M_.endo_names{var_iter_1}).(M_.endo_names{var_iter_2})))>1e-8
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error('Correlations do not match')
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end
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end
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end
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covariance=mean(covariance,3);
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nvars=M_.orig_endo_nbr;
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for var_iter_1=1:nvars
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for var_iter_2=var_iter_1:nvars
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if max(abs(covariance(var_iter_1,var_iter_2)-oo_.PosteriorTheoreticalMoments.dsge.covariance.Mean.(M_.endo_names{var_iter_1}).(M_.endo_names{var_iter_2})))>1e-8
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error('Covariances do not match')
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end
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end
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end
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variance_decomposition=mean(variance_decomposition,3);
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nvars=M_.orig_endo_nbr;
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for var_iter_1=1:nvars
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for shock_iter=1:M_.exo_nbr
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if max(abs(variance_decomposition(var_iter_1,shock_iter)/100-oo_.PosteriorTheoreticalMoments.dsge.VarianceDecomposition.Mean.(M_.endo_names{var_iter_1}).(M_.exo_names{shock_iter})))>1e-8
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error('Variance decomposition does not match')
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end
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end
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end
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variance_decomposition_ME=mean(variance_decomposition_ME,3);
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nvars=length(options_.varobs);
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for var_iter_1=1:nvars
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for shock_iter=1:M_.exo_nbr
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if max(abs(variance_decomposition_ME(obs_order(var_iter_1),shock_iter)/100-oo_.PosteriorTheoreticalMoments.dsge.VarianceDecompositionME.Mean.(options_.varobs{var_iter_1}).(M_.exo_names{shock_iter})))>1e-8
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error('Variance decomposition does not match')
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end
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end
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end
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conditional_variance_decomposition=mean(conditional_variance_decomposition,4);
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nvars=M_.orig_endo_nbr;
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horizon_size=size(conditional_variance_decomposition,2);
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for var_iter_1=1:nvars
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for shock_iter=1:M_.exo_nbr
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for horizon_iter=1:horizon_size
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if max(abs(conditional_variance_decomposition(var_iter_1,horizon_iter,shock_iter)-oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition.Mean.(M_.endo_names{var_iter_1}).(M_.exo_names{shock_iter})(horizon_iter)))>1e-8
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error('Conditional Variance decomposition does not match')
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end
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end
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end
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end
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conditional_variance_decomposition_ME=mean(conditional_variance_decomposition_ME,4);
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exo_names=[M_.exo_names;'ME'];
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nvars=length(options_.varobs);
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horizon_size=size(conditional_variance_decomposition_ME,2);
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for var_iter_1=1:nvars
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for shock_iter=1:M_.exo_nbr+1
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for horizon_iter=1:horizon_size
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if max(abs(conditional_variance_decomposition_ME(obs_order(var_iter_1),horizon_iter,shock_iter)-oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecompositionME.Mean.(options_.varobs{var_iter_1}).(exo_names{shock_iter})(horizon_iter)))>1e-8
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error('Conditional Variance decomposition does not match')
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end
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end
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end
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end
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/*
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* The following lines were used to generate the data file. If you want to
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* generate another random data file, comment the "estimation" line and uncomment
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* the following lines.
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*/
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//stoch_simul(periods=200, order=1);
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//datatomfile('fsdat_simul', char('gy_obs', 'gp_obs'));
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