Add unit test for correctness of posterior moments

tests/Makefile.am

@@ -2,6 +2,7 @@ MODFILES = \
 	walsh.mod \
 	optimizers/fs2000_6.mod \
 	moments/example1_hp_test.mod \
+	moments/fs2000_post_moments.mod \
 	lmmcp/rbcii.mod \
 	ep/rbc_mc.mod \
 	estimation/TaRB/fs2000_tarb.mod \

tests/moments/fs2000_post_moments.mod

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