Add options for providing the variances, an identity matrix , and user...

Add options for providing the variances, an identity matrix , and user specified matrices as proposal densities

Deals with #507 and #112
Includes a unit test

doc/dynare.texi

@@ -4389,6 +4389,7 @@ the total number of Metropolis draws available. Default:
 The fraction of initially generated parameter vectors to be dropped as a burnin before using posterior simulations. Default: @code{0.5}
 
 @item mh_jscale = @var{DOUBLE}
+@anchor{mh_jscale}
 The scale to be used for the jumping distribution in
 Metropolis-Hastings algorithm. The default value is rarely
 satisfactory. This option must be tuned to obtain, ideally, an
@@ -4485,6 +4486,26 @@ value of that function as the posterior mode.
 @noindent
 Default value is @code{4}.
 
+@item MCMC_jumping_covariance = hessian|prior_variance|identity_matrix|@var{filename}
+Tells Dynare which covariance to use for the proposal density of the MCMC sampler. @code{MCMC_jumping_covariance} can be one of the following:
+
+@table @code
+@item hessian 
+Uses the Hessian matrix computed at the mode.
+
+@item prior_variance
+Uses the prior variances. No infinite prior variances are allowed in this case.
+
+@item identity_matrix
+Uses an identity matrix.
+
+@item filename
+Loads an arbitrary user-specified covariance matrix from @code{filename.mat}. The covariance matrix must be saved in a variable named @code{jumping_covariance}, must be square, positive definite, and have the same dimension as the number of estimated parameters.
+
+@end table
+@noindent
+Note that the covariance matrices are stil scaled with @ref{mh_jscale}. Default value is @code{hessian}.
+
 @item mode_check
 Tells Dynare to plot the posterior density for values around the
 computed mode for each estimated parameter in turn. This is helpful to

matlab/dynare_estimation_1.m

@@ -602,8 +602,6 @@ if ~isequal(options_.mode_compute,0) && ~options_.mh_posterior_mode_estimation
 
         [xparam1, fval, nacc, nfcnev, nobds, ier, t, vm] = sa(objective_function,xparam1,maxy,rt_,epsilon,ns,nt ...
                                                               ,neps,maxevl,LB,UB,c,idisp ,t,vm,dataset_,options_,M_,estim_params_,bayestopt_,oo_);
-      case 'prior'
-        hh = diag(bayestopt_.p2.^2);
       otherwise
         if ischar(options_.mode_compute)
             [xparam1, fval, retcode ] = feval(options_.mode_compute,objective_function,xparam1,dataset_,options_,M_,estim_params_,bayestopt_,oo_);
@@ -611,8 +609,8 @@ if ~isequal(options_.mode_compute,0) && ~options_.mh_posterior_mode_estimation
             error(['dynare_estimation:: mode_compute = ' int2str(options_.mode_compute) ' option is unknown!'])
         end
     end
-    if ~isequal(options_.mode_compute,6) && ~isequal(options_.mode_compute,'prior')
-        if options_.cova_compute == 1
+    if ~isequal(options_.mode_compute,6) %always already computes covariance matrix
+        if options_.cova_compute == 1 %user did not request covariance not to be computed
             if options_.analytic_derivation && strcmp(func2str(objective_function),'dsge_likelihood'),
                 ana_deriv = options_.analytic_derivation;
                 options_.analytic_derivation = 2;
@@ -638,6 +636,35 @@ if options_.cova_compute == 0
     hh = [];%NaN(length(xparam1),length(xparam1));
 end
 
+switch options_.MCMC_jumping_covariance
+    case 'hessian' %Baseline
+        %do nothing and use hessian from mode_compute
+    case 'prior_variance' %Use prior variance
+        if any(isinf(bayestopt_.p2))
+            error('Infinite prior variances detected. You cannot use the prior variances as the proposal density, if some variances are Inf.')
+        else            
+            hh = diag(1./(bayestopt_.p2.^2));
+        end
+    case 'identity_matrix' %Use identity
+        hh = eye(nx);   
+    otherwise %user specified matrix in file
+        try 
+            load(options_.MCMC_jumping_covariance,'jumping_covariance')
+            hh=jumping_covariance;
+        catch
+            error(['No matrix named ''jumping_covariance'' could be found in ',options_.MCMC_jumping_covariance,'.mat'])
+        end
+        [nrow, ncol]=size(hh);
+        if ~isequal(nrow,ncol) && ~isequal(nrow,nx) %check if square and right size
+            error(['jumping_covariance matrix must be square and have ',num2str(nx),' rows and columns'])
+        end
+        try %check for positive definiteness
+            chol(hh);
+        catch
+            error(['Specified jumping_covariance is not positive definite'])
+        end
+end
+
 if ~options_.mh_posterior_mode_estimation && options_.cova_compute
     try
         chol(hh);

matlab/global_initialization.m

@@ -381,6 +381,7 @@ options_.mh_nblck = 2;
 options_.mh_recover = 0;
 options_.mh_replic = 20000;
 options_.recursive_estimation_restart = 0;
+options_.MCMC_jumping_covariance='hessian';
 
 options_.mode_compute = 4;
 options_.mode_file = '';

tests/estimation/fs2000_MCMC_jumping_covariance.mod

+// See fs2000.mod in the examples/ directory for details on the model
+
+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;
+
+initval;
+k = 6;
+m = mst;
+P = 2.25;
+c = 0.45;
+e = 1;
+W = 4;
+R = 1.02;
+d = 0.85;
+n = 0.19;
+l = 0.86;
+y = 0.6;
+gy_obs = exp(gam);
+gp_obs = exp(-gam);
+dA = exp(gam);
+end;
+
+shocks;
+var e_a; stderr 0.014;
+var e_m; stderr 0.005;
+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, 0.223;
+psi, beta_pdf, 0.65, 0.05;
+del, beta_pdf, 0.01, 0.005;
+stderr e_a, inv_gamma_pdf, 0.035449, .1;
+stderr e_m, inv_gamma_pdf, 0.008862, .1;
+end;
+
+varobs gp_obs gy_obs;
+
+options_.solve_tolf = 1e-12;
+options_.mode_compute=4;
+options_.plot_priors=0;
+options_.MCMC_jumping_covariance='hessian';
+estimation(order=1,datafile=fsdat_simul,nobs=192,loglinear,mh_replic=1000,mh_nblocks=1,mh_jscale=0.8);
+load fs2000_MCMC_jumping_covariance_mode hh;
+jumping_covariance=diag(diag(hh));
+save test_matrix jumping_covariance;
+options_.MCMC_jumping_covariance='prior_variance';
+estimation(order=1,datafile=fsdat_simul,nobs=192,loglinear,mh_replic=1000,mh_nblocks=1,mh_jscale=0.01);
+options_.MCMC_jumping_covariance='identity_matrix';
+estimation(order=1,datafile=fsdat_simul,nobs=192,loglinear,mh_replic=1000,mh_nblocks=1,mh_jscale=0.0001);
+options_.MCMC_jumping_covariance='test_matrix';
+estimation(order=1,datafile=fsdat_simul,nobs=192,loglinear,mh_replic=1000,mh_nblocks=1,mh_jscale=0.8);

tests/estimation/fs2000_MCMC_jumping_covariance_steadystate.m

+% computes the steady state of fs2000 analyticaly
+% largely inspired by the program of F. Schorfheide
+
+% Copyright (C) 2004-2010 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/>.
+
+function [ys,check] = fs2000_steadystate(ys,exe)
+  global M_
+  
+  alp = M_.params(1); 
+  bet = M_.params(2); 
+  gam = M_.params(3); 
+  mst = M_.params(4); 
+  rho = M_.params(5); 
+  psi = M_.params(6); 
+  del = M_.params(7); 
+
+  check = 0;
+  
+  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;
+  
+  ys =[
+m     
+P     
+c     
+e     
+W     
+R     
+k     
+d     
+n     
+l     
+gy_obs
+gp_obs
+y     
+dA          ];