diff --git a/doc/dynare.texi b/doc/dynare.texi
index 4290d8a8399e3c5fba215378a99656ece3351591..9671a51e5dac5a5301fdb78a198048acedb29e5d 100644
--- a/doc/dynare.texi
+++ b/doc/dynare.texi
@@ -5554,10 +5554,15 @@ distribution of IRFs. The length of the IRFs are controlled by the
@item dsge_var = @var{DOUBLE}
@anchor{dsge_var} Triggers the estimation of a DSGE-VAR model, where the
weight of the DSGE prior of the VAR model is calibrated to the value
-passed (see @cite{Del Negro and Schorfheide (2004)}). It represents ratio of dummy over actual observations. To assure that the prior is proper, the value must be bigger than @math{(k+n)/T}, where @math{k} is the number of estimated parameters, @math{n} is the number of observables, and @math{T} is the number of observations. NB: The previous method
-of declaring @code{dsge_prior_weight} as a parameter and then
+passed (see @cite{Del Negro and Schorfheide (2004)}). It represents ratio of dummy over actual observations.
+To assure that the prior is proper, the value must be bigger than @math{(k+n)/T},
+where @math{k} is the number of estimated parameters, @math{n} is the number of observables, #
+and @math{T} is the number of observations. NB: The previous method
+of declaring @code{dsge_prior_weight} as a parameter and then
calibrating it is now deprecated and will be removed in a future release
of Dynare.
+Some of objects arising during estimation are stored with their values at the mode in
+@ref{oo_.dsge_var.posterior_mode}.
@item dsge_var
Triggers the estimation of a DSGE-VAR model, where the weight of the
@@ -6453,6 +6458,55 @@ oo_.posterior_mean.shocks_std.ex
oo_.posterior_hpdsup.measurement_errors_corr.gdp_conso
@end example
+@defvr {MATLAB/Octave variable} oo_.dsge_var.posterior_mode
+@anchor{oo_.dsge_var.posterior_mode}
+Structure set by the @code{dsge_var} option of the @code{estimation} command after @code{mode_compute}.
+
+The following fields are saved:
+
+@table @code
+
+@item PHI_tilde
+Stacked posterior DSGE-BVAR autoregressive matrices at the mode (equation (28) of
+@cite{Del Negro and Schorfheide (2004)}).
+
+@item SIGMA_u_tilde
+Posterior covariance matrix of the DSGE-BVAR at the mode (equation (29) of
+@cite{Del Negro and Schorfheide (2004)}).
+
+@item iXX
+Posterior population moments in the DSGE-BVAR at the mode (@math{inv(\lambda T \Gamma_{XX}^*+ X'X)}).
+
+@item prior
+Structure storing the DSGE-BVAR prior.
+
+@table @code
+
+
+@item PHI_star
+Stacked prior DSGE-BVAR autoregressive matrices at the mode (equation (22) of
+@cite{Del Negro and Schorfheide (2004)}).
+
+@item SIGMA_star
+Prior covariance matrix of the DSGE-BVAR at the mode (equation (23) of
+@cite{Del Negro and Schorfheide (2004)}).
+
+@item ArtificialSampleSize
+Size of the artifical prior sample (@math{inv(\lambda T)}).
+
+@item DF
+Prior degrees of freedom (@math{inv(\lambda T-k-n)}).
+
+@item iGXX_star
+Inverse of the theoretical prior ``covariance'' between X and X (@math{\Gamma_{xx}^*} in @cite{Del Negro and Schorfheide (2004)}).
+
+@end table
+
+@end table
+
+@end defvr
+
+
@defvr {MATLAB/Octave variable} oo_.RecursiveForecast
@anchor{RecursiveForecast}
Variable set by the @code{forecast} option of the @code{estimation} command when used with the nobs = [@var{INTEGER1}:@var{INTEGER2}] option (@pxref{nobs1,,nobs}).
@@ -13626,7 +13680,7 @@ Corona, Angelo, M. Marchesi, Claudio Martini, and Sandro Ridella (1987):
@i{ACM Transactions on Mathematical Software}, 13(3), 262--280
@item
-Del Negro, Marco and Franck Schorfheide (2004): ``Priors from General Equilibrium Models for VARS'',
+Del Negro, Marco and Franck Schorfheide (2004): ``Priors from General Equilibrium Models for VARs'',
@i{International Economic Review}, 45(2), 643--673
@item
diff --git a/matlab/dsge_var_likelihood.m b/matlab/dsge_var_likelihood.m
index 2dc670e5747ac0be5fff3e431459ac9c6d6cc2a2..4e10d0bb28e91add0aadfc70e04db2c3cd1c04ed 100644
--- a/matlab/dsge_var_likelihood.m
+++ b/matlab/dsge_var_likelihood.m
@@ -1,4 +1,4 @@
-function [fval,info,exit_flag,grad,hess,SteadyState,trend_coeff,PHI,SIGMAu,iXX,prior] = dsge_var_likelihood(xparam1,DynareDataset,DynareInfo,DynareOptions,Model,EstimatedParameters,BayesInfo,BoundsInfo,DynareResults)
+function [fval,info,exit_flag,grad,hess,SteadyState,trend_coeff,PHI_tilde,SIGMA_u_tilde,iXX,prior] = dsge_var_likelihood(xparam1,DynareDataset,DynareInfo,DynareOptions,Model,EstimatedParameters,BayesInfo,BoundsInfo,DynareResults)
% Evaluates the posterior kernel of the bvar-dsge model.
%
% INPUTS
@@ -17,11 +17,23 @@ function [fval,info,exit_flag,grad,hess,SteadyState,trend_coeff,PHI,SIGMAu,iXX,p
% by call to dynare_resolve()
% o trend_coeff [double] place holder for trend coefficients,
% currently not supported by dsge_var
-% o PHI [double] Stacked BVAR-DSGE autoregressive matrices (at the mode associated to xparam1).
-% o SIGMAu [double] Covariance matrix of the BVAR-DSGE (at the mode associated to xparam1).
-% o iXX [double] inv(X'X).
-% o prior [double] a matlab structure describing the dsge-var prior.
+% o PHI_tilde [double] Stacked BVAR-DSGE autoregressive matrices (at the mode associated to xparam1);
+% formula (28), DS (2004)
+% o SIGMA_u_tilde [double] Covariance matrix of the BVAR-DSGE (at the mode associated to xparam1),
+% formula (29), DS (2004)
+% o iXX [double] inv(lambda*T*Gamma_XX^*+ X'*X)
+% o prior [double] a matlab structure describing the dsge-var prior
+% - SIGMA_u_star: prior covariance matrix, formula (23), DS (2004)
+% - PHI_star: prior autoregressive matrices, formula (22), DS (2004)
+% - ArtificialSampleSize: number of artificial observations from the prior (T^* in DS (2004))
+% - DF = prior.ArtificialSampleSize - NumberOfParameters - NumberOfObservedVariables;
+% - iGXX_star: theoretical covariance of regressors ({\Gamma_{XX}^*}^{-1} in DS (2004))
%
+% ALGORITHMS
+% Follows the computations outlined in Del Negro/Schorfheide (2004):
+% Priors from general equilibrium models for VARs, International Economic
+% Review, 45(2), pp. 643-673
+%
% SPECIAL REQUIREMENTS
% None.
@@ -44,12 +56,14 @@ function [fval,info,exit_flag,grad,hess,SteadyState,trend_coeff,PHI,SIGMAu,iXX,p
persistent dsge_prior_weight_idx
+% Initialize some of the output arguments.
+fval = [];
+exit_flag = 1;
grad=[];
hess=[];
-exit_flag = [];
info = zeros(4,1);
-PHI = [];
-SIGMAu = [];
+PHI_tilde = [];
+SIGMA_u_tilde = [];
iXX = [];
prior = [];
trend_coeff=[];
@@ -84,10 +98,6 @@ mYX = evalin('base', 'mYX');
mXY = evalin('base', 'mXY');
mXX = evalin('base', 'mXX');
-% Initialize some of the output arguments.
-fval = [];
-exit_flag = 1;
-
% Return, with endogenous penalty, if some dsge-parameters are smaller than the lower bound of the prior domain.
if DynareOptions.mode_compute ~= 1 && any(xparam1 < BoundsInfo.lb)
k = find(xparam1 < BoundsInfo.lb);
@@ -217,12 +227,16 @@ assignin('base','GYY',GYY);
assignin('base','GXX',GXX);
assignin('base','GYX',GYX);
+iGXX = inv(GXX);
+PHI_star = iGXX*transpose(GYX); %formula (22), DS (2004)
+SIGMA_u_star=GYY - GYX*PHI_star; %formula (23), DS (2004)
if ~isinf(dsge_prior_weight)% Evaluation of the likelihood of the dsge-var model when the dsge prior weight is finite.
- tmp0 = dsge_prior_weight*NumberOfObservations*TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1) + mYY ;
- tmp1 = dsge_prior_weight*NumberOfObservations*GYX + mYX;
- tmp2 = inv(dsge_prior_weight*NumberOfObservations*GXX+mXX);
- SIGMAu = tmp0 - tmp1*tmp2*tmp1'; clear('tmp0');
- [SIGMAu_is_positive_definite, penalty] = ispd(SIGMAu);
+ tmp0 = dsge_prior_weight*NumberOfObservations*TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1) + mYY ; %first term of square bracket in formula (29), DS (2004)
+ tmp1 = dsge_prior_weight*NumberOfObservations*GYX + mYX; %first element of second term of square bracket in formula (29), DS (2004)
+ tmp2 = inv(dsge_prior_weight*NumberOfObservations*GXX+mXX); %middle element of second term of square bracket in formula (29), DS (2004)
+ SIGMA_u_tilde = tmp0 - tmp1*tmp2*tmp1'; %square bracket term in formula (29), DS (2004)
+ clear('tmp0');
+ [SIGMAu_is_positive_definite, penalty] = ispd(SIGMA_u_tilde);
if ~SIGMAu_is_positive_definite
fval = Inf;
info(1) = 52;
@@ -230,29 +244,32 @@ if ~isinf(dsge_prior_weight)% Evaluation of the likelihood of the dsge-var model
exit_flag = 0;
return;
end
- SIGMAu = SIGMAu / (NumberOfObservations*(1+dsge_prior_weight));
- PHI = tmp2*tmp1'; clear('tmp1');
+ SIGMA_u_tilde = SIGMA_u_tilde / (NumberOfObservations*(1+dsge_prior_weight)); %prefactor of formula (29), DS (2004)
+ PHI_tilde = tmp2*tmp1'; %formula (28), DS (2004)
+ clear('tmp1');
prodlng1 = sum(gammaln(.5*((1+dsge_prior_weight)*NumberOfObservations- ...
NumberOfObservedVariables*NumberOfLags ...
- +1-(1:NumberOfObservedVariables)')));
+ +1-(1:NumberOfObservedVariables)'))); %last term in numerator of third line of (A.2), DS (2004)
prodlng2 = sum(gammaln(.5*(dsge_prior_weight*NumberOfObservations- ...
NumberOfObservedVariables*NumberOfLags ...
- +1-(1:NumberOfObservedVariables)')));
- lik = .5*NumberOfObservedVariables*log(det(dsge_prior_weight*NumberOfObservations*GXX+mXX)) ...
- + .5*((dsge_prior_weight+1)*NumberOfObservations-NumberOfParameters)*log(det((dsge_prior_weight+1)*NumberOfObservations*SIGMAu)) ...
- - .5*NumberOfObservedVariables*log(det(dsge_prior_weight*NumberOfObservations*GXX)) ...
- - .5*(dsge_prior_weight*NumberOfObservations-NumberOfParameters)*log(det(dsge_prior_weight*NumberOfObservations*(GYY-GYX*inv(GXX)*GYX'))) ...
- + .5*NumberOfObservedVariables*NumberOfObservations*log(2*pi) ...
- - .5*log(2)*NumberOfObservedVariables*((dsge_prior_weight+1)*NumberOfObservations-NumberOfParameters) ...
- + .5*log(2)*NumberOfObservedVariables*(dsge_prior_weight*NumberOfObservations-NumberOfParameters) ...
+ +1-(1:NumberOfObservedVariables)'))); %last term in denominator of third line of (A.2), DS (2004)
+ %Compute minus log likelihood according to (A.2), DS (2004)
+ lik = .5*NumberOfObservedVariables*log(det(dsge_prior_weight*NumberOfObservations*GXX+mXX)) ... %first term in numerator of second line of (A.2), DS (2004)
+ + .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)
+ - .5*NumberOfObservedVariables*log(det(dsge_prior_weight*NumberOfObservations*GXX)) ... %first term in denominator of second line of (A.2), DS (2004)
+ - .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)
+ + .5*NumberOfObservedVariables*NumberOfObservations*log(2*pi) ... %first term in numerator of third line of (A.2), DS (2004)
+ - .5*log(2)*NumberOfObservedVariables*((dsge_prior_weight+1)*NumberOfObservations-NumberOfParameters) ... %second term in numerator of third line of (A.2), DS (2004)
+ + .5*log(2)*NumberOfObservedVariables*(dsge_prior_weight*NumberOfObservations-NumberOfParameters) ... %first term in denominator of third line of (A.2), DS (2004)
- prodlng1 + prodlng2;
else% Evaluation of the likelihood of the dsge-var model when the dsge prior weight is infinite.
- iGXX = inv(GXX);
- SIGMAu = GYY - GYX*iGXX*transpose(GYX);
- PHI = iGXX*transpose(GYX);
- lik = NumberOfObservations * ( log(det(SIGMAu)) + NumberOfObservedVariables*log(2*pi) + ...
- trace(inv(SIGMAu)*(mYY - transpose(mYX*PHI) - mYX*PHI + transpose(PHI)*mXX*PHI)/NumberOfObservations));
+ PHI_star = iGXX*transpose(GYX);
+ %Compute minus log likelihood according to (33), DS (2004) (where the last term in the trace operator has been multiplied out)
+ lik = NumberOfObservations * ( log(det(SIGMA_u_star)) + NumberOfObservedVariables*log(2*pi) + ...
+ trace(inv(SIGMA_u_star)*(mYY - transpose(mYX*PHI_star) - mYX*PHI_star + transpose(PHI_star)*mXX*PHI_star)/NumberOfObservations));
lik = .5*lik;% Minus likelihood
+ SIGMA_u_tilde=SIGMA_u_star;
+ PHI_tilde=PHI_star;
end
if isnan(lik)
@@ -291,7 +308,7 @@ if imag(fval)~=0
return
end
-if (nargout == 10)
+if (nargout >= 10)
if isinf(dsge_prior_weight)
iXX = iGXX;
else
@@ -300,15 +317,9 @@ if (nargout == 10)
end
if (nargout==11)
- if isinf(dsge_prior_weight)
- iXX = iGXX;
- else
- iXX = tmp2;
- end
- iGXX = inv(GXX);
- prior.SIGMAstar = GYY - GYX*iGXX*GYX';
- prior.PHIstar = iGXX*transpose(GYX);
+ prior.SIGMA_u_star = SIGMA_u_star;
+ prior.PHI_star = PHI_star;
prior.ArtificialSampleSize = fix(dsge_prior_weight*NumberOfObservations);
prior.DF = prior.ArtificialSampleSize - NumberOfParameters - NumberOfObservedVariables;
- prior.iGXX = iGXX;
+ prior.iGXX_star = iGXX;
end
\ No newline at end of file
diff --git a/matlab/dynare_estimation_1.m b/matlab/dynare_estimation_1.m
index 8e317982145b32686ba66d991268345866f9fa1b..688a1951599c9c4a11fd1edc0e85614711a17aed 100644
--- a/matlab/dynare_estimation_1.m
+++ b/matlab/dynare_estimation_1.m
@@ -393,6 +393,12 @@ if any(bayestopt_.pshape > 0) && ~options_.mh_posterior_mode_estimation
disp(sprintf('Log data density [Laplace approximation] is %f.',oo_.MarginalDensity.LaplaceApproximation))
skipline()
end
+ if options_.dsge_var
+ [junk1,junk2,junk3,junk4,junk5,junk6,junk7,oo_.dsge_var.posterior_mode.PHI_tilde,oo_.dsge_var.posterior_mode.SIGMA_u_tilde,oo_.dsge_var.posterior_mode.iXX,oo_.dsge_var.posterior_mode.prior] =...
+ feval(objective_function,xparam1,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,bounds,oo_);
+ clear('junk1','junk2','junk3','junk4','junk5','junk6','junk7');
+ end
+
elseif ~any(bayestopt_.pshape > 0) && ~options_.mh_posterior_mode_estimation
oo_=display_estimation_results_table(xparam1,stdh,M_,options_,estim_params_,bayestopt_,oo_,pnames,'Maximum Likelihood','mle');
end