329 lines
14 KiB
Matlab
329 lines
14 KiB
Matlab
function [fval,info,exit_flag,grad,hess,SteadyState,trend_coeff,PHI_tilde,SIGMA_u_tilde,iXX,prior] = dsge_var_likelihood(xparam1,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,BoundsInfo,dr, endo_steady_state, exo_steady_state, exo_det_steady_state)
|
||
% [fval,info,exit_flag,grad,hess,SteadyState,trend_coeff,PHI_tilde,SIGMA_u_tilde,iXX,prior] = dsge_var_likelihood(xparam1,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,BoundsInfo,dr, endo_steady_state, exo_steady_state, exo_det_steady_state)
|
||
% Evaluates the posterior kernel of the BVAR-DSGE model.
|
||
%
|
||
% INPUTS
|
||
% o xparam1 [double] Vector of model's parameters.
|
||
% o gend [integer] Number of observations (without conditionning observations for the lags).
|
||
% o dataset_ [dseries] object storing the dataset
|
||
% o dataset_info [structure] storing informations about the sample.
|
||
% o options_ [structure] describing the options
|
||
% o M_ [structure] decribing the model
|
||
% o estim_params_ [structure] characterizing parameters to be estimated
|
||
% o bayestopt_ [structure] describing the priors
|
||
% o BoundsInfo [structure] containing prior bounds
|
||
% o dr [structure] Reduced form model.
|
||
% o endo_steady_state [vector] steady state value for endogenous variables
|
||
% o exo_steady_state [vector] steady state value for exogenous variables
|
||
% o exo_det_steady_state [vector] steady state value for exogenous deterministic variables
|
||
%
|
||
% OUTPUTS
|
||
% o fval [double] Value of the posterior kernel at xparam1.
|
||
% o info [integer] Vector of informations about the penalty.
|
||
% o exit_flag [integer] Zero if the function returns a penalty, one otherwise.
|
||
% o grad [double] place holder for gradient of the likelihood
|
||
% currently not supported by dsge_var
|
||
% o hess [double] place holder for hessian matrix of the likelihood
|
||
% currently not supported by dsge_var
|
||
% o SteadyState [double] Steady state vector possibly recomputed
|
||
% by call to dynare_resolve()
|
||
% o trend_coeff [double] place holder for trend coefficients,
|
||
% currently not supported by dsge_var
|
||
% 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.
|
||
|
||
% Copyright © 2006-2023Dynare 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 <https://www.gnu.org/licenses/>.
|
||
|
||
% Initialize some of the output arguments.
|
||
fval = [];
|
||
exit_flag = 1;
|
||
grad=[];
|
||
hess=[];
|
||
info = zeros(4,1);
|
||
PHI_tilde = [];
|
||
SIGMA_u_tilde = [];
|
||
iXX = [];
|
||
prior = [];
|
||
trend_coeff=[];
|
||
|
||
% Ensure that xparam1 is a column vector.
|
||
% (Don't do the transformation if xparam1 is empty, otherwise it would become a
|
||
% 0×1 matrix, which create issues with older MATLABs when comparing with [] in
|
||
% check_bounds_and_definiteness_estimation)
|
||
if ~isempty(xparam1)
|
||
xparam1 = xparam1(:);
|
||
end
|
||
|
||
% Initialization of of the index for parameter dsge_prior_weight in M_.params.
|
||
dsge_prior_weight_idx = strmatch('dsge_prior_weight', M_.param_names);
|
||
|
||
% Get the number of estimated (dsge) parameters.
|
||
nx = estim_params_.nvx + estim_params_.np;
|
||
|
||
% Get the number of observed variables in the VAR model.
|
||
NumberOfObservedVariables = dataset_.vobs;
|
||
|
||
% Get the number of observations.
|
||
NumberOfObservations = dataset_.nobs;
|
||
|
||
|
||
% Get the number of lags in the VAR model.
|
||
NumberOfLags = options_.dsge_varlag;
|
||
|
||
% Get the number of parameters in the VAR model.
|
||
NumberOfParameters = NumberOfObservedVariables*NumberOfLags ;
|
||
if ~options_.noconstant
|
||
NumberOfParameters = NumberOfParameters + 1;
|
||
end
|
||
|
||
% Get empirical second order moments for the observed variables.
|
||
mYY= dataset_info.mYY;
|
||
mYX= dataset_info.mYX;
|
||
mXX= dataset_info.mXX;
|
||
|
||
M_ = set_all_parameters(xparam1,estim_params_,M_);
|
||
|
||
[fval,info,exit_flag,Q]=check_bounds_and_definiteness_estimation(xparam1, M_, estim_params_, BoundsInfo);
|
||
if info(1)
|
||
return
|
||
end
|
||
|
||
% Get the weight of the dsge prior.
|
||
dsge_prior_weight = M_.params(dsge_prior_weight_idx);
|
||
|
||
% Is the dsge prior proper?
|
||
if dsge_prior_weight<(NumberOfParameters+NumberOfObservedVariables)/NumberOfObservations
|
||
fval = Inf;
|
||
exit_flag = 0;
|
||
info(1) = 51;
|
||
info(2)=dsge_prior_weight;
|
||
info(3)=(NumberOfParameters+NumberOfObservedVariables)/dataset_.nobs;
|
||
info(4)=abs(NumberOfObservations*dsge_prior_weight-(NumberOfParameters+NumberOfObservedVariables));
|
||
return
|
||
end
|
||
|
||
%------------------------------------------------------------------------------
|
||
% 2. call model setup & reduction program
|
||
%------------------------------------------------------------------------------
|
||
|
||
% Solve the Dsge model and get the matrices of the reduced form solution. T and R are the matrices of the
|
||
% state equation
|
||
[T,R,SteadyState,info] = dynare_resolve(M_,options_, dr, endo_steady_state, exo_steady_state, exo_det_steady_state,'restrict');
|
||
|
||
% Return, with endogenous penalty when possible, if dynare_resolve issues an error code (defined in resol).
|
||
if info(1)
|
||
if info(1) == 3 || info(1) == 4 || info(1) == 5 || info(1)==6 ||info(1) == 19 ||...
|
||
info(1) == 20 || info(1) == 21 || info(1) == 23 || info(1) == 26 || ...
|
||
info(1) == 81 || info(1) == 84 || info(1) == 85
|
||
%meaningful second entry of output that can be used
|
||
fval = Inf;
|
||
info(4) = info(2);
|
||
exit_flag = 0;
|
||
return
|
||
else
|
||
fval = Inf;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
end
|
||
|
||
% Define the mean/steady state vector.
|
||
if ~options_.noconstant
|
||
if options_.loglinear
|
||
constant = transpose(log(SteadyState(bayestopt_.mfys)));
|
||
else
|
||
constant = transpose(SteadyState(bayestopt_.mfys));
|
||
end
|
||
else
|
||
constant = zeros(1,NumberOfObservedVariables);
|
||
end
|
||
|
||
|
||
%------------------------------------------------------------------------------
|
||
% 3. theoretical moments (second order)
|
||
%------------------------------------------------------------------------------
|
||
|
||
% Compute the theoretical second order moments
|
||
tmp0 = lyapunov_symm(T,R*Q*R',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, [], options_.debug);
|
||
mf = bayestopt_.mf1;
|
||
|
||
% Get the non centered second order moments
|
||
TheoreticalAutoCovarianceOfTheObservedVariables = zeros(NumberOfObservedVariables,NumberOfObservedVariables,NumberOfLags+1);
|
||
TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1) = tmp0(mf,mf)+constant'*constant;
|
||
for lag = 1:NumberOfLags
|
||
tmp0 = T*tmp0;
|
||
TheoreticalAutoCovarianceOfTheObservedVariables(:,:,lag+1) = tmp0(mf,mf) + constant'*constant;
|
||
end
|
||
|
||
% Build the theoretical "covariance" between Y and X
|
||
GYX = zeros(NumberOfObservedVariables,NumberOfParameters);
|
||
for i=1:NumberOfLags
|
||
GYX(:,(i-1)*NumberOfObservedVariables+1:i*NumberOfObservedVariables) = TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1);
|
||
end
|
||
if ~options_.noconstant
|
||
GYX(:,end) = constant';
|
||
end
|
||
|
||
% Build the theoretical "covariance" between X and X
|
||
GXX = kron(eye(NumberOfLags), TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1));
|
||
for i = 1:NumberOfLags-1
|
||
tmp1 = diag(ones(NumberOfLags-i,1),i);
|
||
tmp2 = diag(ones(NumberOfLags-i,1),-i);
|
||
GXX = GXX + kron(tmp1,TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1));
|
||
GXX = GXX + kron(tmp2,TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1)');
|
||
end
|
||
|
||
if ~options_.noconstant
|
||
% Add one row and one column to GXX
|
||
GXX = [GXX , kron(ones(NumberOfLags,1),constant') ; [ kron(ones(1,NumberOfLags),constant) , 1] ];
|
||
end
|
||
|
||
GYY = TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1);
|
||
|
||
iGXX = inv(GXX);
|
||
PHI_star = iGXX*transpose(GYX); %formula (22), DS (2004)
|
||
SIGMA_u_star=GYY - GYX*PHI_star; %formula (23), DS (2004)
|
||
[SIGMA_u_star_is_positive_definite, penalty] = ispd(SIGMA_u_star);
|
||
if ~SIGMA_u_star_is_positive_definite
|
||
fval = Inf;
|
||
info(1) = 53;
|
||
info(4) = penalty;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
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 ; %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;
|
||
info(4) = penalty;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
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- ...
|
||
NumberOfParameters ...
|
||
+1-(1:NumberOfObservedVariables)'))); %last term in numerator of third line of (A.2), DS (2004)
|
||
prodlng2 = sum(gammaln(.5*(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.
|
||
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)
|
||
fval = Inf;
|
||
info(1) = 45;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
if imag(lik)~=0
|
||
fval = Inf;
|
||
info(1) = 46;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
% Add the (logged) prior density for the dsge-parameters.
|
||
lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
|
||
fval = (lik-lnprior);
|
||
|
||
if isnan(fval)
|
||
fval = Inf;
|
||
info(1) = 47;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
if imag(fval)~=0
|
||
fval = Inf;
|
||
info(1) = 48;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
if isinf(fval)
|
||
fval = Inf;
|
||
info(1) = 50;
|
||
info(4) = 0.1;
|
||
exit_flag = 0;
|
||
return
|
||
end
|
||
|
||
if (nargout >= 10)
|
||
if isinf(dsge_prior_weight)
|
||
iXX = iGXX;
|
||
else
|
||
iXX = tmp2;
|
||
end
|
||
end
|
||
|
||
if (nargout==11)
|
||
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_star = iGXX;
|
||
end
|