283 lines
11 KiB
Matlab
283 lines
11 KiB
Matlab
function [fval,grad,hess,exit_flag,info,PHI,SIGMAu,iXX,prior] = DsgeVarLikelihood(xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
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% Evaluates the posterior kernel of the bvar-dsge model.
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%
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% INPUTS
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% o xparam1 [double] Vector of model's parameters.
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% o gend [integer] Number of observations (without conditionning observations for the lags).
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%
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% OUTPUTS
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% o fval [double] Value of the posterior kernel at xparam1.
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% o cost_flag [integer] Zero if the function returns a penalty, one otherwise.
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% o info [integer] Vector of informations about the penalty.
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% o PHI [double] Stacked BVAR-DSGE autoregressive matrices (at the mode associated to xparam1).
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% o SIGMAu [double] Covariance matrix of the BVAR-DSGE (at the mode associated to xparam1).
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% o iXX [double] inv(X'X).
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% o prior [double] a matlab structure describing the dsge-var prior.
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%
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% SPECIAL REQUIREMENTS
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% None.
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% Copyright (C) 2006-2012 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 <http://www.gnu.org/licenses/>.
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global objective_function_penalty_base
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% Declaration of the persistent variables.
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persistent dsge_prior_weight_idx
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grad=[];
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hess=[];
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exit_flag = [];
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info = [];
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PHI = [];
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SIGMAu = [];
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iXX = [];
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prior = [];
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% Initialization of of the index for parameter dsge_prior_weight in Model.params.
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if isempty(dsge_prior_weight_idx)
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dsge_prior_weight_idx = strmatch('dsge_prior_weight',Model.param_names);
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end
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% Get the number of estimated (dsge) parameters.
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ns = EstimatedParameters.nvx + ...
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EstimatedParameters.nvn + ...
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EstimatedParameters.ncx + ...
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EstimatedParameters.ncn;
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nx = ns + EstimatedParameters.np;
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% Get the number of observed variables in the VAR model.
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NumberOfObservedVariables = DynareDataset.info.nvobs;
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% Get the number of lags in the VAR model.
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NumberOfLags = DynareOptions.dsge_varlag;
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% Get the number of parameters in the VAR model.
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NumberOfParameters = NumberOfObservedVariables*NumberOfLags ;
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if ~DynareOptions.noconstant
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NumberOfParameters = NumberOfParameters + 1;
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end
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% Get empirical second order moments for the observed variables.
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mYY = evalin('base', 'mYY');
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mYX = evalin('base', 'mYX');
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mXY = evalin('base', 'mXY');
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mXX = evalin('base', 'mXX');
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% Initialize some of the output arguments.
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fval = [];
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exit_flag = 1;
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% Return, with endogenous penalty, if some dsge-parameters are smaller than the lower bound of the prior domain.
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if DynareOptions.mode_compute ~= 1 && any(xparam1 < BayesInfo.lb)
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k = find(xparam1 < BayesInfo.lb);
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fval = objective_function_penalty_base+sum((BayesInfo.lb(k)-xparam1(k)).^2);
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exit_flag = 0;
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info = 41;
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return;
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end
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% Return, with endogenous penalty, if some dsge-parameters are greater than the upper bound of the prior domain.
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if DynareOptions.mode_compute ~= 1 && any(xparam1 > BayesInfo.ub)
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k = find(xparam1 > BayesInfo.ub);
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fval = objective_function_penalty_base+sum((xparam1(k)-BayesInfo.ub(k)).^2);
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exit_flag = 0;
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info = 42;
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return;
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end
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% Get the variance of each structural innovation.
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Q = Model.Sigma_e;
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for i=1:EstimatedParameters.nvx
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k = EstimatedParameters.var_exo(i,1);
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Q(k,k) = xparam1(i)*xparam1(i);
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end
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offset = EstimatedParameters.nvx;
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% Check that the user does not estimate measurment errors.
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% TODO Check that the user does not declare non estimated measurement errors...
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if EstimatedParameters.nvn
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disp('DsgeVarLikelihood :: Measurement errors are not implemented!')
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return
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end
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% Check that the user does not estimate off diagonal elements in the covariance matrix of the structural innovation.
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% TODO Check that Q is a diagonal matrix...
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if EstimatedParameters.ncx
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disp('DsgeVarLikelihood :: Correlated structural innovations are not implemented!')
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return
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end
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% Update Model.params and Model.Sigma_e.
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Model.params(EstimatedParameters.param_vals(:,1)) = xparam1(offset+1:end);
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Model.Sigma_e = Q;
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% Get the weight of the dsge prior.
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dsge_prior_weight = Model.params(dsge_prior_weight_idx);
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% Is the dsge prior proper?
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if dsge_prior_weight<(NumberOfParameters+NumberOfObservedVariables)/DynareDataset.info.ntobs;
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fval = objective_function_penalty_base+abs(DynareDataset.info.ntobs*dsge_prior_weight-(NumberOfParameters+NumberOfObservedVariables));
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exit_flag = 0;
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info = 51;
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return
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end
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%------------------------------------------------------------------------------
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% 2. call model setup & reduction program
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%------------------------------------------------------------------------------
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% Solve the Dsge model and get the matrices of the reduced form solution. T and R are the matrices of the
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% state equation
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[T,R,SteadyState,info,Model,DynareOptions,DynareResults] = dynare_resolve(Model,DynareOptions,DynareResults,'restrict');
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% Return, with endogenous penalty when possible, if dynare_resolve issues an error code (defined in resol).
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if info(1) == 1 || info(1) == 2 || info(1) == 5 || info(1) == 7 || info(1) ...
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== 8 || info(1) == 22 || info(1) == 24
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fval = objective_function_penalty_base+1;
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info = info(1);
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exit_flag = 0;
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return
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elseif info(1) == 3 || info(1) == 4 || info(1) == 19 || info(1) == 20 || info(1) == 21
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fval = objective_function_penalty_base+info(2);
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info = info(1);
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exit_flag = 0;
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return
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end
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% Define the mean/steady state vector.
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if ~DynareOptions.noconstant
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if DynareOptions.loglinear
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constant = transpose(log(SteadyState(BayesInfo.mfys)));
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else
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constant = transpose(SteadyState(BayesInfo.mfys));
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end
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else
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constant = zeros(1,NumberOfObservedVariables);
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end
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% Dsge-VAR with deterministic trends is not implemented
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if BayesInfo.with_trend == 1
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error('DsgeVarLikelihood :: Linear trend is not yet implemented!')
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end
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%------------------------------------------------------------------------------
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% 3. theoretical moments (second order)
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%------------------------------------------------------------------------------
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% Compute the theoretical second order moments
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tmp0 = lyapunov_symm(T,R*Q*R',DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold);
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mf = BayesInfo.mf1;
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% Get the non centered second order moments
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TheoreticalAutoCovarianceOfTheObservedVariables = zeros(NumberOfObservedVariables,NumberOfObservedVariables,NumberOfLags+1);
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TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1) = tmp0(mf,mf)+constant'*constant;
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for lag = 1:NumberOfLags
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tmp0 = T*tmp0;
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TheoreticalAutoCovarianceOfTheObservedVariables(:,:,lag+1) = tmp0(mf,mf) + constant'*constant;
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end
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% Build the theoretical "covariance" between Y and X
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GYX = zeros(NumberOfObservedVariables,NumberOfParameters);
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for i=1:NumberOfLags
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GYX(:,(i-1)*NumberOfObservedVariables+1:i*NumberOfObservedVariables) = TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1);
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end
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if ~DynareOptions.noconstant
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GYX(:,end) = constant';
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end
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% Build the theoretical "covariance" between X and X
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GXX = kron(eye(NumberOfLags), TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1));
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for i = 1:NumberOfLags-1
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tmp1 = diag(ones(NumberOfLags-i,1),i);
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tmp2 = diag(ones(NumberOfLags-i,1),-i);
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GXX = GXX + kron(tmp1,TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1));
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GXX = GXX + kron(tmp2,TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1)');
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end
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if ~DynareOptions.noconstant
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% Add one row and one column to GXX
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GXX = [GXX , kron(ones(NumberOfLags,1),constant') ; [ kron(ones(1,NumberOfLags),constant) , 1] ];
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end
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GYY = TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1);
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assignin('base','GYY',GYY);
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assignin('base','GXX',GXX);
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assignin('base','GYX',GYX);
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if ~isinf(dsge_prior_weight)% Evaluation of the likelihood of the dsge-var model when the dsge prior weight is finite.
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tmp0 = dsge_prior_weight*DynareDataset.info.ntobs*TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1) + mYY ;
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tmp1 = dsge_prior_weight*DynareDataset.info.ntobs*GYX + mYX;
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tmp2 = inv(dsge_prior_weight*DynareDataset.info.ntobs*GXX+mXX);
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SIGMAu = tmp0 - tmp1*tmp2*tmp1'; clear('tmp0');
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[SIGMAu_is_positive_definite, penalty] = ispd(SIGMAu)
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if ~SIGMAu_is_positive_definite
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fval = objective_function_penalty_base + penalty;
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info = 52;
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exit_flag = 0;
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return;
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end
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SIGMAu = SIGMAu / (DynareDataset.info.ntobs*(1+dsge_prior_weight));
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PHI = tmp2*tmp1'; clear('tmp1');
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prodlng1 = sum(gammaln(.5*((1+dsge_prior_weight)*DynareDataset.info.ntobs- ...
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NumberOfObservedVariables*NumberOfLags ...
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+1-(1:NumberOfObservedVariables)')));
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prodlng2 = sum(gammaln(.5*(dsge_prior_weight*DynareDataset.info.ntobs- ...
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NumberOfObservedVariables*NumberOfLags ...
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+1-(1:NumberOfObservedVariables)')));
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lik = .5*NumberOfObservedVariables*log(det(dsge_prior_weight*DynareDataset.info.ntobs*GXX+mXX)) ...
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+ .5*((dsge_prior_weight+1)*DynareDataset.info.ntobs-NumberOfParameters)*log(det((dsge_prior_weight+1)*DynareDataset.info.ntobs*SIGMAu)) ...
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- .5*NumberOfObservedVariables*log(det(dsge_prior_weight*DynareDataset.info.ntobs*GXX)) ...
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- .5*(dsge_prior_weight*DynareDataset.info.ntobs-NumberOfParameters)*log(det(dsge_prior_weight*DynareDataset.info.ntobs*(GYY-GYX*inv(GXX)*GYX'))) ...
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+ .5*NumberOfObservedVariables*DynareDataset.info.ntobs*log(2*pi) ...
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- .5*log(2)*NumberOfObservedVariables*((dsge_prior_weight+1)*DynareDataset.info.ntobs-NumberOfParameters) ...
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+ .5*log(2)*NumberOfObservedVariables*(dsge_prior_weight*DynareDataset.info.ntobs-NumberOfParameters) ...
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- prodlng1 + prodlng2;
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else% Evaluation of the likelihood of the dsge-var model when the dsge prior weight is infinite.
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iGXX = inv(GXX);
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SIGMAu = GYY - GYX*iGXX*transpose(GYX);
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PHI = iGXX*transpose(GYX);
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lik = DynareDataset.info.ntobs * ( log(det(SIGMAu)) + NumberOfObservedVariables*log(2*pi) + ...
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trace(inv(SIGMAu)*(mYY - transpose(mYX*PHI) - mYX*PHI + transpose(PHI)*mXX*PHI)/DynareDataset.info.ntobs));
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lik = .5*lik;% Minus likelihood
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end
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% Add the (logged) prior density for the dsge-parameters.
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lnprior = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
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fval = (lik-lnprior);
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if (nargout == 8)
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if isinf(dsge_prior_weight)
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iXX = iGXX;
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else
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iXX = tmp2;
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end
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end
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if (nargout==9)
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if isinf(dsge_prior_weight)
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iXX = iGXX;
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else
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iXX = tmp2;
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end
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iGXX = inv(GXX);
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prior.SIGMAstar = GYY - GYX*iGXX*GYX';
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prior.PHIstar = iGXX*transpose(GYX);
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prior.ArtificialSampleSize = fix(dsge_prior_weight*DynareDataset.info.ntobs);
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prior.DF = prior.ArtificialSampleSize - NumberOfParameters - NumberOfObservedVariables;
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prior.iGXX = iGXX;
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end |