310 lines
11 KiB
Matlab
310 lines
11 KiB
Matlab
function [fval,cost_flag,ys,trend_coeff,info] = dsge_posterior_kernel(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
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% function [fval,cost_flag,ys,trend_coeff,info] = dsge_posterior_kernel(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
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% Evaluates the posterior kernel of a dsge model.
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%
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% INPUTS
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% xparam1 [double] vector of model parameters.
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% gend [integer] scalar specifying the number of observations.
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% data [double] matrix of data
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% data_index [cell] cell of column vectors
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% number_of_observations [integer]
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% no_more_missing_observations [integer]
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% OUTPUTS
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% fval : value of the posterior kernel at xparam1.
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% cost_flag : zero if the function returns a penalty, one otherwise.
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% ys : steady state of original endogenous variables
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% trend_coeff :
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% info : vector of informations about the penalty:
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% 41: one (many) parameter(s) do(es) not satisfied the lower bound
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% 42: one (many) parameter(s) do(es) not satisfied the upper bound
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%
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% SPECIAL REQUIREMENTS
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%
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% Copyright (C) 2004-2011 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 bayestopt_ estim_params_ options_ trend_coeff_ M_ oo_
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fval = [];
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ys = [];
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trend_coeff = [];
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cost_flag = 1;
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nobs = size(options_.varobs,1);
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%------------------------------------------------------------------------------
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% 1. Get the structural parameters & define penalties
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%------------------------------------------------------------------------------
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if options_.mode_compute ~= 1 && any(xparam1 < bayestopt_.lb)
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k = find(xparam1 < bayestopt_.lb);
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fval = bayestopt_.penalty+sum((bayestopt_.lb(k)-xparam1(k)).^2);
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cost_flag = 0;
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info = 41;
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return;
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end
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if options_.mode_compute ~= 1 && any(xparam1 > bayestopt_.ub)
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k = find(xparam1 > bayestopt_.ub);
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fval = bayestopt_.penalty+sum((xparam1(k)-bayestopt_.ub(k)).^2);
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cost_flag = 0;
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info = 42;
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return;
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end
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Q = M_.Sigma_e;
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H = M_.H;
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for i=1:estim_params_.nvx
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k =estim_params_.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 = estim_params_.nvx;
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if estim_params_.nvn
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for i=1:estim_params_.nvn
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k = estim_params_.var_endo(i,1);
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H(k,k) = xparam1(i+offset)*xparam1(i+offset);
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end
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offset = offset+estim_params_.nvn;
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end
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if estim_params_.ncx
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for i=1:estim_params_.ncx
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k1 =estim_params_.corrx(i,1);
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k2 =estim_params_.corrx(i,2);
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Q(k1,k2) = xparam1(i+offset)*sqrt(Q(k1,k1)*Q(k2,k2));
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Q(k2,k1) = Q(k1,k2);
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end
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[CholQ,testQ] = chol(Q);
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if testQ %% The variance-covariance matrix of the structural innovations is not definite positive.
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%% We have to compute the eigenvalues of this matrix in order to build the penalty.
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a = diag(eig(Q));
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k = find(a < 0);
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if k > 0
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fval = bayestopt_.penalty+sum(-a(k));
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cost_flag = 0;
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info = 43;
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return
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end
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end
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offset = offset+estim_params_.ncx;
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end
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if estim_params_.ncn
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for i=1:estim_params_.ncn
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k1 = options_.lgyidx2varobs(estim_params_.corrn(i,1));
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k2 = options_.lgyidx2varobs(estim_params_.corrn(i,2));
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H(k1,k2) = xparam1(i+offset)*sqrt(H(k1,k1)*H(k2,k2));
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H(k2,k1) = H(k1,k2);
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end
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[CholH,testH] = chol(H);
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if testH
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a = diag(eig(H));
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k = find(a < 0);
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if k > 0
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fval = bayestopt_.penalty+sum(-a(k));
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cost_flag = 0;
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info = 44;
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return
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end
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end
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offset = offset+estim_params_.ncn;
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end
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if estim_params_.np > 0
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M_.params(estim_params_.param_vals(:,1)) = xparam1(offset+1:end);
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end
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M_.Sigma_e = Q;
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M_.H = H;
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%------------------------------------------------------------------------------
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% 2. call model setup & reduction program
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%------------------------------------------------------------------------------
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[T,R,SteadyState,info] = dynare_resolve('restrict');
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if info(1) == 1 || info(1) == 2 || info(1) == 5
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fval = bayestopt_.penalty+1;
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cost_flag = 0;
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return
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elseif info(1) == 3 || info(1) == 4 || info(1) == 20
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fval = bayestopt_.penalty+info(2);%^2; % penalty power raised in DR1.m and resol already. GP July'08
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cost_flag = 0;
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return
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end
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bayestopt_.mf = bayestopt_.mf1;
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if ~options_.noconstant
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if options_.loglinear == 1
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constant = log(SteadyState(bayestopt_.mfys));
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else
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constant = SteadyState(bayestopt_.mfys);
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end
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else
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constant = zeros(nobs,1);
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end
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if bayestopt_.with_trend == 1
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trend_coeff = zeros(nobs,1);
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t = options_.trend_coeffs;
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for i=1:length(t)
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if ~isempty(t{i})
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trend_coeff(i) = evalin('base',t{i});
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end
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end
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trend = repmat(constant,1,gend)+trend_coeff*[1:gend];
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else
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trend = repmat(constant,1,gend);
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end
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start = options_.presample+1;
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np = size(T,1);
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mf = bayestopt_.mf;
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no_missing_data_flag = (number_of_observations==gend*nobs);
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%------------------------------------------------------------------------------
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% 3. Initial condition of the Kalman filter
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%------------------------------------------------------------------------------
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kalman_algo = options_.kalman_algo;
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if options_.lik_init == 1 % Kalman filter
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if kalman_algo ~= 2
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kalman_algo = 1;
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end
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Pstar = lyapunov_symm(T,R*Q*R',options_.qz_criterium,options_.lyapunov_complex_threshold);
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Pinf = [];
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elseif options_.lik_init == 2 % Old Diffuse Kalman filter
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if kalman_algo ~= 2
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kalman_algo = 1;
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end
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Pstar = 10*eye(np);
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Pinf = [];
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elseif options_.lik_init == 3 % Diffuse Kalman filter
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if kalman_algo ~= 4
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kalman_algo = 3;
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end
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[QT,ST] = schur(T);
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e1 = abs(ordeig(ST)) > 2-options_.qz_criterium;
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[QT,ST] = ordschur(QT,ST,e1);
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k = find(abs(ordeig(ST)) > 2-options_.qz_criterium);
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nk = length(k);
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nk1 = nk+1;
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Pinf = zeros(np,np);
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Pinf(1:nk,1:nk) = eye(nk);
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Pstar = zeros(np,np);
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B = QT'*R*Q*R'*QT;
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for i=np:-1:nk+2
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if ST(i,i-1) == 0
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if i == np
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c = zeros(np-nk,1);
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else
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c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
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ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
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end
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q = eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i);
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Pstar(nk1:i,i) = q\(B(nk1:i,i)+c);
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Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
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else
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if i == np
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c = zeros(np-nk,1);
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c1 = zeros(np-nk,1);
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else
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c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
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ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i)+...
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ST(i,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1);
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c1 = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i-1,i+1:end)')+...
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ST(i-1,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1)+...
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ST(i-1,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
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end
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q = [eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i) -ST(nk1:i,nk1:i)*ST(i,i-1);...
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-ST(nk1:i,nk1:i)*ST(i-1,i) eye(i-nk)-ST(nk1:i,nk1:i)*ST(i-1,i-1)];
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z = q\[B(nk1:i,i)+c;B(nk1:i,i-1)+c1];
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Pstar(nk1:i,i) = z(1:(i-nk));
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Pstar(nk1:i,i-1) = z(i-nk+1:end);
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Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
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Pstar(i-1,nk1:i-2) = Pstar(nk1:i-2,i-1)';
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i = i - 1;
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end
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end
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if i == nk+2
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c = ST(nk+1,:)*(Pstar(:,nk+2:end)*ST(nk1,nk+2:end)')+ST(nk1,nk1)*ST(nk1,nk+2:end)*Pstar(nk+2:end,nk1);
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Pstar(nk1,nk1)=(B(nk1,nk1)+c)/(1-ST(nk1,nk1)*ST(nk1,nk1));
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end
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Z = QT(mf,:);
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R1 = QT'*R;
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[QQ,RR,EE] = qr(Z*ST(:,1:nk),0);
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k = find(abs(diag(RR)) < 1e-8);
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if length(k) > 0
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k1 = EE(:,k);
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dd =ones(nk,1);
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dd(k1) = zeros(length(k1),1);
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Pinf(1:nk,1:nk) = diag(dd);
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end
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end
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if kalman_algo == 2
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no_correlation_flag = 1;
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if length(H)==1
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H = zeros(nobs,1);
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else
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if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
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H = diag(H);
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else
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no_correlation_flag = 0;
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end
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end
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end
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kalman_tol = options_.kalman_tol;
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riccati_tol = options_.riccati_tol;
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mf = bayestopt_.mf1;
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Y = data-trend;
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%------------------------------------------------------------------------------
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% 4. Likelihood evaluation
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%------------------------------------------------------------------------------
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if (kalman_algo==1)% Multivariate Kalman Filter
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if no_missing_data_flag
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LIK = kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol);
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else
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LIK = ...
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missing_observations_kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol, ...
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data_index,number_of_observations,no_more_missing_observations);
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end
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if isinf(LIK)
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kalman_algo = 2;
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end
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end
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if (kalman_algo==2)% Univariate Kalman Filter
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if no_correlation_flag
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LIK = univariate_kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations);
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else
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LIK = univariate_kalman_filter_corr(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations);
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end
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end
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if (kalman_algo==3)% Multivariate Diffuse Kalman Filter
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if no_missing_data_flag
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LIK = diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol,riccati_tol);
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else
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LIK = missing_observations_diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol,riccati_tol,...
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data_index,number_of_observations,no_more_missing_observations);
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end
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if isinf(LIK)
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kalman_algo = 4;
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end
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end
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if (kalman_algo==4)% Univariate Diffuse Kalman Filter
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if no_correlation_flag
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LIK = univariate_diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol,riccati_tol,...
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data_index,number_of_observations,no_more_missing_observations);
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else
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LIK = univariate_diffuse_kalman_filter_corr(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol,riccati_tol,...
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data_index,number_of_observations,no_more_missing_observations);
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end
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end
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if imag(LIK) ~= 0
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likelihood = bayestopt_.penalty;
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else
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likelihood = LIK;
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end
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% ------------------------------------------------------------------------------
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% Adds prior if necessary
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% ------------------------------------------------------------------------------
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lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
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fval = (likelihood-lnprior);
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options_.kalman_algo = kalman_algo;
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