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dynare/mex/sources/estimation/tests/DsgeLikelihood.m

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function [fval,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
% function [fval,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
% Evaluates the posterior kernel of a dsge model.
%
% INPUTS
% xparam1 [double] vector of model parameters.
% gend [integer] scalar specifying the number of observations.
% data [double] matrix of data
% data_index [cell] cell of column vectors
% number_of_observations [integer]
% no_more_missing_observations [integer]
% OUTPUTS
% fval : value of the posterior kernel at xparam1.
% cost_flag : zero if the function returns a penalty, one otherwise.
% ys : steady state of original endogenous variables
% trend_coeff :
% info : vector of informations about the penalty:
% 41: one (many) parameter(s) do(es) not satisfied the lower bound
% 42: one (many) parameter(s) do(es) not satisfied the upper bound
%
% SPECIAL REQUIREMENTS
%
% 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/>.
global bayestopt_ estim_params_ options_ trend_coeff_ M_ oo_
fval = [];
ys = [];
trend_coeff = [];
cost_flag = 1;
nobs = size(options_.varobs,1);
%------------------------------------------------------------------------------
% 1. Get the structural parameters & define penalties
%------------------------------------------------------------------------------
if options_.mode_compute ~= 1 & any(xparam1 < bayestopt_.lb)
k = find(xparam1 < bayestopt_.lb);
fval = bayestopt_.penalty+sum((bayestopt_.lb(k)-xparam1(k)).^2);
cost_flag = 0;
info = 41;
return;
end
if options_.mode_compute ~= 1 & any(xparam1 > bayestopt_.ub)
k = find(xparam1 > bayestopt_.ub);
fval = bayestopt_.penalty+sum((xparam1(k)-bayestopt_.ub(k)).^2);
cost_flag = 0;
info = 42;
return;
end
Q = M_.Sigma_e;
H = M_.H;
for i=1:estim_params_.nvx
k =estim_params_.var_exo(i,1);
Q(k,k) = xparam1(i)*xparam1(i);
end
offset = estim_params_.nvx;
if estim_params_.nvn
for i=1:estim_params_.nvn
k = estim_params_.var_endo(i,1);
H(k,k) = xparam1(i+offset)*xparam1(i+offset);
end
offset = offset+estim_params_.nvn;
end
if estim_params_.ncx
for i=1:estim_params_.ncx
k1 =estim_params_.corrx(i,1);
k2 =estim_params_.corrx(i,2);
Q(k1,k2) = xparam1(i+offset)*sqrt(Q(k1,k1)*Q(k2,k2));
Q(k2,k1) = Q(k1,k2);
end
[CholQ,testQ] = chol(Q);
if testQ %% The variance-covariance matrix of the structural innovations is not definite positive.
%% We have to compute the eigenvalues of this matrix in order to build the penalty.
a = diag(eig(Q));
k = find(a < 0);
if k > 0
fval = bayestopt_.penalty+sum(-a(k));
cost_flag = 0;
info = 43;
return
end
end
offset = offset+estim_params_.ncx;
end
if estim_params_.ncn
for i=1:estim_params_.ncn
k1 = options_.lgyidx2varobs(estim_params_.corrn(i,1));
k2 = options_.lgyidx2varobs(estim_params_.corrn(i,2));
H(k1,k2) = xparam1(i+offset)*sqrt(H(k1,k1)*H(k2,k2));
H(k2,k1) = H(k1,k2);
end
[CholH,testH] = chol(H);
if testH
a = diag(eig(H));
k = find(a < 0);
if k > 0
fval = bayestopt_.penalty+sum(-a(k));
cost_flag = 0;
info = 44;
return
end
end
offset = offset+estim_params_.ncn;
end
if estim_params_.np > 0
M_.params(estim_params_.param_vals(:,1)) = xparam1(offset+1:end);
end
M_.Sigma_e = Q;
M_.H = H;
%------------------------------------------------------------------------------
% 2. call model setup & reduction program
%------------------------------------------------------------------------------
[T,R,SteadyState,info] = dynare_resolve(bayestopt_.restrict_var_list,...
bayestopt_.restrict_columns,...
bayestopt_.restrict_aux);
if info(1) == 1 || info(1) == 2 || info(1) == 5
fval = bayestopt_.penalty+1;
cost_flag = 0;
return
elseif info(1) == 3 || info(1) == 4 || info(1)==6 ||info(1) == 19 || info(1) == 20 || info(1) == 21
fval = bayestopt_.penalty+info(2);
cost_flag = 0;
return
end
bayestopt_.mf = bayestopt_.mf1;
if options_.noconstant
constant = zeros(nobs,1);
else
if options_.loglinear
constant = log(SteadyState(bayestopt_.mfys));
else
constant = SteadyState(bayestopt_.mfys);
end
end
if bayestopt_.with_trend
trend_coeff = zeros(nobs,1);
t = options_.trend_coeffs;
for i=1:length(t)
if ~isempty(t{i})
trend_coeff(i) = evalin('base',t{i});
end
end
trend = repmat(constant,1,gend)+trend_coeff*[1:gend];
else
trend = repmat(constant,1,gend);
end
start = options_.presample+1;
np = size(T,1);
mf = bayestopt_.mf;
no_missing_data_flag = (number_of_observations==gend*nobs);
%------------------------------------------------------------------------------
% 3. Initial condition of the Kalman filter
%------------------------------------------------------------------------------
T
R
Q
R*Q*R'
pause
options_.lik_init = 1;
kalman_algo = options_.kalman_algo;
if options_.lik_init == 1 % Kalman filter
if kalman_algo ~= 2
kalman_algo = 1;
end
Pstar = lyapunov_symm(T,R*Q*R',options_.qz_criterium,options_.lyapunov_complex_threshold);
Pinf = [];
elseif options_.lik_init == 2 % Old Diffuse Kalman filter
if kalman_algo ~= 2
kalman_algo = 1;
end
Pstar = options_.Harvey_scale_factor*eye(np);
Pinf = [];
elseif options_.lik_init == 3 % Diffuse Kalman filter
if kalman_algo ~= 4
kalman_algo = 3;
end
[QT,ST] = schur(T);
e1 = abs(ordeig(ST)) > 2-options_.qz_criterium;
[QT,ST] = ordschur(QT,ST,e1);
k = find(abs(ordeig(ST)) > 2-options_.qz_criterium);
nk = length(k);
nk1 = nk+1;
Pinf = zeros(np,np);
Pinf(1:nk,1:nk) = eye(nk);
Pstar = zeros(np,np);
B = QT'*R*Q*R'*QT;
for i=np:-1:nk+2
if ST(i,i-1) == 0
if i == np
c = zeros(np-nk,1);
else
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
end
q = eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i);
Pstar(nk1:i,i) = q\(B(nk1:i,i)+c);
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
else
if i == np
c = zeros(np-nk,1);
c1 = zeros(np-nk,1);
else
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i)+...
ST(i,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1);
c1 = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i-1,i+1:end)')+...
ST(i-1,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1)+...
ST(i-1,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
end
q = [eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i) -ST(nk1:i,nk1:i)*ST(i,i-1);...
-ST(nk1:i,nk1:i)*ST(i-1,i) eye(i-nk)-ST(nk1:i,nk1:i)*ST(i-1,i-1)];
z = q\[B(nk1:i,i)+c;B(nk1:i,i-1)+c1];
Pstar(nk1:i,i) = z(1:(i-nk));
Pstar(nk1:i,i-1) = z(i-nk+1:end);
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
Pstar(i-1,nk1:i-2) = Pstar(nk1:i-2,i-1)';
i = i - 1;
end
end
if i == nk+2
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);
Pstar(nk1,nk1)=(B(nk1,nk1)+c)/(1-ST(nk1,nk1)*ST(nk1,nk1));
end
Z = QT(mf,:);
R1 = QT'*R;
[QQ,RR,EE] = qr(Z*ST(:,1:nk),0);
k = find(abs(diag([RR; zeros(nk-size(Z,1),size(RR,2))])) < 1e-8);
if length(k) > 0
k1 = EE(:,k);
dd =ones(nk,1);
dd(k1) = zeros(length(k1),1);
Pinf(1:nk,1:nk) = diag(dd);
end
end
if kalman_algo == 2
end
kalman_tol = options_.kalman_tol;
riccati_tol = options_.riccati_tol;
mf = bayestopt_.mf1;
Y = data-trend;
Pstar
pause
%------------------------------------------------------------------------------
% 4. Likelihood evaluation
%------------------------------------------------------------------------------
if (kalman_algo==1)% Multivariate Kalman Filter
if no_missing_data_flag
LIK = kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol);
else
LIK = ...
missing_observations_kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol, ...
data_index,number_of_observations,no_more_missing_observations);
end
if isinf(LIK)
kalman_algo = 2;
end
end
if (kalman_algo==2)% Univariate Kalman Filter
no_correlation_flag = 1;
if length(H)==1 & H == 0
H = zeros(nobs,1);
else
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
H = diag(H);
else
no_correlation_flag = 0;
end
end
if no_correlation_flag
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);
else
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);
end
end
if (kalman_algo==3)% Multivariate Diffuse Kalman Filter
if no_missing_data_flag
LIK = diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol, ...
riccati_tol);
else
LIK = missing_observations_diffuse_kalman_filter(ST,R1,Q,H,Pinf, ...
Pstar,Y,start,Z,kalman_tol,riccati_tol,...
data_index,number_of_observations,...
no_more_missing_observations);
end
if isinf(LIK)
kalman_algo = 4;
end
end
if (kalman_algo==4)% Univariate Diffuse Kalman Filter
no_correlation_flag = 1;
if length(H)==1 & H == 0
H = zeros(nobs,1);
else
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
H = diag(H);
else
no_correlation_flag = 0;
end
end
if no_correlation_flag
LIK = univariate_diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y, ...
start,Z,kalman_tol,riccati_tol,data_index,...
number_of_observations,no_more_missing_observations);
else
LIK = univariate_diffuse_kalman_filter_corr(ST,R1,Q,H,Pinf,Pstar, ...
Y,start,Z,kalman_tol,riccati_tol,...
data_index,number_of_observations,...
no_more_missing_observations);
end
end
if isnan(LIK)
cost_flag = 0;
return
end
if imag(LIK)~=0
likelihood = bayestopt_.penalty;
else
likelihood = LIK;
end
% ------------------------------------------------------------------------------
% Adds prior if necessary
% ------------------------------------------------------------------------------
lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
fval = (likelihood-lnprior);
likelihood
lnprior
fval
pause
LIKDLL=logposterior(xparam1,Y,mexext)
pause
options_.kalman_algo = kalman_algo;
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