237 lines
8.0 KiB
Matlab
237 lines
8.0 KiB
Matlab
function [fval,llik,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data)
|
|
|
|
% function [fval,llik,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data)
|
|
% Evaluates the likelihood at each observation and the marginal density of a dsge model
|
|
% used in the optimization algorithm number 5
|
|
%
|
|
% INPUTS
|
|
% xparam1: vector of model parameters
|
|
% gend : scalar specifying the number of observations
|
|
% data : matrix of data
|
|
%
|
|
% OUTPUTS
|
|
% fval : value of the posterior kernel at xparam1
|
|
% llik : gives the density at each observation
|
|
% 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
|
|
%
|
|
% SPECIAL REQUIREMENTS
|
|
% Adapted from dsgelikelihood.m
|
|
%
|
|
% copyright marco.ratto@jrc.it [13-03-2007]
|
|
|
|
|
|
|
|
global bayestopt_ estim_params_ options_ trend_coeff_ M_ oo_ xparam1_test
|
|
|
|
fval = [];
|
|
ys = [];
|
|
trend_coeff = [];
|
|
xparam1_test = xparam1;
|
|
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);
|
|
llik=fval;
|
|
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);
|
|
llik=fval;
|
|
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));
|
|
llik=fval;
|
|
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));
|
|
llik=fval;
|
|
cost_flag = 0;
|
|
info = 44;
|
|
return
|
|
end
|
|
end
|
|
offset = offset+estim_params_.ncn;
|
|
end
|
|
M_.params(estim_params_.param_vals(:,1)) = xparam1(offset+1:end);
|
|
% for i=1:estim_params_.np
|
|
% M_.params(estim_params_.param_vals(i,1)) = xparam1(i+offset);
|
|
%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;
|
|
llik=fval;
|
|
cost_flag = 0;
|
|
return
|
|
elseif info(1) == 3 | info(1) == 4 | info(1) == 20
|
|
fval = bayestopt_.penalty+info(2)^2;
|
|
llik=fval;
|
|
cost_flag = 0;
|
|
return
|
|
end
|
|
bayestopt_.mf = bayestopt_.mf1;
|
|
if ~options_.noconstant
|
|
if options_.loglinear == 1
|
|
constant = log(SteadyState(bayestopt_.mfys));
|
|
else
|
|
constant = SteadyState(bayestopt_.mfys);
|
|
end
|
|
else
|
|
constant = zeros(nobs,1);
|
|
end
|
|
if bayestopt_.with_trend == 1
|
|
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;
|
|
%------------------------------------------------------------------------------
|
|
% 3. Initial condition of the Kalman filter
|
|
%------------------------------------------------------------------------------
|
|
if options_.lik_init == 1 % Kalman filter
|
|
Pstar = lyapunov_symm(T,R*Q*R',options_.qz_criterium);
|
|
Pinf = [];
|
|
elseif options_.lik_init == 2 % Old Diffuse Kalman filter
|
|
Pstar = 10*eye(np);
|
|
Pinf = [];
|
|
elseif options_.lik_init == 3 % Diffuse Kalman filter
|
|
Pstar = zeros(np,np);
|
|
ivs = bayestopt_.restrict_var_list_stationary;
|
|
ivd = bayestopt_.restrict_var_list_nonstationary;
|
|
RR=T(:,bayestopt_.restrict_var_list_nonstationary);
|
|
i=find(abs(RR)>1.e-10);
|
|
R0=zeros(size(RR));
|
|
R0(i)=sign(RR(i));
|
|
Pinf=R0*R0';
|
|
|
|
T0 = T;
|
|
R1 = R;
|
|
for j=1:size(T,1),
|
|
for i=1:length(ivd),
|
|
T0(j,:) = T0(j,:)-RR(j,i).*T(ivd(i),:);
|
|
R1(j,:) = R1(j,:)-RR(j,i).*R(ivd(i),:);
|
|
end
|
|
end
|
|
Pstar = lyapunov_symm(T0,R1*Q*R1',options_.qz_criterium);
|
|
end
|
|
%------------------------------------------------------------------------------
|
|
% 4. Likelihood evaluation
|
|
%------------------------------------------------------------------------------
|
|
if any(any(H ~= 0)) % should be replaced by a flag
|
|
if options_.kalman_algo == 1
|
|
[LIK, lik] =DiffuseLikelihoodH1(T,R,Q,H,Pinf,Pstar,data,trend,start);
|
|
if isinf(LIK) & ~estim_params_.ncn %% The univariate approach considered here doesn't
|
|
%% apply when H has some off-diagonal elements.
|
|
[LIK, lik] =DiffuseLikelihoodH3(T,R,Q,H,Pinf,Pstar,data,trend,start);
|
|
elseif isinf(LIK) & estim_params_.ncn
|
|
[LIK, lik] =DiffuseLikelihoodH3corr(T,R,Q,H,Pinf,Pstar,data,trend,start);
|
|
end
|
|
elseif options_.kalman_algo == 3
|
|
if ~estim_params_.ncn %% The univariate approach considered here doesn't
|
|
%% apply when H has some off-diagonal elements.
|
|
[LIK, lik] =DiffuseLikelihoodH3(T,R,Q,H,Pinf,Pstar,data,trend,start);
|
|
else
|
|
[LIK, lik] =DiffuseLikelihoodH3corr(T,R,Q,H,Pinf,Pstar,data,trend,start);
|
|
end
|
|
end
|
|
else
|
|
if options_.kalman_algo == 1
|
|
%nv = size(bayestopt_.Z,1);
|
|
%LIK = kalman_filter(bayestopt_.Z,zeros(nv,nv),T,R,Q,data,zeros(size(T,1),1),Pstar,'u');
|
|
[LIK, lik] =DiffuseLikelihood1(T,R,Q,Pinf,Pstar,data,trend,start);
|
|
% LIK = diffuse_likelihood1(T,R,Q,Pinf,Pstar,data-trend,start);
|
|
%if abs(LIK1-LIK)>0.0000000001
|
|
% disp(['LIK1 and LIK are not equal! ' num2str(abs(LIK1-LIK))])
|
|
%end
|
|
if isinf(LIK)
|
|
[LIK, lik] =DiffuseLikelihood3(T,R,Q,Pinf,Pstar,data,trend,start);
|
|
end
|
|
elseif options_.kalman_algo == 3
|
|
[LIK, lik] =DiffuseLikelihood3(T,R,Q,Pinf,Pstar,data,trend,start);
|
|
end
|
|
end
|
|
if imag(LIK) ~= 0
|
|
likelihood = bayestopt_.penalty;
|
|
lik=ones(size(lik)).*bayestopt_.penalty;
|
|
else
|
|
likelihood = LIK;
|
|
end
|
|
% ------------------------------------------------------------------------------
|
|
% Adds prior if necessary
|
|
% ------------------------------------------------------------------------------
|
|
lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p1,bayestopt_.p2,bayestopt_.p3,bayestopt_.p4);
|
|
fval = (likelihood-lnprior);
|
|
llik=[-lnprior; .5*lik(start:end)];
|
|
|