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Fixed Marco's optimization routines (mode_compute==5). 

Added fs2000d.mod in the testsuite (test of Marco's optimization routines).
time-shift
Stéphane Adjemian (Scylla) 2011-10-03 12:19:41 +02:00
parent c5b2afa3c1
commit 1dabbd8806
6 changed files with 453 additions and 301 deletions
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414
matlab/DsgeLikelihood_hh.m
View File

@ -1,15 +1,15 @@
function [fval,llik,cost_flag,ys,trend_coeff,info] = DsgeLikelihood_hh(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
function [fval,llik,cost_flag,ys,trend_coeff,info] = DsgeLikelihood_hh(xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
% 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
% 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
% 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
@ -17,7 +17,7 @@ function [fval,llik,cost_flag,ys,trend_coeff,info] = DsgeLikelihood_hh(xparam1,g
% 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
%
@ -38,234 +38,360 @@ function [fval,llik,cost_flag,ys,trend_coeff,info] = DsgeLikelihood_hh(xparam1,g
% 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_
% Declaration of the penalty as a persistent variable.
persistent penalty
% Initialization of the persistent variable.
if ~nargin || isempty(penalty)
penalty = 1e8;
if ~nargin, return, end
end
if nargin==1
penalty = xparam1;
return
end
fval = [];
ys = [];
trend_coeff = [];
cost_flag = 1;
nobs = size(options_.varobs,1);
llik=NaN;
if DynareOptions.block == 1
error('DsgeLikelihood_hh:: This routine (called if mode_compute==5) is not compatible with the block option!')
end
%------------------------------------------------------------------------------
% 1. Get the structural parameters & define penalties
%------------------------------------------------------------------------------
if ~isequal(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;
% Return, with endogenous penalty, if some parameters are smaller than the lower bound of the prior domain.
if ~isequal(DynareOptions.mode_compute,1) && any(xparam1<BayesInfo.lb)
k = find(xparam1<BayesInfo.lb);
fval = penalty+sum((BayesInfo.lb(k)-xparam1(k)).^2);
exit_flag = 0;
info = 41;
return;
return
end
if ~isequal(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;
% Return, with endogenous penalty, if some parameters are greater than the upper bound of the prior domain.
if ~isequal(DynareOptions.mode_compute,1) && any(xparam1>BayesInfo.ub)
k = find(xparam1>BayesInfo.ub);
fval = penalty+sum((xparam1(k)-BayesInfo.ub(k)).^2);
exit_flag = 0;
info = 42;
return;
return
end
Q = M_.Sigma_e;
H = M_.H;
for i=1:estim_params_.nvx
k =estim_params_.var_exo(i,1);
% Get the diagonal elements of the covariance matrices for the structural innovations (Q) and the measurement error (H).
Q = Model.Sigma_e;
H = Model.H;
for i=1:EstimatedParameters.nvx
k =EstimatedParameters.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);
offset = EstimatedParameters.nvx;
if EstimatedParameters.nvn
for i=1:EstimatedParameters.nvn
k = EstimatedParameters.var_endo(i,1);
H(k,k) = xparam1(i+offset)*xparam1(i+offset);
end
offset = offset+estim_params_.nvn;
offset = offset+EstimatedParameters.nvn;
else
H = zeros(DynareDataset.info.nvobs);
end
if estim_params_.ncx
for i=1:estim_params_.ncx
k1 =estim_params_.corrx(i,1);
k2 =estim_params_.corrx(i,2);
% Get the off-diagonal elements of the covariance matrix for the structural innovations. Test if Q is positive definite.
if EstimatedParameters.ncx
for i=1:EstimatedParameters.ncx
k1 =EstimatedParameters.corrx(i,1);
k2 =EstimatedParameters.corrx(i,2);
Q(k1,k2) = xparam1(i+offset)*sqrt(Q(k1,k1)*Q(k2,k2));
Q(k2,k1) = Q(k1,k2);
end
% Try to compute the cholesky decomposition of Q (possible iff Q is positive definite)
[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.
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 endogenous penalty.
a = diag(eig(Q));
k = find(a < 0);
if k > 0
fval = bayestopt_.penalty+sum(-a(k));
cost_flag = 0;
fval = BayesInfo.penalty+sum(-a(k));
exit_flag = 0;
info = 43;
return
end
end
offset = offset+estim_params_.ncx;
offset = offset+EstimatedParameters.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));
% Get the off-diagonal elements of the covariance matrix for the measurement errors. Test if H is positive definite.
if EstimatedParameters.ncn
for i=1:EstimatedParameters.ncn
k1 = DynareOptions.lgyidx2varobs(EstimatedParameters.corrn(i,1));
k2 = DynareOptions.lgyidx2varobs(EstimatedParameters.corrn(i,2));
H(k1,k2) = xparam1(i+offset)*sqrt(H(k1,k1)*H(k2,k2));
H(k2,k1) = H(k1,k2);
end
% Try to compute the cholesky decomposition of H (possible iff H is positive definite)
[CholH,testH] = chol(H);
if testH
% 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 endogenous penalty.
a = diag(eig(H));
k = find(a < 0);
if k > 0
fval = bayestopt_.penalty+sum(-a(k));
cost_flag = 0;
fval = BayesInfo.penalty+sum(-a(k));
exit_flag = 0;
info = 44;
return
end
end
offset = offset+estim_params_.ncn;
offset = offset+EstimatedParameters.ncn;
end
if estim_params_.np > 0
M_.params(estim_params_.param_vals(:,1)) = xparam1(offset+1:end);
% Update estimated structural parameters in Mode.params.
if EstimatedParameters.np > 0
Model.params(EstimatedParameters.param_vals(:,1)) = xparam1(offset+1:end);
end
M_.Sigma_e = Q;
M_.H = H;
% Update Model.Sigma_e and Model.H.
Model.Sigma_e = Q;
Model.H = H;
%------------------------------------------------------------------------------
% 2. call model setup & reduction program
%------------------------------------------------------------------------------
[T,R,SteadyState,info,M_,options_,oo_] = dynare_resolve(M_,otions_,oo_);
if info(1) == 1 || info(1) == 2 || info(1) == 5
fval = bayestopt_.penalty+1;
cost_flag = 0;
% Linearize the model around the deterministic sdteadystate and extract the matrices of the state equation (T and R).
[T,R,SteadyState,info,Model,DynareOptions,DynareResults] = dynare_resolve(Model,DynareOptions,DynareResults,'restrict');
% Return, with endogenous penalty when possible, if dynare_resolve issues an error code (defined in resol).
if info(1) == 1 || info(1) == 2 || info(1) == 5 || info(1) == 22 || info(1) == 24
fval = penalty+1;
info = info(1);
exit_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;
elseif info(1) == 3 || info(1) == 4 || info(1)==6 ||info(1) == 19 || info(1) == 20 || info(1) == 21 || info(1) == 23
fval = penalty+info(2);
info = info(1);
exit_flag = 0;
return
end
bayestopt_.mf = bayestopt_.mf1;
if options_.noconstant
constant = zeros(nobs,1);
else
if options_.loglinear
constant = log(SteadyState(bayestopt_.mfys));
% Define a vector of indices for the observed variables. Is this really usefull?...
BayesInfo.mf = BayesInfo.mf1;
% Define the constant vector of the measurement equation.
if DynareOptions.noconstant
constant = zeros(DynareDataset.info.nvobs,1);
else
if DynareOptions.loglinear
constant = log(SteadyState(BayesInfo.mfys));
else
constant = SteadyState(bayestopt_.mfys);
constant = SteadyState(BayesInfo.mfys);
end
end
if bayestopt_.with_trend
trend_coeff = zeros(nobs,1);
t = options_.trend_coeffs;
% Define the deterministic linear trend of the measurement equation.
if BayesInfo.with_trend
trend_coeff = zeros(DynareDataset.info.nvobs,1);
t = DynareOptions.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];
trend = repmat(constant,1,DynareDataset.info.ntobs)+trend_coeff*[1:DynareDataset.info.ntobs];
else
trend = repmat(constant,1,gend);
trend = repmat(constant,1,DynareDataset.info.ntobs);
end
start = options_.presample+1;
np = size(T,1);
mf = bayestopt_.mf;
no_missing_data_flag = (number_of_observations==gend*nobs);
% Get needed informations for kalman filter routines.
start = DynareOptions.presample+1;
Z = BayesInfo.mf; % old mf
no_missing_data_flag = ~DynareDataset.missing.state;
mm = length(T); % old np
pp = DynareDataset.info.nvobs;
rr = length(Q);
kalman_tol = DynareOptions.kalman_tol;
riccati_tol = DynareOptions.riccati_tol;
Y = DynareDataset.data-trend;
%------------------------------------------------------------------------------
% 3. Initial condition of the Kalman filter
%------------------------------------------------------------------------------
kalman_algo = options_.kalman_algo;
if options_.lik_init == 1 % Kalman filter
if kalman_algo ~= 2
kalman_algo = DynareOptions.kalman_algo;
diffuse_periods = 0;
switch DynareOptions.lik_init
case 1% Standard initialization with the steady state of the state equation.
if kalman_algo~=2
% Use standard kalman filter except if the univariate filter is explicitely choosen.
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
Pstar = lyapunov_symm(T,R*Q*R',DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold);
Pinf = [];
a = zeros(mm,1);
Zflag = 0;
case 2% Initialization with large numbers on the diagonal of the covariance matrix if the states (for non stationary models).
if kalman_algo ~= 2
% Use standard kalman filter except if the univariate filter is explicitely choosen.
kalman_algo = 1;
end
Pstar = options_.Harvey_scale_factor*eye(np);
Pinf = [];
elseif options_.lik_init == 3 % Diffuse Kalman filter
Pstar = DynareOptions.Harvey_scale_factor*eye(mm);
Pinf = [];
a = zeros(mm,1);
Zflag = 0;
case 3% Diffuse Kalman filter (Durbin and Koopman)
if kalman_algo ~= 4
% Use standard kalman filter except if the univariate filter is explicitely choosen.
kalman_algo = 3;
end
[Z,ST,R1,QT,Pstar,Pinf] = schur_statespace_transformation(mf,T,R,Q,options_.qz_criterium);
[Z,T,R,QT,Pstar,Pinf] = schur_statespace_transformation(Z,T,R,Q,DynareOptions.qz_criterium);
Zflag = 1;
% Run diffuse kalman filter on first periods.
if (kalman_algo==3)
% Multivariate Diffuse Kalman Filter
if no_missing_data_flag
[dLIK,dlik,a,Pstar] = kalman_filter_d(Y, 1, size(Y,2), ...
zeros(mm,1), Pinf, Pstar, ...
kalman_tol, riccati_tol, DynareOptions.presample, ...
T,R,Q,H,Z,mm,pp,rr);
else
[dLIK,dlik,a,Pstar] = missing_observations_kalman_filter_d(DynareDataset.missing.aindex,DynareDataset.missing.number_of_observations,DynareDataset.missing.no_more_missing_observations, ...
Y, 1, size(Y,2), ...
zeros(mm,1), Pinf, Pstar, ...
kalman_tol, riccati_tol, DynareOptions.presample, ...
T,R,Q,H,Z,mm,pp,rr);
end
diffuse_periods = length(dlik);
if isinf(dLIK)
% Go to univariate diffuse filter if singularity problem.
kalman_algo = 4;
end
end
if (kalman_algo==4)
% Univariate Diffuse Kalman Filter
if no_correlation_flag
mmm = mm;
else
Z = [Z, eye(pp)];
T = blkdiag(T,zeros(pp));
Q = blkdiag(Q,H);
R = blkdiag(R,eye(pp));
Pstar = blkdiag(Pstar,H);
Pinf = blckdiag(Pinf,zeros(pp));
mmm = mm+pp;
end
[dLIK,dlik,a,Pstar] = univariate_kalman_filter_d(DynareDataset.missing.aindex,DynareDataset.missing.number_of_observations,DynareDataset.missing.no_more_missing_observations, ...
Y, 1, size(Y,2), ...
zeros(mmm,1), Pinf, Pstar, ...
kalman_tol, riccati_tol, DynareOptions.presample, ...
T,R,Q,H,Z,mmm,pp,rr);
diffuse_periods = length(dlik);
end
case 4% Start from the solution of the Riccati equation.
if kalman_algo ~= 2
kalman_algo = 1;
end
if isequal(H,0)
[err,Pstar] = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(mf,np,length(mf))));
else
[err,Pstar] = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(mf,np,length(mf))),H);
end
if err
disp(['DsgeLikelihood:: I am not able to solve the Riccati equation, so I switch to lik_init=1!']);
DynareOptions.lik_init = 1;
Pstar = lyapunov_symm(T,R*Q*R',DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold);
end
Pinf = [];
otherwise
error('DsgeLikelihood:: Unknown initialization approach for the Kalman filter!')
end
kalman_tol = options_.kalman_tol;
riccati_tol = options_.riccati_tol;
mf = bayestopt_.mf1;
Y = data-trend;
%------------------------------------------------------------------------------
% 4. Likelihood evaluation
%------------------------------------------------------------------------------
if (kalman_algo==1)% Multivariate Kalman Filter
singularity_flag = 0;
if ((kalman_algo==1) || (kalman_algo==3))% Multivariate Kalman Filter
if no_missing_data_flag
[LIK, lik] = kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol);
[LIK,lik] = kalman_filter(Y,diffuse_periods+1,size(Y,2), ...
a,Pstar, ...
kalman_tol, riccati_tol, ...
DynareOptions.presample, ...
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods);
else
[LIK, 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);
[LIK,lik] = missing_observations_kalman_filter(DynareDataset.missing.aindex,DynareDataset.missing.number_of_observations,DynareDataset.missing.no_more_missing_observations,Y,diffuse_periods+1,size(Y,2), ...
a, Pstar, ...
kalman_tol, DynareOptions.riccati_tol, ...
DynareOptions.presample, ...
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods);
end
if isinf(LIK)
kalman_algo = 2;
end
end
if (kalman_algo==2)% Univariate Kalman Filter
no_correlation_flag = 1;
if isequal(H,0)
H = zeros(nobs,1);
singularity_flag = 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;
if DynareOptions.lik_init==3
LIK = LIK + dLIK;
lik = [dlik; lik];
end
end
if no_correlation_flag
[LIK, 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, 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, lik] = diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol, ...
riccati_tol);
else
[LIK, 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 isequal(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);
if ( (singularity_flag) || (kalman_algo==2) || (kalman_algo==4) )% Univariate Kalman Filter
if singularity_flag
if no_correlation
mmm = mm;
else
no_correlation_flag = 0;
Z = [Z, eye(pp)];
T = blkdiag(T,zeros(pp));
Q = blkdiag(Q,H);
R = blkdiag(R,eye(pp));
Pstar = blkdiag(Pstar,H);
Pinf = blckdiag(Pinf,zeros(pp));
mmm = mm+pp;
a = [a; zeros(pp,1)];
end
end
if no_correlation_flag
[LIK, 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, 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);
[LIK,lik] = univariate_kalman_filter(DynareDataset.missing.aindex,DynareDataset.missing.number_of_observations,DynareDataset.missing.no_more_missing_observations,Y,diffuse_periods+1,size(Y,2), ...
a,Pstar, ...
DynareOptions.kalman_tol, ...
DynareOptions.riccati_tol, ...
DynareOptions.presample, ...
T,Q,R,H,Z,mmm,pp,rr,diffuse_periods);
if DynareOptions.lik_init==3
LIK = LIK+dLIK;
lik = [dlik; lik];
end
end
if imag(LIK) ~= 0
likelihood = bayestopt_.penalty;
if isnan(LIK)
info = 45;
exit_flag = 0;
return
end
if imag(LIK)~=0
likelihood = penalty;
else
likelihood = LIK;
end
% ------------------------------------------------------------------------------
% Adds prior if necessary
% 5. Adds prior if necessary
% ------------------------------------------------------------------------------
lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
lnprior = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
fval = (likelihood-lnprior);
options_.kalman_algo = kalman_algo;
% Update DynareOptions.kalman_algo.
DynareOptions.kalman_algo = kalman_algo;
% Update the penalty.
penalty = fval;
% Add the prior density at the top of the vector for the density of each observation.
lik=lik(start:end,:);
llik=[-lnprior; lik(:)];
% llik=[-lnprior; lik(start:end)];
llik=[-lnprior; lik(:)];

31
matlab/mr_gstep.m
View File

@ -1,6 +1,6 @@
function [f0, x, ig] = mr_gstep(h1,x,func0,htol0,varargin)
function [f0, x, ig] = mr_gstep(h1,x,func0,htol0,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
% function [f0, x, ig] = mr_gstep(h1,x,func0,htol0,varargin)
%
%
% Gibbs type step in optimisation
% Copyright (C) 2006-2011 Dynare Team
@ -22,13 +22,12 @@ function [f0, x, ig] = mr_gstep(h1,x,func0,htol0,varargin)
n=size(x,1);
if nargin<4,
if isempty(htol0)
htol = 1.e-6;
else
htol = htol0;
end
func = str2func(func0);
f0=feval(func,x,varargin{:});
f0=feval(func0,x,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
xh1=x;
f1=zeros(size(f0,1),n);
@ -36,37 +35,29 @@ f_1=f1;
i=0;
ig=zeros(n,1);
while i<n,
while i<n
i=i+1;
h10=h1(i);
hcheck=0;
dx=[];
xh1(i)=x(i)+h1(i);
fx = feval(func,xh1,varargin{:});
fx = feval(func0,xh1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
f1(:,i)=fx;
xh1(i)=x(i)-h1(i);
fx = feval(func,xh1,varargin{:});
fx = feval(func0,xh1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
f_1(:,i)=fx;
if hcheck && htol<1,
if hcheck && htol<1
htol=min(1,max(min(abs(dx))*2,htol*10));
h1(i)=h10;
xh1(i)=x(i);
i=i-1;
else
gg=zeros(size(x));
gg=zeros(size(x));
hh=gg;
gg(i)=(f1(i)'-f_1(i)')./(2.*h1(i));
hh(i) = 1/max(1.e-9,abs( (f1(i)+f_1(i)-2*f0)./(h1(i)*h1(i)) ));
% if abs(f1(i)+f_1(i)-2*f0)>1.e-12,
% hh(i) = abs(1/( (f1(i)+f_1(i)-2*f0)./(h1(i)*h1(i)) ));
% else
% hh(i) = 1;
% end
if gg(i)*(hh(i)*gg(i))/2 > htol,
[f0 x fc retcode] = csminit(func0,x,f0,gg,0,diag(hh),varargin{:});
if gg(i)*(hh(i)*gg(i))/2 > htol
[f0 x fc retcode] = csminit(func0,x,f0,gg,0,diag(hh),DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
ig(i)=1;
end
xh1=x;

96
matlab/mr_hessian.m
View File

@ -1,12 +1,12 @@
function [hessian_mat, gg, htol1, ihh, hh_mat0, hh1] = mr_hessian(init,x,func,hflag,htol0,varargin)
function [hessian_mat, gg, htol1, ihh, hh_mat0, hh1] = mr_hessian(init,x,func,hflag,htol0,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
% [hessian_mat, gg, htol1, ihh, hh_mat0, hh1] = mr_hessian(init,x,func,hflag,htol0,varargin)
%
% numerical gradient and Hessian, with 'automatic' check of numerical
% error
% error
%
% adapted from Michel Juillard original rutine hessian.m
%
% func = name of the function: func must give two outputs:
% func = name of the function: func must give two outputs:
% - the log-likelihood AND the single contributions at times t=1,...,T
% of the log-likelihood to compute outer product gradient
% x = parameter values
@ -41,26 +41,24 @@ function [hessian_mat, gg, htol1, ihh, hh_mat0, hh1] = mr_hessian(init,x,func,hf
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
global options_ bayestopt_
persistent h1 htol
n=size(x,1);
if init,
gstep_=options_.gstep;
if init
gstep_=DynareOptions.gstep;
htol = 1.e-4;
%h1=max(abs(x),sqrt(gstep_)*ones(n,1))*eps^(1/4);
h1=options_.gradient_epsilon*ones(n,1);
return,
h1=DynareOptions.gradient_epsilon*ones(n,1);
return
end
func = str2func(func);
[f0, ff0]=feval(func,x,varargin{:});
h2=bayestopt_.ub-bayestopt_.lb;
hmax=bayestopt_.ub-x;
hmax=min(hmax,x-bayestopt_.lb);
[f0, ff0]=feval(func,x,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
h2=BayesInfo.ub-BayesInfo.lb;
hmax=BayesInfo.ub-x;
hmax=min(hmax,x-BayesInfo.lb);
h1 = min(h1,0.5.*hmax);
if htol0<htol,
if htol0<htol
htol=htol0;
end
xh1=x;
@ -71,24 +69,22 @@ ff_1=ff1;
ggh=zeros(size(ff0,1),n);
i=0;
while i<n,
while i<n
i=i+1;
h10=h1(i);
hcheck=0;
xh1(i)=x(i)+h1(i);
try
[fx, ffx]=feval(func,xh1,varargin{:});
[fx, ffx]=feval(func,xh1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
catch
fx=1.e8;
end
it=1;
dx=(fx-f0);
ic=0;
icount = 0;
h0=h1(i);
while (abs(dx(it))<0.5*htol || abs(dx(it))>(3*htol)) && icount<10 && ic==0,
%while abs(dx(it))<0.5*htol && icount< 10 && ic==0,
while (abs(dx(it))<0.5*htol || abs(dx(it))>(3*htol)) && icount<10 && ic==0
icount=icount+1;
if abs(dx(it))<0.5*htol
if abs(dx(it)) ~= 0,
@ -99,51 +95,51 @@ while i<n,
h1(i) = min(h1(i),0.5*hmax(i));
xh1(i)=x(i)+h1(i);
try
[fx, ffx]=feval(func,xh1,varargin{:});
[fx, ffx]=feval(func,xh1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
catch
fx=1.e8;
end
end
if abs(dx(it))>(3*htol),
if abs(dx(it))>(3*htol)
h1(i)= htol/abs(dx(it))*h1(i);
xh1(i)=x(i)+h1(i);
try
[fx, ffx]=feval(func,xh1,varargin{:});
[fx, ffx]=feval(func,xh1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
catch
fx=1.e8;
end
while (fx-f0)==0,
while (fx-f0)==0
h1(i)= h1(i)*2;
xh1(i)=x(i)+h1(i);
[fx, ffx]=feval(func,xh1,varargin{:});
[fx, ffx]=feval(func,xh1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
ic=1;
end
end
it=it+1;
dx(it)=(fx-f0);
h0(it)=h1(i);
if (h1(i)<1.e-12*min(1,h2(i)) && h1(i)<0.5*hmax(i)),% || (icount==10 && abs(dx(it))>(3*htol)),
if (h1(i)<1.e-12*min(1,h2(i)) && h1(i)<0.5*hmax(i))% || (icount==10 && abs(dx(it))>(3*htol)),
ic=1;
hcheck=1;
end
end
f1(:,i)=fx;
if any(isnan(ffx)),
if any(isnan(ffx))
ff1=ones(size(ff0)).*fx/length(ff0);
else
ff1=ffx;
end
xh1(i)=x(i)-h1(i);
[fx, ffx]=feval(func,xh1,varargin{:});
[fx, ffx]=feval(func,xh1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
f_1(:,i)=fx;
if any(isnan(ffx)),
if any(isnan(ffx))
ff_1=ones(size(ff0)).*fx/length(ff0);
else
ff_1=ffx;
end
ggh(:,i)=(ff1-ff_1)./(2.*h1(i));
xh1(i)=x(i);
if hcheck && htol<1,
if hcheck && htol<1
htol=min(1,max(min(abs(dx))*2,htol*10));
h1(i)=h10;
i=0;
@ -157,14 +153,14 @@ xh_1=xh1;
gg=(f1'-f_1')./(2.*h1);
if hflag==2,
if hflag==2
gg=(f1'-f_1')./(2.*h1);
hessian_mat = zeros(size(f0,1),n*n);
for i=1:n
if i > 1
k=[i:n:n*(i-1)];
hessian_mat(:,(i-1)*n+1:(i-1)*n+i-1)=hessian_mat(:,k);
end
end
hessian_mat(:,(i-1)*n+i)=(f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i));
temp=f1+f_1-f0*ones(1,n);
for j=i+1:n
@ -172,10 +168,8 @@ if hflag==2,
xh1(j)=x(j)+h_1(j);
xh_1(i)=x(i)-h1(i);
xh_1(j)=x(j)-h_1(j);
temp1 = feval(func,xh1,varargin{:});
temp2 = feval(func,xh_1,varargin{:});
temp1 = feval(func,xh1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
temp2 = feval(func,xh_1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
hessian_mat(:,(i-1)*n+j)=-(-temp1 -temp2+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j));
xh1(i)=x(i);
xh1(j)=x(j);
@ -186,27 +180,25 @@ if hflag==2,
end
i=i+1;
end
elseif hflag==1,
elseif hflag==1
hessian_mat = zeros(size(f0,1),n*n);
for i=1:n,
for i=1:n
dum = (f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i));
if dum>eps,
if dum>eps
hessian_mat(:,(i-1)*n+i)=dum;
else
hessian_mat(:,(i-1)*n+i)=max(eps, gg(i)^2);
end
end
end
%hessian_mat2=hh_mat(:)';
end
gga=ggh.*kron(ones(size(ff1)),2.*h1'); % re-scaled gradient
hh_mat=gga'*gga; % rescaled outer product hessian
hh_mat=gga'*gga; % rescaled outer product hessian
hh_mat0=ggh'*ggh; % outer product hessian
A=diag(2.*h1); % rescaling matrix
% igg=inv(hh_mat); % inverted rescaled outer product hessian
ihh=A'*(hh_mat\A); % inverted outer product hessian
if hflag>0 && min(eig(reshape(hessian_mat,n,n)))>0,
if hflag>0 && min(eig(reshape(hessian_mat,n,n)))>0
hh0 = A*reshape(hessian_mat,n,n)*A'; %rescaled second order derivatives
hh = reshape(hessian_mat,n,n); %rescaled second order derivatives
sd0=sqrt(diag(hh0)); %rescaled 'standard errors' using second order derivatives
@ -217,10 +209,9 @@ if hflag>0 && min(eig(reshape(hessian_mat,n,n)))>0,
hh_mat0=inv(A)'*hh_mat*inv(A); % outer product hessian with 'true' std's
sd=sqrt(diag(ihh)); %standard errors
sdh=sqrt(1./diag(hh)); %diagonal standard errors
for j=1:length(sd),
sd0(j,1)=min(bayestopt_.p2(j), sd(j)); %prior std
for j=1:length(sd)
sd0(j,1)=min(BayesInfo.p2(j), sd(j)); %prior std
sd0(j,1)=10^(0.5*(log10(sd0(j,1))+log10(sdh(j,1))));
%sd0(j,1)=0.5*(sd0(j,1)+sdh(j,1));
end
ihh=ihh./(sd*sd').*(sd0*sd0'); %inverse outer product with modified std's
igg=inv(A)'*ihh*inv(A); % inverted rescaled outer product hessian with modified std's
@ -233,18 +224,15 @@ if hflag>0 && min(eig(reshape(hessian_mat,n,n)))>0,
% ihh=A'*igg*A; % inverted outer product hessian
% hh_mat0=inv(A)'*hh_mat*inv(A); % outer product hessian with 'true' std's
end
if hflag<2,
if hflag<2
hessian_mat=hh_mat0(:);
end
if any(isnan(hessian_mat)),
if any(isnan(hessian_mat))
hh_mat0=eye(length(hh_mat0));
ihh=hh_mat0;
hessian_mat=hh_mat0(:);
hessian_mat=hh_mat0(:);
end
hh1=h1;
htol1=htol;
save hess.mat
% 11/25/03 SA Created from Hessian_sparse (removed sparse)
save hess.mat

137
matlab/newrat.m
View File

@ -1,4 +1,4 @@
function [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit, flagg, varargin)
function [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit, flagg, DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
% [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit, flagg, varargin)
%
% Optimiser with outer product gradient and with sequences of univariate steps
@ -13,17 +13,17 @@ function [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit
% hh = initial Hessian [OPTIONAL]
% gg = initial gradient [OPTIONAL]
% igg = initial inverse Hessian [OPTIONAL]
% ftol0 = ending criterion for function change
% ftol0 = ending criterion for function change
% nit = maximum number of iterations
%
% In each iteration, Hessian is computed with outer product gradient.
% for final Hessian (to start Metropolis):
% flagg = 0, final Hessian computed with outer product gradient
% flagg = 1, final 'mixed' Hessian: diagonal elements computed with numerical second order derivatives
% with correlation structure as from outer product gradient,
% with correlation structure as from outer product gradient,
% flagg = 2, full numerical Hessian
%
% varargin = list of parameters for func0
% varargin = list of parameters for func0
% Copyright (C) 2004-2011 Dynare Team
%
@ -42,7 +42,6 @@ function [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit
% 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_
icount=0;
nx=length(x);
xparam1=x;
@ -53,29 +52,27 @@ ftol=ftol0;
gtol=1.e-3;
htol=htol_base;
htol0=htol_base;
gibbstol=length(bayestopt_.pshape)/50; %25;
gibbstol=length(BayesInfo.pshape)/50; %25;
func_hh = [func0,'_hh'];
func = str2func(func0);
fval0=feval(func,x,varargin{:});
func_hh = str2func([func2str(func0),'_hh']);
fval0=feval(func0,x,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
fval=fval0;
% initialize mr_gstep and mr_hessian
% mr_gstep(1,x);
mr_hessian(1,x);
mr_hessian(1,x,[],[],[],DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
if isempty(hh)
[dum, gg, htol0, igg, hhg, h1]=mr_hessian(0,x,func_hh,flagit,htol,varargin{:});
[dum, gg, htol0, igg, hhg, h1]=mr_hessian(0,x,func_hh,flagit,htol,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
hh0 = reshape(dum,nx,nx);
hh=hhg;
if min(eig(hh0))<0,
if min(eig(hh0))<0
hh0=hhg; %generalized_cholesky(hh0);
elseif flagit==2,
elseif flagit==2
hh=hh0;
igg=inv(hh);
end
if htol0>htol,
if htol0>htol
htol=htol0;
%ftol=htol0;
end
else
hh0=hh;
@ -99,73 +96,67 @@ jit=0;
nig=[];
ig=ones(nx,1);
ggx=zeros(nx,1);
while norm(gg)>gtol && check==0 && jit<nit,
while norm(gg)>gtol && check==0 && jit<nit
jit=jit+1;
tic
icount=icount+1;
bayestopt_.penalty = fval0(icount);
disp([' '])
disp(['Iteration ',num2str(icount)])
[fval x0 fc retcode] = csminit(func0,xparam1,fval0(icount),gg,0,H,varargin{:});
if igrad,
[fval1 x01 fc retcode1] = csminit(func0,x0,fval,gg,0,inx,varargin{:});
if (fval-fval1)>1, %(fval0(icount)-fval),
[fval,x0,fc,retcode] = csminit1(func0,xparam1,fval0(icount),gg,0,H,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
if igrad
[fval1,x01,fc,retcode1] = csminit1(func0,x0,fval,gg,0,inx,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
if (fval-fval1)>1
disp('Gradient step!!')
else
igrad=0;
end
fval=fval1;
x0=x01;
x0=x01;
end
if (fval0(icount)-fval)<1.e-2*(gg'*(H*gg))/2 && igibbs,
if length(find(ig))<nx,
if (fval0(icount)-fval)<1.e-2*(gg'*(H*gg))/2 && igibbs
if length(find(ig))<nx
ggx=ggx*0;
ggx(find(ig))=gg(find(ig));
hhx = reshape(dum,nx,nx);
iggx=eye(length(gg));
iggx(find(ig),find(ig)) = inv( hhx(find(ig),find(ig)) );
[fvala x0 fc retcode] = csminit(func0,x0,fval,ggx,0,iggx,varargin{:});
[fvala,x0,fc,retcode] = csminit1(func0,x0,fval,ggx,0,iggx,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
end
[fvala, x0, ig] = mr_gstep(h1,x0,func0,htol,varargin{:});
% if length(find(ig))==0,
% [fvala, x0, ig] = mr_gstep(h1,x0,func0,htol/10,varargin{:});
% end
[fvala, x0, ig] = mr_gstep(h1,x0,func0,htol,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
nig=[nig ig];
disp('Sequence of univariate steps!!')
fval=fvala;
end
if (fval0(icount)-fval)<ftol && flagit==0,
if (fval0(icount)-fval)<ftol && flagit==0
disp('Try diagonal Hessian')
ihh=diag(1./(diag(hhg)));
[fval2 x0 fc retcode2] = csminit(func2str(func),x0,fval,gg,0,ihh,varargin{:});
if (fval-fval2)>=ftol ,
%hh=diag(diag(hh));
disp('Diagonal Hessian successful')
ihh=diag(1./(diag(hhg)));
[fval2,x0,fc,retcode2] = csminit1(func0,x0,fval,gg,0,ihh,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
if (fval-fval2)>=ftol
disp('Diagonal Hessian successful')
end
fval=fval2;
end
if (fval0(icount)-fval)<ftol && flagit==0,
end
if (fval0(icount)-fval)<ftol && flagit==0
disp('Try gradient direction')
ihh0=inx.*1.e-4;
[fval3 x0 fc retcode3] = csminit(func2str(func),x0,fval,gg,0,ihh0,varargin{:});
if (fval-fval3)>=ftol ,
%hh=hh0;
%ihh=ihh0;
disp('Gradient direction successful')
ihh0=inx.*1.e-4;
[fval3,x0,fc,retcode3] = csminit1(func0,x0,fval,gg,0,ihh0,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
if (fval-fval3)>=ftol
disp('Gradient direction successful')
end
fval=fval3;
end
end
xparam1=x0;
x(:,icount+1)=xparam1;
fval0(icount+1)=fval;
if (fval0(icount)-fval)<ftol,
if (fval0(icount)-fval)<ftol
disp('No further improvement is possible!')
check=1;
if flagit==2,
if flagit==2
hh=hh0;
elseif flagg>0,
[dum, gg, htol0, igg, hhg,h1]=mr_hessian(0,xparam1,func_hh,flagg,ftol0,varargin{:});
if flagg==2,
elseif flagg>0
[dum, gg, htol0, igg, hhg,h1]=mr_hessian(0,xparam1,func_hh,flagg,ftol0,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
if flagg==2
hh = reshape(dum,nx,nx);
ee=eig(hh);
if min(ee)<0
@ -186,48 +177,38 @@ while norm(gg)>gtol && check==0 && jit<nit,
disp(['Maximum Hessian eigenvalue ',num2str(max(ee))])
g(:,icount+1)=gg;
else
df = fval0(icount)-fval;
disp(['Actual dxnorm ',num2str(norm(x(:,end)-x(:,end-1)))])
disp(['FVAL ',num2str(fval)])
disp(['Improvement ',num2str(df)])
disp(['Ftol ',num2str(ftol)])
disp(['Htol ',num2str(htol0)])
% if df<htol0,
% htol=max(htol_base,df/10);
% end
htol=htol_base;
if norm(x(:,icount)-xparam1)>1.e-12,
try
if norm(x(:,icount)-xparam1)>1.e-12
try
save m1.mat x fval0 nig -append
catch
save m1.mat x fval0 nig
save m1.mat x fval0 nig
end
[dum, gg, htol0, igg, hhg, h1]=mr_hessian(0,xparam1,func_hh,flagit,htol,varargin{:});
if htol0>htol, %ftol,
%ftol=htol0;
[dum, gg, htol0, igg, hhg, h1]=mr_hessian(0,xparam1,func_hh,flagit,htol,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
if htol0>htol
htol=htol0;
disp(' ')
disp('Numerical noise in the likelihood')
disp('Tolerance has to be relaxed')
disp(' ')
% elseif htol0<ftol,
% ftol=max(htol0, ftol0);
end
hh0 = reshape(dum,nx,nx);
hh=hhg;
if flagit==2,
if min(eig(hh0))<=0,
if flagit==2
if min(eig(hh0))<=0
hh0=hhg; %generalized_cholesky(hh0);
else
else
hh=hh0;
igg=inv(hh);
end
end
end
disp(['Gradient norm ',num2str(norm(gg))])
ee=eig(hh);
disp(['Minimum Hessian eigenvalue ',num2str(min(ee))])
@ -235,29 +216,27 @@ while norm(gg)>gtol && check==0 && jit<nit,
if max(eig(hh))<0, disp('Negative definite Hessian! Local maximum!'), pause, end,
t=toc;
disp(['Elapsed time for iteration ',num2str(t),' s.'])
g(:,icount+1)=gg;
% H = bfgsi(H,g(:,end)-g(:,end-1),x(:,end)-x(:,end-1));
H = igg;
save m1.mat x hh g hhg igg fval0 nig H
end
end
save m1.mat x hh g hhg igg fval0 nig
if ftol>ftol0,
if ftol>ftol0
disp(' ')
disp('Numerical noise in the likelihood')
disp('Tolerance had to be relaxed')
disp(' ')
end
if jit==nit,
if jit==nit
disp(' ')
disp('Maximum number of iterations reached')
disp(' ')
end
if norm(gg)<=gtol,
if norm(gg)<=gtol
disp(['Estimation ended:'])
disp(['Gradient norm < ', num2str(gtol)])
end
@ -267,15 +246,7 @@ end
return
%
function f00 = lsearch(lam,func,x,dx,varargin)
x0=x-dx*lam;
f00=feval(func,x0,varargin{:});
function f00 = lsearch(lam,func,x,dx,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
x0=x-dx*lam;
f00=feval(func,x0,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);

1
tests/Makefile.am
View File

@ -48,6 +48,7 @@ MODFILES = \
fs2000/fs2000.mod \
fs2000/fs2000a.mod \
fs2000/fs2000c.mod \
fs2000/fs2000d.mod \
homotopy/homotopy1_test.mod \
homotopy/homotopy2_test.mod \
homotopy/homotopy3_test.mod \

75
tests/fs2000/fs2000d.mod Normal file
View File

@ -0,0 +1,75 @@
// See fs2000.mod in the examples/ directory for details on the model
var m P c e W R k d n l gy_obs gp_obs y dA;
varexo e_a e_m;
parameters alp bet gam mst rho psi del;
alp = 0.33;
bet = 0.99;
gam = 0.003;
mst = 1.011;
rho = 0.7;
psi = 0.787;
del = 0.02;
model;
dA = exp(gam+e_a);
log(m) = (1-rho)*log(mst) + rho*log(m(-1))+e_m;
-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c(+2)*P(+2)*m(+1))=0;
W = l/n;
-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
P*c = m;
m-1+d = l;
e = exp(e_a);
y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
gy_obs = dA*y/y(-1);
gp_obs = (P/P(-1))*m(-1)/dA;
end;
initval;
k = 6;
m = mst;
P = 2.25;
c = 0.45;
e = 1;
W = 4;
R = 1.02;
d = 0.85;
n = 0.19;
l = 0.86;
y = 0.6;
gy_obs = exp(gam);
gp_obs = exp(-gam);
dA = exp(gam);
end;
shocks;
var e_a; stderr 0.014;
var e_m; stderr 0.005;
end;
steady;
check;
estimated_params;
alp, beta_pdf, 0.356, 0.02;
bet, beta_pdf, 0.993, 0.002;
gam, normal_pdf, 0.0085, 0.003;
mst, normal_pdf, 1.0002, 0.007;
rho, beta_pdf, 0.129, 0.223;
psi, beta_pdf, 0.65, 0.05;
del, beta_pdf, 0.01, 0.005;
stderr e_a, inv_gamma_pdf, 0.035449, inf;
stderr e_m, inv_gamma_pdf, 0.008862, inf;
end;
varobs gp_obs gy_obs;
options_.solve_tolf = 1e-12;
estimation(order=1,datafile=fsdat_simul,nobs=192,mode_compute=5,loglinear,mh_replic=0);