904 lines
35 KiB
Matlab
904 lines
35 KiB
Matlab
function [fval,info,exit_flag,DLIK,Hess,SteadyState,trend_coeff,Model,DynareOptions,BayesInfo,DynareResults] = dsge_likelihood(xparam1,DynareDataset,DatasetInfo,DynareOptions,Model,EstimatedParameters,BayesInfo,BoundsInfo,DynareResults,derivatives_info)
|
|
% Evaluates the posterior kernel of a dsge model using the specified
|
|
% kalman_algo; the resulting posterior includes the 2*pi constant of the
|
|
% likelihood function
|
|
|
|
%@info:
|
|
%! @deftypefn {Function File} {[@var{fval},@var{exit_flag},@var{ys},@var{trend_coeff},@var{info},@var{Model},@var{DynareOptions},@var{BayesInfo},@var{DynareResults},@var{DLIK},@var{AHess}] =} dsge_likelihood (@var{xparam1},@var{DynareDataset},@var{DynareOptions},@var{Model},@var{EstimatedParameters},@var{BayesInfo},@var{DynareResults},@var{derivatives_flag})
|
|
%! @anchor{dsge_likelihood}
|
|
%! @sp 1
|
|
%! Evaluates the posterior kernel of a dsge model.
|
|
%! @sp 2
|
|
%! @strong{Inputs}
|
|
%! @sp 1
|
|
%! @table @ @var
|
|
%! @item xparam1
|
|
%! Vector of doubles, current values for the estimated parameters.
|
|
%! @item DynareDataset
|
|
%! Matlab's structure describing the dataset (initialized by dynare, see @ref{dataset_}).
|
|
%! @item DynareOptions
|
|
%! Matlab's structure describing the options (initialized by dynare, see @ref{options_}).
|
|
%! @item Model
|
|
%! Matlab's structure describing the Model (initialized by dynare, see @ref{M_}).
|
|
%! @item EstimatedParamemeters
|
|
%! Matlab's structure describing the estimated_parameters (initialized by dynare, see @ref{estim_params_}).
|
|
%! @item BayesInfo
|
|
%! Matlab's structure describing the priors (initialized by dynare, see @ref{bayesopt_}).
|
|
%! @item DynareResults
|
|
%! Matlab's structure gathering the results (initialized by dynare, see @ref{oo_}).
|
|
%! @item derivates_flag
|
|
%! Integer scalar, flag for analytical derivatives of the likelihood.
|
|
%! @end table
|
|
%! @sp 2
|
|
%! @strong{Outputs}
|
|
%! @sp 1
|
|
%! @table @ @var
|
|
%! @item fval
|
|
%! Double scalar, value of (minus) the likelihood.
|
|
%! @item info
|
|
%! Double vector, second entry stores penalty, first entry the error code.
|
|
%! @table @ @code
|
|
%! @item info==0
|
|
%! No error.
|
|
%! @item info==1
|
|
%! The model doesn't determine the current variables uniquely.
|
|
%! @item info==2
|
|
%! MJDGGES returned an error code.
|
|
%! @item info==3
|
|
%! Blanchard & Kahn conditions are not satisfied: no stable equilibrium.
|
|
%! @item info==4
|
|
%! Blanchard & Kahn conditions are not satisfied: indeterminacy.
|
|
%! @item info==5
|
|
%! Blanchard & Kahn conditions are not satisfied: indeterminacy due to rank failure.
|
|
%! @item info==6
|
|
%! The jacobian evaluated at the deterministic steady state is complex.
|
|
%! @item info==19
|
|
%! The steadystate routine has thrown an exception (inconsistent deep parameters).
|
|
%! @item info==20
|
|
%! Cannot find the steady state, info(4) contains the sum of square residuals (of the static equations).
|
|
%! @item info==21
|
|
%! The steady state is complex, info(4) contains the sum of square of imaginary parts of the steady state.
|
|
%! @item info==22
|
|
%! The steady has NaNs.
|
|
%! @item info==23
|
|
%! M_.params has been updated in the steadystate routine and has complex valued scalars.
|
|
%! @item info==24
|
|
%! M_.params has been updated in the steadystate routine and has some NaNs.
|
|
%! @item info==26
|
|
%! M_.params has been updated in the steadystate routine and has negative/0 values in loglinear model.
|
|
%! @item info==30
|
|
%! Ergodic variance can't be computed.
|
|
%! @item info==41
|
|
%! At least one parameter is violating a lower bound condition.
|
|
%! @item info==42
|
|
%! At least one parameter is violating an upper bound condition.
|
|
%! @item info==43
|
|
%! The covariance matrix of the structural innovations is not positive definite.
|
|
%! @item info==44
|
|
%! The covariance matrix of the measurement errors is not positive definite.
|
|
%! @item info==45
|
|
%! Likelihood is not a number (NaN).
|
|
%! @item info==46
|
|
%! Likelihood is a complex valued number.
|
|
%! @item info==47
|
|
%! Posterior kernel is not a number (logged prior density is NaN)
|
|
%! @item info==48
|
|
%! Posterior kernel is a complex valued number (logged prior density is complex).
|
|
%! @end table
|
|
%! @item exit_flag
|
|
%! Integer scalar, equal to zero if the routine return with a penalty (one otherwise).
|
|
%! @item DLIK
|
|
%! Vector of doubles, score of the likelihood.
|
|
%! @item AHess
|
|
%! Matrix of doubles, asymptotic hessian matrix.
|
|
%! @item SteadyState
|
|
%! Vector of doubles, steady state level for the endogenous variables.
|
|
%! @item trend_coeff
|
|
%! Matrix of doubles, coefficients of the deterministic trend in the measurement equation.
|
|
%! @item Model
|
|
%! Matlab's structure describing the model (initialized by dynare, see @ref{M_}).
|
|
%! @item DynareOptions
|
|
%! Matlab's structure describing the options (initialized by dynare, see @ref{options_}).
|
|
%! @item BayesInfo
|
|
%! Matlab's structure describing the priors (initialized by dynare, see @ref{bayesopt_}).
|
|
%! @item DynareResults
|
|
%! Matlab's structure gathering the results (initialized by dynare, see @ref{oo_}).
|
|
%! @end table
|
|
%! @sp 2
|
|
%! @strong{This function is called by:}
|
|
%! @sp 1
|
|
%! @ref{dynare_estimation_1}, @ref{mode_check}
|
|
%! @sp 2
|
|
%! @strong{This function calls:}
|
|
%! @sp 1
|
|
%! @ref{dynare_resolve}, @ref{lyapunov_symm}, @ref{lyapunov_solver}, @ref{compute_Pinf_Pstar}, @ref{kalman_filter_d}, @ref{missing_observations_kalman_filter_d}, @ref{univariate_kalman_filter_d}, @ref{kalman_steady_state}, @ref{get_perturbation_params_deriv}, @ref{kalman_filter}, @ref{score}, @ref{AHessian}, @ref{missing_observations_kalman_filter}, @ref{univariate_kalman_filter}, @ref{priordens}
|
|
%! @end deftypefn
|
|
%@eod:
|
|
|
|
% Copyright (C) 2004-2020 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/>.
|
|
|
|
% AUTHOR(S) stephane DOT adjemian AT univ DASH lemans DOT FR
|
|
|
|
% Initialization of the returned variables and others...
|
|
fval = [];
|
|
SteadyState = [];
|
|
trend_coeff = [];
|
|
exit_flag = 1;
|
|
info = zeros(4,1);
|
|
DLIK = [];
|
|
Hess = [];
|
|
|
|
% Ensure that xparam1 is a column vector.
|
|
xparam1 = xparam1(:);
|
|
|
|
if DynareOptions.estimation_dll
|
|
[fval,exit_flag,SteadyState,trend_coeff,info,params,H,Q] ...
|
|
= logposterior(xparam1,DynareDataset, DynareOptions,Model, ...
|
|
EstimatedParameters,BayesInfo,DynareResults);
|
|
if exit_flag
|
|
error("Error encountered in logposterior")
|
|
end
|
|
Model.params = params;
|
|
if ~isequal(Model.H,0)
|
|
Model.H = H;
|
|
end
|
|
Model.Sigma_e = Q;
|
|
DynareResults.dr.ys = SteadyState;
|
|
return
|
|
end
|
|
|
|
% Set flag related to analytical derivatives.
|
|
analytic_derivation = DynareOptions.analytic_derivation;
|
|
|
|
if analytic_derivation && DynareOptions.loglinear
|
|
error('The analytic_derivation and loglinear options are not compatible')
|
|
end
|
|
|
|
if nargout==1
|
|
analytic_derivation=0;
|
|
end
|
|
|
|
if analytic_derivation
|
|
kron_flag=DynareOptions.analytic_derivation_mode;
|
|
end
|
|
|
|
%------------------------------------------------------------------------------
|
|
% 1. Get the structural parameters & define penalties
|
|
%------------------------------------------------------------------------------
|
|
|
|
% Return, with endogenous penalty, if some parameters are smaller than the lower bound of the prior domain.
|
|
if isestimation(DynareOptions) && ~isequal(DynareOptions.mode_compute,1) && any(xparam1<BoundsInfo.lb)
|
|
k = find(xparam1<BoundsInfo.lb);
|
|
fval = Inf;
|
|
exit_flag = 0;
|
|
info(1) = 41;
|
|
info(4)= sum((BoundsInfo.lb(k)-xparam1(k)).^2);
|
|
if analytic_derivation
|
|
DLIK=ones(length(xparam1),1);
|
|
end
|
|
return
|
|
end
|
|
|
|
% Return, with endogenous penalty, if some parameters are greater than the upper bound of the prior domain.
|
|
if isestimation(DynareOptions) && ~isequal(DynareOptions.mode_compute,1) && any(xparam1>BoundsInfo.ub)
|
|
k = find(xparam1>BoundsInfo.ub);
|
|
fval = Inf;
|
|
exit_flag = 0;
|
|
info(1) = 42;
|
|
info(4)= sum((xparam1(k)-BoundsInfo.ub(k)).^2);
|
|
if analytic_derivation
|
|
DLIK=ones(length(xparam1),1);
|
|
end
|
|
return
|
|
end
|
|
|
|
% Get the diagonal elements of the covariance matrices for the structural innovations (Q) and the measurement error (H).
|
|
Model = set_all_parameters(xparam1,EstimatedParameters,Model);
|
|
|
|
Q = Model.Sigma_e;
|
|
H = Model.H;
|
|
|
|
% Test if Q is positive definite.
|
|
if ~issquare(Q) || EstimatedParameters.ncx || isfield(EstimatedParameters,'calibrated_covariances')
|
|
[Q_is_positive_definite, penalty] = ispd(Q(EstimatedParameters.Sigma_e_entries_to_check_for_positive_definiteness,EstimatedParameters.Sigma_e_entries_to_check_for_positive_definiteness));
|
|
if ~Q_is_positive_definite
|
|
fval = Inf;
|
|
exit_flag = 0;
|
|
info(1) = 43;
|
|
info(4) = penalty;
|
|
return
|
|
end
|
|
if isfield(EstimatedParameters,'calibrated_covariances')
|
|
correct_flag=check_consistency_covariances(Q);
|
|
if ~correct_flag
|
|
penalty = sum(Q(EstimatedParameters.calibrated_covariances.position).^2);
|
|
fval = Inf;
|
|
exit_flag = 0;
|
|
info(1) = 71;
|
|
info(4) = penalty;
|
|
return
|
|
end
|
|
end
|
|
end
|
|
|
|
% Test if H is positive definite.
|
|
if ~issquare(H) || EstimatedParameters.ncn || isfield(EstimatedParameters,'calibrated_covariances_ME')
|
|
[H_is_positive_definite, penalty] = ispd(H(EstimatedParameters.H_entries_to_check_for_positive_definiteness,EstimatedParameters.H_entries_to_check_for_positive_definiteness));
|
|
if ~H_is_positive_definite
|
|
fval = Inf;
|
|
info(1) = 44;
|
|
info(4) = penalty;
|
|
exit_flag = 0;
|
|
return
|
|
end
|
|
if isfield(EstimatedParameters,'calibrated_covariances_ME')
|
|
correct_flag=check_consistency_covariances(H);
|
|
if ~correct_flag
|
|
penalty = sum(H(EstimatedParameters.calibrated_covariances_ME.position).^2);
|
|
fval = Inf;
|
|
exit_flag = 0;
|
|
info(1) = 72;
|
|
info(4) = penalty;
|
|
return
|
|
end
|
|
end
|
|
end
|
|
|
|
|
|
%------------------------------------------------------------------------------
|
|
% 2. call model setup & reduction program
|
|
%------------------------------------------------------------------------------
|
|
|
|
% Linearize the model around the deterministic steady state 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)
|
|
if info(1) == 3 || info(1) == 4 || info(1) == 5 || info(1)==6 ||info(1) == 19 ||...
|
|
info(1) == 20 || info(1) == 21 || info(1) == 23 || info(1) == 26 || ...
|
|
info(1) == 81 || info(1) == 84 || info(1) == 85 || info(1) == 86
|
|
%meaningful second entry of output that can be used
|
|
fval = Inf;
|
|
info(4) = info(2);
|
|
exit_flag = 0;
|
|
if analytic_derivation
|
|
DLIK=ones(length(xparam1),1);
|
|
end
|
|
return
|
|
else
|
|
fval = Inf;
|
|
info(4) = 0.1;
|
|
exit_flag = 0;
|
|
if analytic_derivation
|
|
DLIK=ones(length(xparam1),1);
|
|
end
|
|
return
|
|
end
|
|
end
|
|
|
|
% check endogenous prior restrictions
|
|
info=endogenous_prior_restrictions(T,R,Model,DynareOptions,DynareResults);
|
|
if info(1)
|
|
fval = Inf;
|
|
info(4)=info(2);
|
|
exit_flag = 0;
|
|
if analytic_derivation
|
|
DLIK=ones(length(xparam1),1);
|
|
end
|
|
return
|
|
end
|
|
|
|
% 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.vobs,1);
|
|
else
|
|
if DynareOptions.loglinear
|
|
constant = log(SteadyState(BayesInfo.mfys));
|
|
else
|
|
constant = SteadyState(BayesInfo.mfys);
|
|
end
|
|
end
|
|
|
|
% Define the deterministic linear trend of the measurement equation.
|
|
if BayesInfo.with_trend
|
|
[trend_addition, trend_coeff]=compute_trend_coefficients(Model,DynareOptions,DynareDataset.vobs,DynareDataset.nobs);
|
|
trend = repmat(constant,1,DynareDataset.nobs)+trend_addition;
|
|
else
|
|
trend_coeff = zeros(DynareDataset.vobs,1);
|
|
trend = repmat(constant,1,DynareDataset.nobs);
|
|
end
|
|
|
|
% Get needed informations for kalman filter routines.
|
|
start = DynareOptions.presample+1;
|
|
Z = BayesInfo.mf; %selector for observed variables
|
|
no_missing_data_flag = ~DatasetInfo.missing.state;
|
|
mm = length(T); %number of states
|
|
pp = DynareDataset.vobs; %number of observables
|
|
rr = length(Q); %number of shocks
|
|
kalman_tol = DynareOptions.kalman_tol;
|
|
diffuse_kalman_tol = DynareOptions.diffuse_kalman_tol;
|
|
riccati_tol = DynareOptions.riccati_tol;
|
|
Y = transpose(DynareDataset.data)-trend;
|
|
|
|
%------------------------------------------------------------------------------
|
|
% 3. Initial condition of the Kalman filter
|
|
%------------------------------------------------------------------------------
|
|
kalman_algo = DynareOptions.kalman_algo;
|
|
|
|
|
|
diffuse_periods = 0;
|
|
expanded_state_vector_for_univariate_filter=0;
|
|
singular_diffuse_filter = 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_solver(T,R,Q,DynareOptions);
|
|
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 = DynareOptions.Harvey_scale_factor*eye(mm);
|
|
Pinf = [];
|
|
a = zeros(mm,1);
|
|
Zflag = 0;
|
|
case 3% Diffuse Kalman filter (Durbin and Koopman)
|
|
% Use standard kalman filter except if the univariate filter is explicitely choosen.
|
|
if kalman_algo == 0
|
|
kalman_algo = 3;
|
|
elseif ~((kalman_algo == 3) || (kalman_algo == 4))
|
|
error(['The model requires Diffuse filter, but you specified a different Kalman filter. You must set options_.kalman_algo ' ...
|
|
'to 0 (default), 3 or 4'])
|
|
end
|
|
[Pstar,Pinf] = compute_Pinf_Pstar(Z,T,R,Q,DynareOptions.qz_criterium);
|
|
Z =zeros(length(BayesInfo.mf),size(T,1));
|
|
for i = 1:length(BayesInfo.mf)
|
|
Z(i,BayesInfo.mf(i))=1;
|
|
end
|
|
Zflag = 1;
|
|
% Run diffuse kalman filter on first periods.
|
|
if (kalman_algo==3)
|
|
% Multivariate Diffuse Kalman Filter
|
|
Pstar0 = Pstar; % store Pstar
|
|
if no_missing_data_flag
|
|
[dLIK,dlik,a,Pstar] = kalman_filter_d(Y, 1, size(Y,2), ...
|
|
zeros(mm,1), Pinf, Pstar, ...
|
|
kalman_tol, diffuse_kalman_tol, riccati_tol, DynareOptions.presample, ...
|
|
T,R,Q,H,Z,mm,pp,rr);
|
|
else
|
|
[dLIK,dlik,a,Pstar] = missing_observations_kalman_filter_d(DatasetInfo.missing.aindex,DatasetInfo.missing.number_of_observations,DatasetInfo.missing.no_more_missing_observations, ...
|
|
Y, 1, size(Y,2), ...
|
|
zeros(mm,1), Pinf, Pstar, ...
|
|
kalman_tol, diffuse_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.
|
|
singular_diffuse_filter = 1;
|
|
Pstar = Pstar0;
|
|
end
|
|
end
|
|
if singular_diffuse_filter || (kalman_algo==4)
|
|
% Univariate Diffuse Kalman Filter
|
|
if isequal(H,0)
|
|
H1 = zeros(pp,1);
|
|
mmm = mm;
|
|
else
|
|
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
|
|
H1 = diag(H);
|
|
mmm = mm;
|
|
else
|
|
%Augment state vector (follows Section 6.4.3 of DK (2012))
|
|
expanded_state_vector_for_univariate_filter=1;
|
|
if Zflag
|
|
Z1=Z;
|
|
else
|
|
Z1=zeros(pp,size(T,2));
|
|
for jz=1:length(Z)
|
|
Z1(jz,Z(jz))=1;
|
|
end
|
|
end
|
|
Z = [Z1, eye(pp)];
|
|
Zflag=1;
|
|
T = blkdiag(T,zeros(pp));
|
|
Q = blkdiag(Q,H);
|
|
R = blkdiag(R,eye(pp));
|
|
Pstar = blkdiag(Pstar,H);
|
|
Pinf = blkdiag(Pinf,zeros(pp));
|
|
H1 = zeros(pp,1);
|
|
mmm = mm+pp;
|
|
|
|
end
|
|
end
|
|
|
|
[dLIK,dlik,a,Pstar] = univariate_kalman_filter_d(DatasetInfo.missing.aindex,...
|
|
DatasetInfo.missing.number_of_observations,...
|
|
DatasetInfo.missing.no_more_missing_observations, ...
|
|
Y, 1, size(Y,2), ...
|
|
zeros(mmm,1), Pinf, Pstar, ...
|
|
kalman_tol, diffuse_kalman_tol, riccati_tol, DynareOptions.presample, ...
|
|
T,R,Q,H1,Z,mmm,pp,rr);
|
|
diffuse_periods = size(dlik,1);
|
|
end
|
|
if isnan(dLIK)
|
|
fval = Inf;
|
|
info(1) = 45;
|
|
info(4) = 0.1;
|
|
exit_flag = 0;
|
|
return
|
|
end
|
|
|
|
case 4% Start from the solution of the Riccati equation.
|
|
if kalman_algo ~= 2
|
|
kalman_algo = 1;
|
|
end
|
|
try
|
|
if isequal(H,0)
|
|
Pstar = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(Z,mm,length(Z))));
|
|
else
|
|
Pstar = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(Z,mm,length(Z))),H);
|
|
end
|
|
catch ME
|
|
disp(ME.message)
|
|
disp(['dsge_likelihood:: I am not able to solve the Riccati equation, so I switch to lik_init=1!']);
|
|
DynareOptions.lik_init = 1;
|
|
Pstar=lyapunov_solver(T,R,Q,DynareOptions);
|
|
end
|
|
Pinf = [];
|
|
a = zeros(mm,1);
|
|
Zflag = 0;
|
|
case 5 % Old diffuse Kalman filter only for the non stationary variables
|
|
[eigenvect, eigenv] = eig(T);
|
|
eigenv = diag(eigenv);
|
|
nstable = length(find(abs(abs(eigenv)-1) > 1e-7));
|
|
unstable = find(abs(abs(eigenv)-1) < 1e-7);
|
|
V = eigenvect(:,unstable);
|
|
indx_unstable = find(sum(abs(V),2)>1e-5);
|
|
stable = find(sum(abs(V),2)<1e-5);
|
|
nunit = length(eigenv) - nstable;
|
|
Pstar = DynareOptions.Harvey_scale_factor*eye(nunit);
|
|
if kalman_algo ~= 2
|
|
kalman_algo = 1;
|
|
end
|
|
R_tmp = R(stable, :);
|
|
T_tmp = T(stable,stable);
|
|
Pstar_tmp=lyapunov_solver(T_tmp,R_tmp,Q,DynareOptions);
|
|
Pstar(stable, stable) = Pstar_tmp;
|
|
Pinf = [];
|
|
a = zeros(mm,1);
|
|
Zflag = 0;
|
|
otherwise
|
|
error('dsge_likelihood:: Unknown initialization approach for the Kalman filter!')
|
|
end
|
|
|
|
if analytic_derivation
|
|
offset = EstimatedParameters.nvx;
|
|
offset = offset+EstimatedParameters.nvn;
|
|
offset = offset+EstimatedParameters.ncx;
|
|
offset = offset+EstimatedParameters.ncn;
|
|
no_DLIK = 0;
|
|
full_Hess = analytic_derivation==2;
|
|
asy_Hess = analytic_derivation==-2;
|
|
outer_product_gradient = analytic_derivation==-1;
|
|
if asy_Hess
|
|
analytic_derivation=1;
|
|
end
|
|
if outer_product_gradient
|
|
analytic_derivation=1;
|
|
end
|
|
DLIK = [];
|
|
AHess = [];
|
|
iv = DynareResults.dr.restrict_var_list;
|
|
if nargin<10 || isempty(derivatives_info)
|
|
[A,B,nou,nou,Model,DynareOptions,DynareResults] = dynare_resolve(Model,DynareOptions,DynareResults);
|
|
if ~isempty(EstimatedParameters.var_exo)
|
|
indexo=EstimatedParameters.var_exo(:,1);
|
|
else
|
|
indexo=[];
|
|
end
|
|
if ~isempty(EstimatedParameters.param_vals)
|
|
indparam=EstimatedParameters.param_vals(:,1);
|
|
else
|
|
indparam=[];
|
|
end
|
|
old_order = DynareOptions.order;
|
|
if DynareOptions.order > 1%not sure whether this check is necessary
|
|
DynareOptions.order = 1; fprintf('Reset order to 1 for analytical parameter derivatives.\n');
|
|
end
|
|
old_analytic_derivation_mode = DynareOptions.analytic_derivation_mode;
|
|
DynareOptions.analytic_derivation_mode = kron_flag;
|
|
if full_Hess
|
|
DERIVS = get_perturbation_params_derivs(Model, DynareOptions, EstimatedParameters, DynareResults, indparam, indexo, [], true);
|
|
indD2T = reshape(1:Model.endo_nbr^2, Model.endo_nbr, Model.endo_nbr);
|
|
indD2Om = dyn_unvech(1:Model.endo_nbr*(Model.endo_nbr+1)/2);
|
|
D2T = DERIVS.d2KalmanA(indD2T(iv,iv),:);
|
|
D2Om = DERIVS.d2Om(dyn_vech(indD2Om(iv,iv)),:);
|
|
D2Yss = DERIVS.d2Yss(iv,:,:);
|
|
else
|
|
DERIVS = get_perturbation_params_derivs(Model, DynareOptions, EstimatedParameters, DynareResults, indparam, indexo, [], false);
|
|
end
|
|
DT = zeros(Model.endo_nbr, Model.endo_nbr, size(DERIVS.dghx,3));
|
|
DT(:,Model.nstatic+(1:Model.nspred),:) = DERIVS.dghx;
|
|
DT = DT(iv,iv,:);
|
|
DOm = DERIVS.dOm(iv,iv,:);
|
|
DYss = DERIVS.dYss(iv,:);
|
|
DynareOptions.order = old_order; %make sure order is reset (not sure if necessary)
|
|
DynareOptions.analytic_derivation_mode = old_analytic_derivation_mode;%make sure analytic_derivation_mode is reset (not sure if necessary)
|
|
else
|
|
DT = derivatives_info.DT(iv,iv,:);
|
|
DOm = derivatives_info.DOm(iv,iv,:);
|
|
DYss = derivatives_info.DYss(iv,:);
|
|
if isfield(derivatives_info,'full_Hess')
|
|
full_Hess = derivatives_info.full_Hess;
|
|
end
|
|
if full_Hess
|
|
D2T = derivatives_info.D2T;
|
|
D2Om = derivatives_info.D2Om;
|
|
D2Yss = derivatives_info.D2Yss;
|
|
end
|
|
if isfield(derivatives_info,'no_DLIK')
|
|
no_DLIK = derivatives_info.no_DLIK;
|
|
end
|
|
clear('derivatives_info');
|
|
end
|
|
DYss = [zeros(size(DYss,1),offset) DYss];
|
|
DH=zeros([length(H),length(H),length(xparam1)]);
|
|
DQ=zeros([size(Q),length(xparam1)]);
|
|
DP=zeros([size(T),length(xparam1)]);
|
|
if full_Hess
|
|
for j=1:size(D2Yss,1)
|
|
tmp(j,:,:) = blkdiag(zeros(offset,offset), squeeze(D2Yss(j,:,:)));
|
|
end
|
|
D2Yss = tmp;
|
|
D2H=sparse(size(D2Om,1),size(D2Om,2)); %zeros([size(H),length(xparam1),length(xparam1)]);
|
|
D2P=sparse(size(D2Om,1),size(D2Om,2)); %zeros([size(T),length(xparam1),length(xparam1)]);
|
|
jcount=0;
|
|
end
|
|
if DynareOptions.lik_init==1
|
|
for i=1:EstimatedParameters.nvx
|
|
k =EstimatedParameters.var_exo(i,1);
|
|
DQ(k,k,i) = 2*sqrt(Q(k,k));
|
|
dum = lyapunov_symm(T,DOm(:,:,i),DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],DynareOptions.debug);
|
|
% kk = find(abs(dum) < 1e-12);
|
|
% dum(kk) = 0;
|
|
DP(:,:,i)=dum;
|
|
if full_Hess
|
|
for j=1:i
|
|
jcount=jcount+1;
|
|
dum = lyapunov_symm(T,dyn_unvech(D2Om(:,jcount)),DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],DynareOptions.debug);
|
|
% kk = (abs(dum) < 1e-12);
|
|
% dum(kk) = 0;
|
|
D2P(:,jcount)=dyn_vech(dum);
|
|
% D2P(:,:,j,i)=dum;
|
|
end
|
|
end
|
|
end
|
|
end
|
|
offset = EstimatedParameters.nvx;
|
|
for i=1:EstimatedParameters.nvn
|
|
k = EstimatedParameters.var_endo(i,1);
|
|
DH(k,k,i+offset) = 2*sqrt(H(k,k));
|
|
if full_Hess
|
|
D2H(k,k,i+offset,i+offset) = 2;
|
|
end
|
|
end
|
|
offset = offset + EstimatedParameters.nvn;
|
|
if DynareOptions.lik_init==1
|
|
for j=1:EstimatedParameters.np
|
|
dum = lyapunov_symm(T,DT(:,:,j+offset)*Pstar*T'+T*Pstar*DT(:,:,j+offset)'+DOm(:,:,j+offset),DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],DynareOptions.debug);
|
|
% kk = find(abs(dum) < 1e-12);
|
|
% dum(kk) = 0;
|
|
DP(:,:,j+offset)=dum;
|
|
if full_Hess
|
|
DTj = DT(:,:,j+offset);
|
|
DPj = dum;
|
|
for i=1:j+offset
|
|
jcount=jcount+1;
|
|
DTi = DT(:,:,i);
|
|
DPi = DP(:,:,i);
|
|
D2Tij = reshape(D2T(:,jcount),size(T));
|
|
D2Omij = dyn_unvech(D2Om(:,jcount));
|
|
tmp = D2Tij*Pstar*T' + T*Pstar*D2Tij' + DTi*DPj*T' + DTj*DPi*T' + T*DPj*DTi' + T*DPi*DTj' + DTi*Pstar*DTj' + DTj*Pstar*DTi' + D2Omij;
|
|
dum = lyapunov_symm(T,tmp,DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],DynareOptions.debug);
|
|
% dum(abs(dum)<1.e-12) = 0;
|
|
D2P(:,jcount) = dyn_vech(dum);
|
|
% D2P(:,:,j+offset,i) = dum;
|
|
end
|
|
end
|
|
end
|
|
end
|
|
if analytic_derivation==1
|
|
analytic_deriv_info={analytic_derivation,DT,DYss,DOm,DH,DP,asy_Hess};
|
|
else
|
|
analytic_deriv_info={analytic_derivation,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P};
|
|
clear DT DYss DOm DP D2T D2Yss D2Om D2H D2P
|
|
end
|
|
else
|
|
analytic_deriv_info={0};
|
|
end
|
|
|
|
%------------------------------------------------------------------------------
|
|
% 4. Likelihood evaluation
|
|
%------------------------------------------------------------------------------
|
|
|
|
singularity_has_been_detected = false;
|
|
% First test multivariate filter if specified; potentially abort and use univariate filter instead
|
|
if ((kalman_algo==1) || (kalman_algo==3))% Multivariate Kalman Filter
|
|
if no_missing_data_flag
|
|
if DynareOptions.block
|
|
LIK = block_kalman_filter(T,R,Q,H,Pstar,Y,start,Z,kalman_tol,riccati_tol, Model.nz_state_var, Model.n_diag, Model.nobs_non_statevar);
|
|
elseif DynareOptions.fast_kalman_filter
|
|
if diffuse_periods
|
|
%kalman_algo==3 requires no diffuse periods (stationary
|
|
%observables) as otherwise FE matrix will not be positive
|
|
%definite
|
|
fval = Inf;
|
|
info(1) = 55;
|
|
info(4) = 0.1;
|
|
exit_flag = 0;
|
|
return
|
|
end
|
|
[LIK,lik] = kalman_filter_fast(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, ...
|
|
analytic_deriv_info{:});
|
|
else
|
|
[LIK,lik] = kalman_filter(Y,diffuse_periods+1,size(Y,2), ...
|
|
a,Pstar, ...
|
|
kalman_tol, riccati_tol, ...
|
|
DynareOptions.rescale_prediction_error_covariance, ...
|
|
DynareOptions.presample, ...
|
|
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods, ...
|
|
analytic_deriv_info{:});
|
|
end
|
|
else
|
|
if 0 %DynareOptions.block
|
|
[LIK,lik] = block_kalman_filter(DatasetInfo.missing.aindex,DatasetInfo.missing.number_of_observations,DatasetInfo.missing.no_more_missing_observations,...
|
|
T,R,Q,H,Pstar,Y,start,Z,kalman_tol,riccati_tol, Model.nz_state_var, Model.n_diag, Model.nobs_non_statevar);
|
|
else
|
|
[LIK,lik] = missing_observations_kalman_filter(DatasetInfo.missing.aindex,DatasetInfo.missing.number_of_observations,DatasetInfo.missing.no_more_missing_observations,Y,diffuse_periods+1,size(Y,2), ...
|
|
a, Pstar, ...
|
|
kalman_tol, DynareOptions.riccati_tol, ...
|
|
DynareOptions.rescale_prediction_error_covariance, ...
|
|
DynareOptions.presample, ...
|
|
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods);
|
|
end
|
|
end
|
|
if analytic_derivation
|
|
LIK1=LIK;
|
|
LIK=LIK1{1};
|
|
lik1=lik;
|
|
lik=lik1{1};
|
|
end
|
|
if isinf(LIK)
|
|
if DynareOptions.use_univariate_filters_if_singularity_is_detected
|
|
singularity_has_been_detected = true;
|
|
if kalman_algo == 1
|
|
kalman_algo = 2;
|
|
else
|
|
kalman_algo = 4;
|
|
end
|
|
else
|
|
fval = Inf;
|
|
info(1) = 50;
|
|
info(4) = 0.1;
|
|
exit_flag = 0;
|
|
return
|
|
end
|
|
else
|
|
if DynareOptions.lik_init==3
|
|
LIK = LIK + dLIK;
|
|
if analytic_derivation==0 && nargout>3
|
|
if ~singular_diffuse_filter
|
|
lik = [dlik; lik];
|
|
else
|
|
lik = [sum(dlik,2); lik];
|
|
end
|
|
end
|
|
end
|
|
end
|
|
end
|
|
|
|
if (kalman_algo==2) || (kalman_algo==4)
|
|
% Univariate Kalman Filter
|
|
% resetting measurement error covariance matrix when necessary following DK (2012), Section 6.4.3 %
|
|
if isequal(H,0)
|
|
H1 = zeros(pp,1);
|
|
mmm = mm;
|
|
if analytic_derivation
|
|
DH = zeros(pp,length(xparam1));
|
|
end
|
|
else
|
|
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
|
|
H1 = diag(H);
|
|
mmm = mm;
|
|
clear('tmp')
|
|
if analytic_derivation
|
|
for j=1:pp
|
|
tmp(j,:)=DH(j,j,:);
|
|
end
|
|
DH=tmp;
|
|
end
|
|
else
|
|
if ~expanded_state_vector_for_univariate_filter
|
|
Z1=zeros(pp,size(T,2));
|
|
for jz=1:length(Z)
|
|
Z1(jz,Z(jz))=1;
|
|
end
|
|
Z = [Z1, eye(pp)];
|
|
Zflag=1;
|
|
T = blkdiag(T,zeros(pp));
|
|
Q = blkdiag(Q,H);
|
|
R = blkdiag(R,eye(pp));
|
|
Pstar = blkdiag(Pstar,H);
|
|
Pinf = blkdiag(Pinf,zeros(pp));
|
|
H1 = zeros(pp,1);
|
|
Zflag=1;
|
|
end
|
|
mmm = mm+pp;
|
|
if singularity_has_been_detected
|
|
a = zeros(mmm,1);
|
|
elseif ~expanded_state_vector_for_univariate_filter
|
|
a = [a; zeros(pp,1)];
|
|
end
|
|
end
|
|
end
|
|
if analytic_derivation
|
|
analytic_deriv_info{5}=DH;
|
|
end
|
|
[LIK, lik] = univariate_kalman_filter(DatasetInfo.missing.aindex,DatasetInfo.missing.number_of_observations,DatasetInfo.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,H1,Z,mmm,pp,rr,Zflag,diffuse_periods,analytic_deriv_info{:});
|
|
if analytic_derivation
|
|
LIK1=LIK;
|
|
LIK=LIK1{1};
|
|
lik1=lik;
|
|
lik=lik1{1};
|
|
end
|
|
if DynareOptions.lik_init==3
|
|
LIK = LIK+dLIK;
|
|
if analytic_derivation==0 && nargout>3
|
|
lik = [dlik; lik];
|
|
end
|
|
end
|
|
end
|
|
|
|
if analytic_derivation
|
|
if no_DLIK==0
|
|
DLIK = LIK1{2};
|
|
% [DLIK] = score(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,start,Z,kalman_tol,riccati_tol);
|
|
end
|
|
if full_Hess
|
|
Hess = -LIK1{3};
|
|
% [Hess, DLL] = get_Hessian(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P,start,Z,kalman_tol,riccati_tol);
|
|
% Hess0 = getHessian(Y,T,DT,D2T, R*Q*transpose(R),DOm,D2Om,Z,DYss,D2Yss);
|
|
end
|
|
if asy_Hess
|
|
% if ~((kalman_algo==2) || (kalman_algo==4)),
|
|
% [Hess] = AHessian(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,start,Z,kalman_tol,riccati_tol);
|
|
% else
|
|
Hess = LIK1{3};
|
|
% end
|
|
end
|
|
end
|
|
|
|
if isnan(LIK)
|
|
fval = Inf;
|
|
info(1) = 45;
|
|
info(4) = 0.1;
|
|
exit_flag = 0;
|
|
return
|
|
end
|
|
|
|
if imag(LIK)~=0
|
|
fval = Inf;
|
|
info(1) = 46;
|
|
info(4) = 0.1;
|
|
exit_flag = 0;
|
|
return
|
|
end
|
|
|
|
if isinf(LIK)~=0
|
|
fval = Inf;
|
|
info(1) = 50;
|
|
info(4) = 0.1;
|
|
exit_flag = 0;
|
|
return
|
|
end
|
|
|
|
likelihood = LIK;
|
|
|
|
% ------------------------------------------------------------------------------
|
|
% 5. Adds prior if necessary
|
|
% ------------------------------------------------------------------------------
|
|
if analytic_derivation
|
|
if full_Hess
|
|
[lnprior, dlnprior, d2lnprior] = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
|
|
Hess = Hess - d2lnprior;
|
|
else
|
|
[lnprior, dlnprior] = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
|
|
end
|
|
if no_DLIK==0
|
|
DLIK = DLIK - dlnprior';
|
|
end
|
|
if outer_product_gradient
|
|
dlik = lik1{2};
|
|
dlik=[- dlnprior; dlik(start:end,:)];
|
|
Hess = dlik'*dlik;
|
|
end
|
|
else
|
|
lnprior = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
|
|
end
|
|
|
|
if DynareOptions.endogenous_prior==1
|
|
if DynareOptions.lik_init==2 || DynareOptions.lik_init==3
|
|
error('Endogenous prior not supported with non-stationary models')
|
|
else
|
|
[lnpriormom] = endogenous_prior(Y,Pstar,BayesInfo,H);
|
|
fval = (likelihood-lnprior-lnpriormom);
|
|
end
|
|
else
|
|
fval = (likelihood-lnprior);
|
|
end
|
|
|
|
if DynareOptions.prior_restrictions.status
|
|
tmp = feval(DynareOptions.prior_restrictions.routine, Model, DynareResults, DynareOptions, DynareDataset, DatasetInfo);
|
|
fval = fval - tmp;
|
|
end
|
|
|
|
if isnan(fval)
|
|
fval = Inf;
|
|
info(1) = 47;
|
|
info(4) = 0.1;
|
|
exit_flag = 0;
|
|
return
|
|
end
|
|
|
|
if imag(fval)~=0
|
|
fval = Inf;
|
|
info(1) = 48;
|
|
info(4) = 0.1;
|
|
exit_flag = 0;
|
|
return
|
|
end
|
|
|
|
if ~DynareOptions.kalman.keep_kalman_algo_if_singularity_is_detected
|
|
% Update DynareOptions.kalman_algo.
|
|
DynareOptions.kalman_algo = kalman_algo;
|
|
end
|
|
|
|
if analytic_derivation==0 && nargout>3
|
|
lik=lik(start:end,:);
|
|
DLIK=[-lnprior; lik(:)];
|
|
end
|