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