302 lines
16 KiB
Matlab
302 lines
16 KiB
Matlab
function [fval, info, exit_flag, df, junk1, oo_, M_, options_mom_] = objective_function(xparam1, Bounds, oo_, estim_params_, M_, options_mom_)
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% [fval, info, exit_flag, df, junk1, oo_, M_, options_mom_] = objective_function(xparam1, Bounds, oo_, estim_params_, M_, options_mom_)
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% -------------------------------------------------------------------------
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% This function evaluates the objective function for GMM/SMM estimation
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% =========================================================================
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% INPUTS
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% o xparam1: current value of estimated parameters as returned by set_prior()
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% o Bounds: structure containing parameter bounds
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% o oo_: structure for results
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% o estim_params_: structure describing the estimated_parameters
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% o M_ structure describing the model
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% o options_mom_: structure information about all settings (specified by the user, preprocessor, and taken from global options_)
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% -------------------------------------------------------------------------
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% OUTPUTS
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% o fval: value of the quadratic form of the moment difference (except for lsqnonlin, where this is done implicitly)
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% o info: vector storing error code and penalty
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% o exit_flag: 0 if error, 1 if no error
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% o df: analytical parameter Jacobian of the quadratic form of the moment difference (for GMM only)
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% o junk1: empty matrix required for optimizer interface (Hessian would go here)
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% o oo_: structure containing the results with the following updated fields:
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% - mom.model_moments [numMom x 1] vector with model moments
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% - mom.Q value of the quadratic form of the moment difference
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% - mom.model_moments_params_derivs
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% [numMom x numParams] Jacobian matrix of derivatives of model_moments with respect to estimated parameters
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% (only for GMM with analytical derivatives)
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% o M_: Matlab's structure describing the model
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% o options_mom_: structure information about all settings (specified by the user, preprocessor, and taken from global options_)
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% -------------------------------------------------------------------------
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% This function is called by
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% o mom.run.m
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% o dynare_minimize_objective.m
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% -------------------------------------------------------------------------
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% This function calls
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% o check_bounds_and_definiteness_estimation
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% o pruned_state_space_system
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% o resol
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% o set_all_parameters
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% =========================================================================
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% Copyright © 2020-2021 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 <https://www.gnu.org/licenses/>.
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% -------------------------------------------------------------------------
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% Author(s):
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% o Willi Mutschler (willi@mutschler.eu)
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% o Johannes Pfeifer (jpfeifer@uni-koeln.de)
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% =========================================================================
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%------------------------------------------------------------------------------
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% 0. Initialization of the returned variables and others...
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%------------------------------------------------------------------------------
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if options_mom_.mom.compute_derivs && options_mom_.mom.analytic_jacobian
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if options_mom_.vector_output == 1
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if options_mom_.mom.penalized_estimator
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df = nan(size(oo_.mom.data_moments,1)+length(xparam1),length(xparam1));
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else
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df = nan(size(oo_.mom.data_moments,1),length(xparam1));
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end
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else
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df = nan(1,length(xparam1));
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end
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else
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df=[]; %required to be empty by e.g. newrat
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end
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junk1 = [];
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junk2 = [];
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%--------------------------------------------------------------------------
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% 1. Get the structural parameters & define penalties
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%--------------------------------------------------------------------------
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% Ensure that xparam1 is a column vector; particleswarm.m requires this.
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xparam1 = xparam1(:);
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M_ = set_all_parameters(xparam1, estim_params_, M_);
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[fval,info,exit_flag]=check_bounds_and_definiteness_estimation(xparam1, M_, estim_params_, Bounds);
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if info(1)
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if options_mom_.vector_output == 1 % lsqnonlin requires vector output
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fval = ones(size(oo_.mom.data_moments,1),1)*options_mom_.huge_number;
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end
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return
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end
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%--------------------------------------------------------------------------
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% 2. call resol to compute steady state and model solution
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%--------------------------------------------------------------------------
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% Compute linear approximation around the deterministic steady state
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[dr, info, M_, oo_] = resol(0, M_, options_mom_, oo_);
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% Return, with endogenous penalty when possible, if resol issues an error code
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if info(1)
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if info(1) == 3 || info(1) == 4 || info(1) == 5 || info(1)==6 ||info(1) == 19 ||...
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info(1) == 20 || info(1) == 21 || info(1) == 23 || info(1) == 26 || ...
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info(1) == 81 || info(1) == 84 || info(1) == 85 || info(1) == 86
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%meaningful second entry of output that can be used
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fval = Inf;
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info(4) = info(2);
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exit_flag = 0;
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if options_mom_.vector_output == 1 % lsqnonlin requires vector output
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fval = ones(size(oo_.mom.data_moments,1),1)*options_mom_.huge_number;
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end
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return
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else
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fval = Inf;
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info(4) = 0.1;
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exit_flag = 0;
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if options_mom_.vector_output == 1 % lsqnonlin requires vector output
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fval = ones(size(oo_.mom.data_moments,1),1)*options_mom_.huge_number;
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end
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return
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end
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end
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if strcmp(options_mom_.mom.mom_method,'GMM')
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%--------------------------------------------------------------------------
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% 3. Set up pruned state-space system and compute model moments
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%--------------------------------------------------------------------------
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if options_mom_.mom.compute_derivs && ( options_mom_.mom.analytic_standard_errors || options_mom_.mom.analytic_jacobian )
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indpmodel = []; %initialize index for model parameters
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if ~isempty(estim_params_.param_vals)
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indpmodel = estim_params_.param_vals(:,1); %values correspond to parameters declaration order, row number corresponds to order in estimated_params
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end
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indpstderr=[]; %initialize index for stderr parameters
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if ~isempty(estim_params_.var_exo)
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indpstderr = estim_params_.var_exo(:,1); %values correspond to varexo declaration order, row number corresponds to order in estimated_params
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end
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indpcorr=[]; %initialize matrix for corr paramters
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if ~isempty(estim_params_.corrx)
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indpcorr = estim_params_.corrx(:,1:2); %values correspond to varexo declaration order, row number corresponds to order in estimated_params
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end
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if estim_params_.nvn || estim_params_.ncn %nvn is number of stderr parameters and ncn is number of corr parameters of measurement innovations as declared in estimated_params
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error('Analytic computation of standard errrors does not (yet) support measurement errors.\nInstead, define them explicitly as varexo and provide measurement equations in the model definition.\nAlternatively, use numerical standard errors.')
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end
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modparam_nbr = estim_params_.np; % number of model parameters as declared in estimated_params
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stderrparam_nbr = estim_params_.nvx; % number of stderr parameters
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corrparam_nbr = estim_params_.ncx; % number of corr parameters
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totparam_nbr = stderrparam_nbr+corrparam_nbr+modparam_nbr;
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dr.derivs = get_perturbation_params_derivs(M_, options_mom_, estim_params_, oo_, indpmodel, indpstderr, indpcorr, 0); %analytic derivatives of perturbation matrices
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oo_.mom.model_moments_params_derivs = NaN(options_mom_.mom.mom_nbr,totparam_nbr);
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pruned_state_space = pruned_state_space_system(M_, options_mom_, dr, oo_.dr.obs_var, options_mom_.ar, 0, 1);
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else
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pruned_state_space = pruned_state_space_system(M_, options_mom_, dr, oo_.dr.obs_var, options_mom_.ar, 0, 0);
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end
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oo_.mom.model_moments = NaN(options_mom_.mom.mom_nbr,1);
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for jm = 1:size(M_.matched_moments,1)
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% First moments
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if ~options_mom_.prefilter && (sum(M_.matched_moments{jm,3}) == 1)
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idx1 = (oo_.dr.obs_var == find(oo_.dr.order_var==M_.matched_moments{jm,1}) );
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oo_.mom.model_moments(jm,1) = pruned_state_space.E_y(idx1);
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if options_mom_.mom.compute_derivs && ( options_mom_.mom.analytic_standard_errors || options_mom_.mom.analytic_jacobian )
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oo_.mom.model_moments_params_derivs(jm,:) = pruned_state_space.dE_y(idx1,:);
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end
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end
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% Second moments
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if (sum(M_.matched_moments{jm,3}) == 2)
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idx1 = (oo_.dr.obs_var == find(oo_.dr.order_var==M_.matched_moments{jm,1}(1)) );
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idx2 = (oo_.dr.obs_var == find(oo_.dr.order_var==M_.matched_moments{jm,1}(2)) );
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if nnz(M_.matched_moments{jm,2}) == 0
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% Covariance
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if options_mom_.prefilter
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oo_.mom.model_moments(jm,1) = pruned_state_space.Var_y(idx1,idx2);
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if options_mom_.mom.compute_derivs && ( options_mom_.mom.analytic_standard_errors || options_mom_.mom.analytic_jacobian )
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oo_.mom.model_moments_params_derivs(jm,:) = pruned_state_space.dVar_y(idx1,idx2,:);
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end
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else
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oo_.mom.model_moments(jm,1) = pruned_state_space.Var_y(idx1,idx2) + pruned_state_space.E_y(idx1)*pruned_state_space.E_y(idx2)';
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if options_mom_.mom.compute_derivs && ( options_mom_.mom.analytic_standard_errors || options_mom_.mom.analytic_jacobian )
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for jp=1:totparam_nbr
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oo_.mom.model_moments_params_derivs(jm,jp) = pruned_state_space.dVar_y(idx1,idx2,jp) + pruned_state_space.dE_y(idx1,jp)*pruned_state_space.E_y(idx2)' + pruned_state_space.E_y(idx1)*pruned_state_space.dE_y(idx2,jp)';
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end
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end
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end
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else
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% Autocovariance
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lag = -M_.matched_moments{jm,2}(2); %note that leads/lags in matched_moments are transformed such that first entry is always 0 and the second is a lag
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if options_mom_.prefilter
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oo_.mom.model_moments(jm,1) = pruned_state_space.Var_yi(idx1,idx2,lag);
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if options_mom_.mom.compute_derivs && ( options_mom_.mom.analytic_standard_errors || options_mom_.mom.analytic_jacobian )
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oo_.mom.model_moments_params_derivs(jm,:) = pruned_state_space.dVar_yi(idx1,idx2,lag,:);
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end
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else
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oo_.mom.model_moments(jm,1) = pruned_state_space.Var_yi(idx1,idx2,lag) + pruned_state_space.E_y(idx1)*pruned_state_space.E_y(idx2)';
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if options_mom_.mom.compute_derivs && ( options_mom_.mom.analytic_standard_errors || options_mom_.mom.analytic_jacobian )
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for jp=1:totparam_nbr
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oo_.mom.model_moments_params_derivs(jm,jp) = vec( pruned_state_space.dVar_yi(idx1,idx2,lag,jp) + pruned_state_space.dE_y(idx1,jp)*pruned_state_space.E_y(idx2)' + pruned_state_space.E_y(idx1)*pruned_state_space.dE_y(idx2,jp)');
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end
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end
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end
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end
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end
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end
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elseif strcmp(options_mom_.mom.mom_method,'SMM')
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%------------------------------------------------------------------------------
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% 3. Compute Moments of the model solution for normal innovations
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%------------------------------------------------------------------------------
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% create shock series with correct covariance matrix from iid standard normal shocks
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i_exo_var = setdiff(1:M_.exo_nbr, find(diag(M_.Sigma_e) == 0 )); %find singular entries in covariance
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chol_S = chol(M_.Sigma_e(i_exo_var,i_exo_var));
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scaled_shock_series = zeros(size(options_mom_.mom.shock_series)); %initialize
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scaled_shock_series(:,i_exo_var) = options_mom_.mom.shock_series(:,i_exo_var)*chol_S; %set non-zero entries
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% simulate series
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y_sim = simult_(M_, options_mom_, dr.ys, dr, scaled_shock_series, options_mom_.order);
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% provide meaningful penalty if data is nan or inf
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if any(any(isnan(y_sim))) || any(any(isinf(y_sim)))
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if options_mom_.vector_output == 1 % lsqnonlin requires vector output
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fval = Inf(size(oo_.mom.Sw,1),1);
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else
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fval = Inf;
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end
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info(1)=180;
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info(4) = 0.1;
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exit_flag = 0;
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if options_mom_.vector_output == 1 % lsqnonlin requires vector output
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fval = ones(size(oo_.mom.data_moments,1),1)*options_mom_.huge_number;
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end
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return
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end
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% Remove burn-in and focus on observables (note that y_sim is in declaration order)
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y_sim = y_sim(oo_.dr.order_var(oo_.dr.obs_var) , end-options_mom_.mom.long+1:end)';
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if ~all(diag(M_.H)==0)
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i_ME = setdiff([1:size(M_.H,1)],find(diag(M_.H) == 0)); % find ME with 0 variance
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chol_S = chol(M_.H(i_ME,i_ME)); %decompose rest
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shock_mat=zeros(size(options_mom_.mom.ME_shock_series)); %initialize
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shock_mat(:,i_ME)=options_mom_.mom.ME_shock_series(:,i_ME)*chol_S;
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y_sim = y_sim+shock_mat;
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end
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% Remove mean if centered moments
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if options_mom_.prefilter
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y_sim = bsxfun(@minus, y_sim, mean(y_sim,1));
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end
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oo_.mom.model_moments = mom.data_moments(y_sim, oo_, M_.matched_moments, options_mom_);
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end
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%--------------------------------------------------------------------------
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% 4. Compute quadratic target function
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%--------------------------------------------------------------------------
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moments_difference = oo_.mom.data_moments - oo_.mom.model_moments;
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residuals = sqrt(options_mom_.mom.weighting_matrix_scaling_factor)*oo_.mom.Sw*moments_difference;
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oo_.mom.Q = residuals'*residuals;
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if options_mom_.vector_output == 1 % lsqnonlin requires vector output
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fval = residuals;
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if options_mom_.mom.penalized_estimator
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fval=[fval;(xparam1-oo_.prior.mean)./sqrt(diag(oo_.prior.variance))];
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end
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else
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fval = oo_.mom.Q;
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if options_mom_.mom.penalized_estimator
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fval=fval+(xparam1-oo_.prior.mean)'/oo_.prior.variance*(xparam1-oo_.prior.mean);
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end
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end
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if options_mom_.mom.compute_derivs && options_mom_.mom.analytic_jacobian
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if options_mom_.mom.penalized_estimator
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dxparam1 = eye(length(xparam1));
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end
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for jp=1:length(xparam1)
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dmoments_difference = - oo_.mom.model_moments_params_derivs(:,jp);
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dresiduals = sqrt(options_mom_.mom.weighting_matrix_scaling_factor)*oo_.mom.Sw*dmoments_difference;
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if options_mom_.vector_output == 1 % lsqnonlin requires vector output
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if options_mom_.mom.penalized_estimator
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df(:,jp)=[dresiduals;dxparam1(:,jp)./sqrt(diag(oo_.prior.variance))];
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else
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df(:,jp) = dresiduals;
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end
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else
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df(:,jp) = dresiduals'*residuals + residuals'*dresiduals;
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if options_mom_.mom.penalized_estimator
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df(:,jp)=df(:,jp)+(dxparam1(:,jp))'/oo_.prior.variance*(xparam1-oo_.prior.mean)+(xparam1-oo_.prior.mean)'/oo_.prior.variance*(dxparam1(:,jp));
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end
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end
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end
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end
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end%main function end
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