119 lines
5.8 KiB
Matlab
119 lines
5.8 KiB
Matlab
function [SE_values, Asympt_Var] = standard_errors(xparam, objective_function, Bounds, oo_, estim_params_, M_, options_mom_, Wopt_flag)
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% [SE_values, Asympt_Var] = standard_errors(xparam, objective_function, Bounds, oo_, estim_params_, M_, options_mom_, Wopt_flag)
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% -------------------------------------------------------------------------
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% This function computes standard errors to the method of moments estimates
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% Adapted from replication codes of
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% o Andreasen, Fernández-Villaverde, Rubio-Ramírez (2018): "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications", Review of Economic Studies, 85(1):1-49.
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% =========================================================================
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% INPUTS
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% o xparam: value of estimated parameters as returned by set_prior()
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% o objective_function string of objective function
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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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% o Wopt_flag: indicator whether the optimal weighting is actually used
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% -------------------------------------------------------------------------
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% OUTPUTS
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% o SE_values [nparam x 1] vector of standard errors
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% o Asympt_Var [nparam x nparam] asymptotic covariance matrix
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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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% -------------------------------------------------------------------------
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% This function calls:
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% o get_the_name
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% o get_error_message
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% o mom.objective_function
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% o mom.optimal_weighting_matrix
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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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% Some dimensions
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num_mom = size(oo_.mom.model_moments,1);
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dim_params = size(xparam,1);
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D = zeros(num_mom,dim_params);
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eps_value = options_mom_.mom.se_tolx;
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if strcmp(options_mom_.mom.mom_method,'GMM') && options_mom_.mom.analytic_standard_errors
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fprintf('\nComputing standard errors using analytical derivatives of moments\n');
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D = oo_.mom.model_moments_params_derivs; %already computed in objective function via get_perturbation_params.m
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idx_nan = find(any(isnan(D)));
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if any(idx_nan)
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for i = idx_nan
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fprintf('No standard errors available for parameter %s\n',get_the_name(i,options_mom_.TeX, M_, estim_params_, options_mom_))
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end
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warning('There are NaN in the analytical Jacobian of Moments. Check your bounds and/or priors, or use a different optimizer.')
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Asympt_Var = NaN(length(xparam),length(xparam));
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SE_values = NaN(length(xparam),1);
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return
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end
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else
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fprintf('\nComputing standard errors using numerical derivatives of moments\n');
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for i=1:dim_params
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%Positive step
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xparam_eps_p = xparam;
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xparam_eps_p(i,1) = xparam_eps_p(i) + eps_value;
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[~, info_p, ~, ~,~, oo__p] = feval(objective_function, xparam_eps_p, Bounds, oo_, estim_params_, M_, options_mom_);
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% Negative step
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xparam_eps_m = xparam;
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xparam_eps_m(i,1) = xparam_eps_m(i) - eps_value;
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[~, info_m, ~, ~,~, oo__m] = feval(objective_function, xparam_eps_m, Bounds, oo_, estim_params_, M_, options_mom_);
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% The Jacobian:
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if nnz(info_p)==0 && nnz(info_m)==0
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D(:,i) = (oo__p.mom.model_moments - oo__m.mom.model_moments)/(2*eps_value);
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else
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problpar = get_the_name(i,options_mom_.TeX, M_, estim_params_, options_mom_);
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message_p = get_error_message(info_p, options_mom_);
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message_m = get_error_message(info_m, options_mom_);
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warning('method_of_moments:info','Cannot compute the Jacobian for parameter %s - no standard errors available\n %s %s\nCheck your bounds and/or priors, or use a different optimizer.\n',problpar, message_p, message_m)
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Asympt_Var = NaN(length(xparam),length(xparam));
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SE_values = NaN(length(xparam),1);
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return
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end
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end
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end
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T = options_mom_.nobs; %Number of observations
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if isfield(options_mom_,'variance_correction_factor')
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T = T*options_mom_.variance_correction_factor;
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end
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WW = oo_.mom.Sw'*oo_.mom.Sw;
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if Wopt_flag
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% We have the optimal weighting matrix
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Asympt_Var = 1/T*((D'*WW*D)\eye(dim_params));
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else
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% We do not have the optimal weighting matrix yet
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WWopt = mom.optimal_weighting_matrix(oo_.mom.m_data, oo_.mom.model_moments, options_mom_.mom.bartlett_kernel_lag);
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S = WWopt\eye(size(WWopt,1));
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AA = (D'*WW*D)\eye(dim_params);
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Asympt_Var = 1/T*AA*D'*WW*S*WW*D*AA;
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end
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SE_values = sqrt(diag(Asympt_Var));
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