irfmatching: add mode_compute_irf_matching function

matlab/+mom/mode_compute_irf_matching.m

+function [xparam1, hessian_xparam1, fval, mom_verbose] = mode_compute_irf_matching(xparam0, hessian_xparam0, objective_function, doBayesianEstimation, weighting_info, data_moments, options_mom_, M_, estim_params_, bayestopt_, BoundsInfo, dr, endo_steady_state, exo_steady_state, exo_det_steady_state)
+% [xparam1, hessian_xparam1, fval, mom_verbose] = mode_compute_irf_matching(xparam0, hessian_xparam0, objective_function, doBayesianEstimation, weighting_info, data_moments, options_mom_, M_, estim_params_, bayestopt_, BoundsInfo, dr, endo_steady_state, exo_steady_state, exo_det_steady_state)
+% -------------------------------------------------------------------------
+% Computes the minimum of the objective function (distance between data irfs
+% and model irfs) for a sequence of optimizers.
+% Note that we call a "mode" the minimum of the objective function, i.e.
+% the parameter vector that minimizes the distance between the irfs
+% computed from the model and the irfs computed from the data.
+% -------------------------------------------------------------------------
+% INPUTS
+% xparam0:               [vector]       initialized parameters
+% hessian_xparam0:       [matrix]       initialized hessian at xparam0
+% objective_function:    [func handle]  name of the objective function
+% doBayesianEstimation:  [logical]      true if Bayesian estimation
+% weighting_info:        [structure]    information on weighting matrix
+% data_moments:          [vector]       data moments
+% options_mom_:          [structure]    options
+% M_:                    [structure]    model information
+% estim_params_:         [structure]    information on estimated parameters
+% bayestopt_:            [structure]    information on priors
+% BoundsInfo:            [structure]    bounds for optimization
+% dr:                    [structure]    information reduced-form model
+% endo_steady_state:     [vector]       steady state of endogenous variables (initval)
+% exo_steady_state:      [vector]       steady state of exogenous variables (initval)
+% exo_det_steady_state:  [vector]       steady state of deterministic exogenous variables (initval)
+% -------------------------------------------------------------------------
+% OUTPUT
+% xparam1:               [vector]       mode of objective function
+% hessian_xparam1:       [matrix]       hessian at xparam1
+% fval:                  [double]       function value at mode
+% mom_verbose:           [structure]    information on intermediate estimation results
+% Also saves the computed mode and hessian to a file.
+% -------------------------------------------------------------------------
+% This function is called by
+%  o mom.run
+% -------------------------------------------------------------------------
+% This function calls
+%  o display_estimation_results_table
+%  o dynare_minimize_objective
+%  o hessian
+%  o mom.objective_function
+% -------------------------------------------------------------------------
+
+% Copyright © 2023 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 <https://www.gnu.org/licenses/>.
+
+
+mom_verbose = [];
+for optim_iter = 1:length(options_mom_.optimizer_vec)
+    options_mom_.current_optimizer = options_mom_.optimizer_vec{optim_iter};
+    if options_mom_.optimizer_vec{optim_iter}==0
+        % no minimization, evaluate objective at current values
+        xparam1 = xparam0;
+        hessian_xparam1 = hessian_xparam0;
+        fval = feval(objective_function, xparam1, data_moments, weighting_info, options_mom_, M_, estim_params_, bayestopt_, BoundsInfo, dr, endo_steady_state, exo_steady_state, exo_det_steady_state);
+    else
+        [xparam1, fval, exitflag, hessian_xparam1, options_mom_, Scale, new_rat_hess_info] = dynare_minimize_objective(objective_function, xparam0, options_mom_.optimizer_vec{optim_iter}, options_mom_, [BoundsInfo.lb BoundsInfo.ub], bayestopt_.name, bayestopt_, hessian_xparam0,...
+                                                                                                                       data_moments, weighting_info, options_mom_, M_, estim_params_, bayestopt_, BoundsInfo, dr, endo_steady_state, exo_steady_state, exo_det_steady_state);        
+    end
+    fprintf('\nMode Compute Iteration %d: Value of minimized moment distance objective function: %12.10f.\n',optim_iter,fval);
+    if options_mom_.mom.verbose
+        fprintf('\n''verbose'' option: ');
+        if options_mom_.cova_compute
+            if options_mom_.optimizer_vec{optim_iter}==0
+                hessian_xparam1_iter = hessian_xparam1;
+            else
+                fprintf('computing hessian');
+                hessian_xparam1_iter = hessian(objective_function, xparam1, options_mom_.gstep,...
+                                               data_moments, weighting_info, options_mom_, M_, estim_params_, bayestopt_, BoundsInfo, dr, endo_steady_state, exo_steady_state, exo_det_steady_state);
+                hessian_xparam1_iter = reshape(hessian_xparam1_iter, length(xparam1), length(xparam1));
+            end
+            hsd_iter = sqrt(diag(hessian_xparam1_iter));
+            invhessian_xparam1_iter = inv(hessian_xparam1_iter./(hsd_iter*hsd_iter'))./(hsd_iter*hsd_iter');
+            std_via_invhessian_xparam1_iter = sqrt(diag(invhessian_xparam1_iter));
+        else
+            std_via_invhessian_xparam1_iter = NaN(size(xparam1));
+        end
+        fprintf(' and displaying intermediate results.');
+        if doBayesianEstimation
+            tbl_title_iter = sprintf('BAYESIAN %s (OPTIM ITERATION %d) VERBOSE',strrep(options_mom_.mom.mom_method,'_',' '),optim_iter);
+            field_name_iter = sprintf('posterior_iter_%d',optim_iter);
+        else
+            tbl_title_iter = sprintf('FREQUENTIST %s (OPTIM ITERATION %d) VERBOSE',strrep(options_mom_.mom.mom_method,'_',' '),optim_iter);
+            field_name_iter = sprintf('iter_%d',optim_iter);
+        end
+        mom_verbose.(field_name_iter) = display_estimation_results_table(xparam1,std_via_invhessian_xparam1_iter,M_,options_mom_,estim_params_,bayestopt_,[],prior_dist_names,tbl_title_iter,field_name_iter);
+    end
+    xparam0 = xparam1;
+    hessian_xparam0 = hessian_xparam1;
+end
+
+if options_mom_.cova_compute
+    if options_mom_.mom.verbose
+        hessian_xparam1 = hessian_xparam1_iter;
+    else
+        fprintf('\nComputing Hessian at the mode.\n');
+        hessian_xparam1 = hessian(objective_function, xparam1, options_mom_.gstep,...
+                                  data_moments, weighting_info, options_mom_, M_, estim_params_, bayestopt_, BoundsInfo, dr, endo_steady_state, exo_steady_state, exo_det_steady_state);
+        hessian_xparam1 = reshape(hessian_xparam1, length(xparam1), length(xparam1));
+    end
+end
+parameter_names = bayestopt_.name;
+if options_mom_.cova_compute || options_mom_.mode_compute==5 || options_mom_.mode_compute==6
+    hh = hessian_xparam1;
+    save([M_.dname filesep 'method_of_moments' filesep M_.fname '_mode.mat'],'xparam1','hh','parameter_names','fval');
+else
+    save([M_.dname filesep 'method_of_moments' filesep M_.fname '_mode.mat'],'xparam1','parameter_names','fval');
+end
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