112 lines
6.9 KiB
Matlab
112 lines
6.9 KiB
Matlab
function out = numerical_objective(params, outputflag, estim_params_, M_, options_, indpmodel, indpstderr, indvar, useautocorr, nlags, grid_nbr, dr, steady_state, exo_steady_state, exo_det_steady_state)
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% out = numerical_objective(params, outputflag, estim_params_, M_, options_, indpmodel, indpstderr, indvar, useautocorr, nlags, grid_nbr, dr, steady_state, exo_steady_state, exo_det_steady_state)
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% -------------------------------------------------------------------------
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% Objective function to compute numerically the Jacobians used for identification analysis
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% Previously this function was called thet2tau.m
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% =========================================================================
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% INPUTS
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% params: [vector] parameter values at which to evaluate objective function
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% stderr parameters come first, corr parameters second, model parameters third
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% outputflag: [integer] flag which objective to compute (see below)
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% estim_params_: [structure] storing the estimation information
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% M_: [structure] storing the model information
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% options_: [structure] storing the options
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% indpmodel: [vector] Index of model parameters
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% indpstderr: [vector] Index of stderr parameters
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% indvar: [vector] Index of selected or observed variables
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% dr [structure] Reduced form model.
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% endo_steady_state [vector] steady state value for endogenous variables
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% exo_steady_state [vector] steady state value for exogenous variables
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% exo_det_steady_state [vector] steady state value for exogenous deterministic variables
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% -------------------------------------------------------------------------
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% OUTPUTS
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% out: dependent on outputflag
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% * 0: out = [Yss; vec(A); vec(B); dyn_vech(Sig_e)]; of indvar variables only, in DR order. This is needed to compute dTAU and Komunjer and Ng's D.
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% Note that Jacobian of Om is computed in identification.get_jacobians.m (previously getJJ.m) or get_first_order_solution_params_deriv.m (previously getH.m) from Jacobian of B and Sigma_e, because this is more efficient due to some testing with analytical derivatives from An and Schorfheide model
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% * 1: out = [vech(cov(Y_t,Y_t)); vec(cov(Y_t,Y_{t-1}); ...; vec(cov(Y_t,Y_{t-nlags})] of indvar variables, in DR order. This is needed to compute Iskrev's J.
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% * 2: out = vec(spectral density) with dimension [var_nbr^2*grid_nbr,1] Spectral density of indvar variables evaluated at (grid_nbr/2+1) discretized points in the interval [0;pi]. This is needed for Qu and Tkachenko's G.
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% * -1: out = g1(:); of all variables, in DR order. This is needed to compute dLRE.
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% * -2: out = [Yss; vec(A); dyn_vech(B*Sigma_e*B')]; of indvar variables only, in DR order. This is used to compute numerically second derivatives d2A, d2Om d2Yss in get_first_order_solution_params_deriv.m (previously getH.m) for kronflag=1
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% where Yss is steady in DR order, A and B solution matrices of Kalman
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% transition equation, Sig_e the covariance of exogenous shocks, g1 the
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% Jacobian of the dynamic model equations, and Y_t selected variables
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% -------------------------------------------------------------------------
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% This function is called by
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% * identification.get_jacobians.m (previously getJJ.m)
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% -------------------------------------------------------------------------
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% This function calls
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% * [M_.fname,'.dynamic']
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% * dyn_vech
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% * resol
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% * vec
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% =========================================================================
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% Copyright © 2011-2020 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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%% Update stderr, corr and model parameters
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%note that if no estimated_params_block is given, then all stderr and model parameters are selected but no corr parameters
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if length(params) > length(indpmodel)
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if isempty(indpstderr)==0 && isempty(estim_params_.var_exo) %if there are stderr parameters but no estimated_params_block
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%provide temporary necessary information for stderr parameters
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estim_params_.nvx = length(indpstderr);
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estim_params_.var_exo = indpstderr';
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end
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if isempty(indpmodel)==0 && isempty(estim_params_.param_vals) %if there are model parameters but no estimated_params_block
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%provide temporary necessary information for model parameters
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estim_params_.np = length(indpmodel);
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estim_params_.param_vals = indpmodel';
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end
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M_ = set_all_parameters(params,estim_params_,M_); %this function can only be used if there is some information in estim_params_
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else
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%if there are only model parameters, we don't need to use set_all_parameters
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M_.params(indpmodel) = params;
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end
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%% compute Kalman transition matrices and steady state with updated parameters
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[dr,info,M_.params] = compute_decision_rules(M_,options_,dr, steady_state, exo_steady_state, exo_det_steady_state);
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options_ = rmfield(options_,'options_ident');
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pruned = pruned_SS.pruned_state_space_system(M_, options_, dr, indvar, nlags, useautocorr, 0);
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%% out = [vech(cov(Y_t,Y_t)); vec(cov(Y_t,Y_{t-1}); ...; vec(cov(Y_t,Y_{t-nlags})] of indvar variables, in DR order. This is Iskrev (2010)'s J matrix.
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if outputflag == 1
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out = dyn_vech(pruned.Var_y);
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for i = 1:nlags
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if useautocorr
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out = [out;vec(pruned.Corr_yi(:,:,i))];
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else
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out = [out;vec(pruned.Var_yi(:,:,i))];
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end
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end
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end
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%% out = vec(g_omega). This is needed for Qu and Tkachenko (2012)'s G matrix.
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if outputflag == 2
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% This computes the spectral density g_omega where the interval [-pi;\pi] is discretized by grid_nbr points
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freqs = (0 : pi/(grid_nbr/2):pi);% we focus only on positive values including the 0 frequency
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tpos = exp( sqrt(-1)*freqs); %Fourier frequencies
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IA = eye(size(pruned.A,1));
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var_nbr = size(pruned.C,1);
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out = zeros(var_nbr^2*length(freqs),1);
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kk = 0;
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for ig = 1:length(freqs)
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Transferfct = pruned.D + pruned.C*((tpos(ig)*IA-pruned.A)\pruned.B);
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g_omega = (1/(2*pi))*(Transferfct*pruned.Varinov*Transferfct'); % note that ' is the conjugate transpose
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kk = kk+1;
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out(1 + (kk-1)*var_nbr^2 : kk*var_nbr^2) = g_omega(:);
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end
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end |