64 lines
3.6 KiB
Matlab
64 lines
3.6 KiB
Matlab
function var_decomp=compute_variance_decomposition(M_,options_,var_stationary,A,A_stationary,ghu,ghu_states_only,stationary_vars,index_stationary_vars,nvars_requested)
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% function var_decomp=compute_variance_decomposition(M_,options_,var_stationary,A,A_stationary,ghu,ghu_states_only,stationary_vars,index_stationary_vars,nvars_requested)
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% Computes the theoretical auto-covariances, Gamma_y, for an AR(p) process
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% with coefficients dr.ghx and dr.ghu and shock variances Sigma_e
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% for a subset of variables ivar.
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% Theoretical HP-filtering and band-pass filtering is available as an option
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%
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% INPUTS
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% M_ [structure] Global dynare's structure, description of the DSGE model.
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% options_ [structure] Global dynare's structure.
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% var_stationary [double] unconditional variance of stationary
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% variables
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% A [double] State transition matrix
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% A_stationary [double] Reaction of stationary variables to states
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% ghu [double] Reaction of variables to shocks
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% ghu_states_only [double] Reaction of stationary variables to shocks
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% stationary_vars [integer] index of stationary vars in requested output
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% index_stationary_vars [integer] index of stationary vars in decision rules
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% nvars_requested [integer] number of originally requested variables
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%
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% OUTPUTS
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% stationary_vars [double] [#stationary vars by shocks] Matrix containing the variance decomposition
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%
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% Copyright © 2001-2023 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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if M_.exo_nbr == 1
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var_decomp = ones(size(ghu,1),1);
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else
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var_decomp = NaN(nvars_requested,M_.exo_nbr);
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cs = get_lower_cholesky_covariance(M_.Sigma_e,options_.add_tiny_number_to_cholesky);
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b1 = ghu_states_only*cs;
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b2 = ghu(index_stationary_vars,:)*cs;
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variance_sum_loop = 0;
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for i=1:M_.exo_nbr
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if i==1 % first time, do Schur decomposition
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variance_states = lyapunov_symm(A,b1(:,i)*b1(:,i)',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,1,options_.debug);
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else
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variance_states = lyapunov_symm(A,b1(:,i)*b1(:,i)',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,2,options_.debug);
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end
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vx2 = diag(A_stationary*variance_states*A_stationary'+b2(:,i)*b2(:,i)');
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var_decomp(stationary_vars,i) = vx2;
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variance_sum_loop = variance_sum_loop +vx2; %track overall variance over shocks
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end
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if ~options_.pruning && max(abs(variance_sum_loop-var_stationary)./var_stationary) > 1e-4 && max(abs(variance_sum_loop-var_stationary))>1e-7
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warning(['Aggregate variance and sum of variances by shocks ' ...
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'differ by more than 0.01 %'])
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end
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var_decomp(stationary_vars,:) = var_decomp(stationary_vars,:)./repmat(variance_sum_loop,1,M_.exo_nbr);
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end |