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Identification: use the sparse representation of the static model

dprior
Sébastien Villemot 2024-02-06 17:38:16 +01:00
parent a623cb1d12
commit 641cf6a95c
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1 changed files with 7 additions and 5 deletions
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12
matlab/+identification/get_perturbation_params_derivs.m
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@ -93,7 +93,8 @@ function DERIVS = get_perturbation_params_derivs(M_, options_, estim_params_, dr
% This function calls
% * [fname,'.dynamic']
% * [fname,'.dynamic_params_derivs']
% * [fname,'.static']
% * [fname,'.sparse.static_g1']
% * [fname,'.sparse.static_g2']
% * [fname,'.static_params_derivs']
% * commutation
% * dyn_vech
@ -109,7 +110,7 @@ function DERIVS = get_perturbation_params_derivs(M_, options_, estim_params_, dr
% * sylvester3a
% * get_perturbation_params_derivs_numerical_objective
% =========================================================================
% Copyright © 2019-2020 Dynare Team
% Copyright © 2019-2024 Dynare Team
%
% This file is part of Dynare.
%
@ -454,12 +455,13 @@ elseif (analytic_derivation_mode == 0 || analytic_derivation_mode == 1)
error('For analytical parameter derivatives ''dynamic_params_derivs.m'' file is needed, this can be created by putting identification(order=%d) into your mod file.',order)
end
%% Analytical computation of Jacobian and Hessian (wrt selected model parameters) of steady state, i.e. dYss and d2Yss
[~, g1_static] = feval([fname,'.static'], ys, exo_steady_state', params); %g1_static is [endo_nbr by endo_nbr] first-derivative (wrt all endogenous variables) of static model equations f, i.e. df/dys, in declaration order
[g1_static, T_order_static, T_static] = feval([fname,'.sparse.static_g1'], ys, exo_steady_state', params, M_.static_g1_sparse_rowval, M_.static_g1_sparse_colval, M_.static_g1_sparse_colptr); %g1_static is [endo_nbr by endo_nbr] first-derivative (wrt all endogenous variables) of static model equations f, i.e. df/dys, in declaration order
rp_static = feval([fname,'.static_params_derivs'], ys, exo_steady_state', params); %rp_static is [endo_nbr by param_nbr] first-derivative (wrt all model parameters) of static model equations f, i.e. df/dparams, in declaration order
dys = -g1_static\rp_static; %use implicit function theorem (equation 5 of Ratto and Iskrev (2012) to compute [endo_nbr by param_nbr] first-derivative (wrt all model parameters) of steady state for all endogenous variables analytically, note that dys is in declaration order
d2ys = zeros(endo_nbr, param_nbr, param_nbr); %initialize in tensor notation, note that d2ys is only needed for d2flag, i.e. for g1pp
if d2flag
[~, ~, g2_static] = feval([fname,'.static'], ys, exo_steady_state', params); %g2_static is [endo_nbr by endo_nbr^2] second derivative (wrt all endogenous variables) of static model equations f, i.e. d(df/dys)/dys, in declaration order
g2_static_v = feval([fname,'.sparse.static_g2'], ys, exo_steady_state', params, T_order_static, T_static);
g2_static = build_two_dim_hessian(M_.static_g2_sparse_indices, g2_static_v, endo_nbr, endo_nbr); %g2_static is [endo_nbr by endo_nbr^2] second derivative (wrt all endogenous variables) of static model equations f, i.e. d(df/dys)/dys, in declaration order
if order < 3
[~, g1, g2, g3] = feval([fname,'.dynamic'], ys(I), exo_steady_state', params, ys, 1); %note that g3 does not contain symmetric elements
g3 = identification.unfold_g3(g3, yy0ex0_nbr); %add symmetric elements to g3
@ -505,7 +507,7 @@ elseif (analytic_derivation_mode == 0 || analytic_derivation_mode == 1)
end
%handling of steady state for nonstationary variables
if any(any(isnan(dys)))
[U,T] = schur(g1_static);
[U,T] = schur(full(g1_static));
e1 = abs(ordeig(T)) < qz_criterium-1;
k = sum(e1); % Number of non stationary variables.
% Number of stationary variables: n = length(e1)-k