705 lines
30 KiB
Matlab
705 lines
30 KiB
Matlab
function [dr,info,M_,options_,oo_] = dr_block(dr,task,M_,options_,oo_,varargin)
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% function [dr,info,M_,options_,oo_] = dr_block(dr,task,M_,options_,oo_,varargin)
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% computes the reduced form solution of a rational expectations model
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% (first order approximation of the stochastic model around the deterministic steady state).
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%
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% INPUTS
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% dr [matlab structure] Decision rules for stochastic simulations.
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% task [integer] if task = 0 then dr_block computes decision rules.
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% if task = 1 then dr_block computes eigenvalues.
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% M_ [matlab structure] Definition of the model.
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% options_ [matlab structure] Global options.
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% oo_ [matlab structure] Results
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% oo_ [matlab cell] Other input arguments
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%
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% OUTPUTS
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% dr [matlab structure] Decision rules for stochastic simulations.
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% info [integer] info=1: the model doesn't define current variables uniquely
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% info=2: problem in mjdgges.dll info(2) contains error code.
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% info=3: BK order condition not satisfied info(2) contains "distance"
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% absence of stable trajectory.
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% info=4: BK order condition not satisfied info(2) contains "distance"
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% indeterminacy.
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% info=5: BK rank condition not satisfied.
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% info=6: The jacobian matrix evaluated at the steady state is complex.
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% M_ [matlab structure]
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% options_ [matlab structure]
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% oo_ [matlab structure]
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%
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% ALGORITHM
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% first order block relaxation method applied to the model
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% E[A Yt-1 + B Yt + C Yt+1 + ut] = 0
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%
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% SPECIAL REQUIREMENTS
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% none.
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%
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% Copyright (C) 2010-2020 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 <http://www.gnu.org/licenses/>.
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info = 0;
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verbose = 0;
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if nargin > 5
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verbose = varargin{1};
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end
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%verbose = options_.verbosity;
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if options_.order > 1
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error('2nd and 3rd order approximation not implemented with block option')
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end
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z = repmat(dr.ys,1,M_.maximum_lead + M_.maximum_lag + 1);
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zx = repmat([oo_.exo_simul oo_.exo_det_simul],M_.maximum_lead + M_.maximum_lag + 1, 1);
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if (isfield(M_,'block_structure'))
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data = M_.block_structure.block;
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Size = length(M_.block_structure.block);
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else
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data = M_;
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Size = 1;
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end
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if (options_.bytecode)
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[zz, data]= bytecode('dynamic','evaluate', z, zx, M_.params, dr.ys, 1, data);
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else
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[r, data] = feval([M_.fname '.dynamic'], options_, M_, oo_, z', zx, M_.params, dr.ys, M_.maximum_lag+1, data);
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end
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dr.full_rank = 1;
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dr.eigval = [];
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dr.nd = 0;
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dr.ghx = [];
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dr.ghu = [];
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%Determine the global list of state variables:
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dr.state_var = M_.state_var;
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M_.block_structure.state_var = dr.state_var;
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n_sv = size(dr.state_var, 2);
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dr.ghx = zeros(M_.endo_nbr, length(dr.state_var));
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dr.exo_var = 1:M_.exo_nbr;
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dr.ghu = zeros(M_.endo_nbr, M_.exo_nbr);
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for i = 1:Size
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ghx = [];
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indexi_0 = 0;
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if (verbose)
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disp('======================================================================');
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disp(['Block ' int2str(i)]);
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disp('-----------');
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data(i)
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end
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n_pred = data(i).n_backward;
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n_fwrd = data(i).n_forward;
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n_both = data(i).n_mixed;
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n_static = data(i).n_static;
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nd = n_pred + n_fwrd + 2*n_both;
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dr.nd = dr.nd + nd;
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n_dynamic = n_pred + n_fwrd + n_both;
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exo_nbr = M_.block_structure.block(i).exo_nbr;
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exo_det_nbr = M_.block_structure.block(i).exo_det_nbr;
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other_endo_nbr = M_.block_structure.block(i).other_endo_nbr;
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jacob = full(data(i).g1);
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lead_lag_incidence = data(i).lead_lag_incidence;
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endo = data(i).variable;
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exo = data(i).exogenous;
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if (verbose)
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disp('jacob');
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disp(jacob);
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disp('lead_lag_incidence');
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disp(lead_lag_incidence);
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end
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maximum_lag = data(i).maximum_endo_lag;
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maximum_lead = data(i).maximum_endo_lead;
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n = n_dynamic + n_static;
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block_type = M_.block_structure.block(i).Simulation_Type;
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if task ~= 1
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if block_type == 2 || block_type == 4 || block_type == 7
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block_type = 8;
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end
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end
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if maximum_lag > 0 && (n_pred > 0 || n_both > 0) && block_type ~= 1
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indexi_0 = min(lead_lag_incidence(2,:));
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end
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switch block_type
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case 1
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%% ------------------------------------------------------------------
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%Evaluate Forward
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if maximum_lag > 0 && n_pred > 0
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indx_r = find(M_.block_structure.block(i).lead_lag_incidence(1,:));
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indx_c = M_.block_structure.block(i).lead_lag_incidence(1,indx_r);
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data(i).eigval = diag(jacob(indx_r, indx_c));
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data(i).rank = 0;
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else
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data(i).eigval = [];
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data(i).rank = 0;
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end
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dr.eigval = [dr.eigval ; data(i).eigval];
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%First order approximation
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if task ~= 1
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[tmp1, tmp2, indx_c] = find(M_.block_structure.block(i).lead_lag_incidence(2,:));
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B = jacob(:,indx_c);
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if (maximum_lag > 0 && n_pred > 0)
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[indx_r, tmp1, indx_r_v] = find(M_.block_structure.block(i).lead_lag_incidence(1,:));
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ghx = - B \ jacob(:,indx_r_v);
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end
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if other_endo_nbr
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fx = data(i).g1_o;
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% retrieves the derivatives with respect to endogenous
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% variable belonging to previous blocks
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fx_tm1 = zeros(n,other_endo_nbr);
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fx_t = zeros(n,other_endo_nbr);
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fx_tp1 = zeros(n,other_endo_nbr);
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% stores in fx_tm1 the lagged values of fx
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[r, c, lag] = find(data(i).lead_lag_incidence_other(1,:));
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fx_tm1(:,c) = fx(:,lag);
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% stores in fx the current values of fx
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[r, c, curr] = find(data(i).lead_lag_incidence_other(2,:));
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fx_t(:,c) = fx(:,curr);
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% stores in fx_tp1 the leaded values of fx
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[r, c, lead] = find(data(i).lead_lag_incidence_other(3,:));
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fx_tp1(:,c) = fx(:,lead);
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l_x = dr.ghx(data(i).other_endogenous,:);
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l_x_sv = dr.ghx(dr.state_var, 1:n_sv);
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selector_tm1 = M_.block_structure.block(i).tm1;
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ghx_other = - B \ (fx_t * l_x + (fx_tp1 * l_x * l_x_sv) + fx_tm1 * selector_tm1);
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dr.ghx(endo, :) = dr.ghx(endo, :) + ghx_other;
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end
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if exo_nbr
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fu = data(i).g1_x;
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exo = dr.exo_var;
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if other_endo_nbr > 0
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l_u_sv = dr.ghu(dr.state_var,:);
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l_x = dr.ghx(data(i).other_endogenous,:);
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l_u = dr.ghu(data(i).other_endogenous,:);
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fu_complet = zeros(n, M_.exo_nbr);
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fu_complet(:,data(i).exogenous) = fu;
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ghu = - B \ (fu_complet + fx_tp1 * l_x * l_u_sv + (fx_t) * l_u );
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else
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fu_complet = zeros(n, M_.exo_nbr);
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fu_complet(:,data(i).exogenous) = fu;
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ghu = - B \ fu_complet;
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end
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else
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exo = dr.exo_var;
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if other_endo_nbr > 0
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l_u_sv = dr.ghu(dr.state_var,:);
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l_x = dr.ghx(data(i).other_endogenous,:);
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l_u = dr.ghu(data(i).other_endogenous,:);
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ghu = -B \ (fx_tp1 * l_x * l_u_sv + (fx_t) * l_u );
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else
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ghu = [];
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end
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end
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end
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case 2
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%% ------------------------------------------------------------------
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%Evaluate Backward
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if maximum_lead > 0 && n_fwrd > 0
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indx_r = find(M_.block_structure.block(i).lead_lag_incidence(3,:));
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indx_c = M_.block_structure.block(i).lead_lag_incidence(3,indx_r);
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data(i).eigval = 1 ./ diag(jacob(indx_r, indx_c));
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data(i).rank = sum(abs(data(i).eigval) > 0);
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full_rank = (rcond(jacob(indx_r, indx_c)) > 1e-9);
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else
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data(i).eigval = [];
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data(i).rank = 0;
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full_rank = 1;
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end
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dr.eigval = [dr.eigval ; data(i).eigval];
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dr.full_rank = dr.full_rank && full_rank;
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%First order approximation
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if task ~= 1
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if (maximum_lag > 0)
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indx_r = find(M_.block_structure.block(i).lead_lag_incidence(3,:));
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indx_c = M_.block_structure.block(i).lead_lag_incidence(3,indx_r);
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ghx = - inv(jacob(indx_r, indx_c));
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end
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ghu = - inv(jacob(indx_r, indx_c)) * data(i).g1_x;
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end
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case 3
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%% ------------------------------------------------------------------
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%Solve Forward single equation
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if maximum_lag > 0 && n_pred > 0
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data(i).eigval = - jacob(1 , 1 : n_pred) / jacob(1 , n_pred + n_static + 1 : n_pred + n_static + n_pred + n_both);
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data(i).rank = 0;
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else
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data(i).eigval = [];
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data(i).rank = 0;
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end
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dr.eigval = [dr.eigval ; data(i).eigval];
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%First order approximation
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if task ~= 1
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if (maximum_lag > 0)
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ghx = - jacob(1 , 1 : n_pred) / jacob(1 , n_pred + n_static + 1 : n_pred + n_static + n_pred + n_both);
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else
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ghx = 0;
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end
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if other_endo_nbr
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fx = data(i).g1_o;
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% retrieves the derivatives with respect to endogenous
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% variable belonging to previous blocks
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fx_tm1 = zeros(n,other_endo_nbr);
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fx_t = zeros(n,other_endo_nbr);
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fx_tp1 = zeros(n,other_endo_nbr);
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% stores in fx_tm1 the lagged values of fx
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[r, c, lag] = find(data(i).lead_lag_incidence_other(1,:));
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fx_tm1(:,c) = fx(:,lag);
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% stores in fx the current values of fx
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[r, c, curr] = find(data(i).lead_lag_incidence_other(2,:));
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fx_t(:,c) = fx(:,curr);
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% stores in fx_tm1 the leaded values of fx
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[r, c, lead] = find(data(i).lead_lag_incidence_other(3,:));
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fx_tp1(:,c) = fx(:,lead);
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l_x = dr.ghx(data(i).other_endogenous,:);
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l_x_sv = dr.ghx(dr.state_var, 1:n_sv);
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selector_tm1 = M_.block_structure.block(i).tm1;
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ghx_other = - (fx_t * l_x + (fx_tp1 * l_x * l_x_sv) + fx_tm1 * selector_tm1) / jacob(1 , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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dr.ghx(endo, :) = dr.ghx(endo, :) + ghx_other;
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end
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if exo_nbr
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fu = data(i).g1_x;
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if other_endo_nbr > 0
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l_u_sv = dr.ghu(dr.state_var,:);
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l_x = dr.ghx(data(i).other_endogenous,:);
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l_u = dr.ghu(data(i).other_endogenous,:);
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fu_complet = zeros(n, M_.exo_nbr);
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fu_complet(:,data(i).exogenous) = fu;
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ghu = -(fu_complet + fx_tp1 * l_x * l_u_sv + (fx_t) * l_u ) / jacob(1 , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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exo = dr.exo_var;
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else
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ghu = - fu / jacob(1 , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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end
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else
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if other_endo_nbr > 0
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l_u_sv = dr.ghu(dr.state_var,:);
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l_x = dr.ghx(data(i).other_endogenous,:);
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l_u = dr.ghu(data(i).other_endogenous,:);
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ghu = -(fx_tp1 * l_x * l_u_sv + (fx_t) * l_u ) / jacob(1 , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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exo = dr.exo_var;
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else
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ghu = [];
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end
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end
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end
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case 4
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%% ------------------------------------------------------------------
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%Solve Backward single equation
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if maximum_lead > 0 && n_fwrd > 0
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data(i).eigval = - jacob(1 , n_pred + n - n_fwrd + 1 : n_pred + n) / jacob(1 , n_pred + n + 1 : n_pred + n + n_fwrd) ;
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data(i).rank = sum(abs(data(i).eigval) > 0);
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full_rank = (abs(jacob(1,n_pred+n+1: n_pred+n+n_fwrd)) > 1e-9);
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else
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data(i).eigval = [];
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data(i).rank = 0;
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full_rank = 1;
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end
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dr.full_rank = dr.full_rank && full_rank;
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dr.eigval = [dr.eigval ; data(i).eigval];
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case 6
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%% ------------------------------------------------------------------
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%Solve Forward complete
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if (maximum_lag > 0)
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ghx = - jacob(: , n_pred + 1 : n_pred + n_static ...
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+ n_pred + n_both) \ jacob(: , 1 : n_pred);
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else
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ghx = 0;
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end
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if maximum_lag > 0 && n_pred > 0
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data(i).eigval = -eig(ghx(n_static+1:end,:));
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data(i).rank = 0;
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full_rank = (rcond(ghx(n_static+1:end,:)) > 1e-9);
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else
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data(i).eigval = [];
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data(i).rank = 0;
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full_rank = 1;
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end
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dr.eigval = [dr.eigval ; data(i).eigval];
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dr.full_rank = dr.full_rank && full_rank;
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if task ~= 1
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if other_endo_nbr
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fx = data(i).g1_o;
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% retrieves the derivatives with respect to endogenous
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% variable belonging to previous blocks
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fx_tm1 = zeros(n,other_endo_nbr);
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fx_t = zeros(n,other_endo_nbr);
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fx_tp1 = zeros(n,other_endo_nbr);
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% stores in fx_tm1 the lagged values of fx
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[r, c, lag] = find(data(i).lead_lag_incidence_other(1,:));
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fx_tm1(:,c) = fx(:,lag);
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% stores in fx the current values of fx
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[r, c, curr] = find(data(i).lead_lag_incidence_other(2,:));
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fx_t(:,c) = fx(:,curr);
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% stores in fx_tm1 the leaded values of fx
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[r, c, lead] = find(data(i).lead_lag_incidence_other(3,:));
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fx_tp1(:,c) = fx(:,lead);
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l_x = dr.ghx(data(i).other_endogenous,:);
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l_x_sv = dr.ghx(dr.state_var, 1:n_sv);
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selector_tm1 = M_.block_structure.block(i).tm1;
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ghx_other = - (fx_t * l_x + (fx_tp1 * l_x * l_x_sv) + fx_tm1 * selector_tm1) / jacob(: , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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dr.ghx(endo, :) = dr.ghx(endo, :) + ghx_other;
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end
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if exo_nbr
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fu = data(i).g1_x;
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if other_endo_nbr > 0
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l_u_sv = dr.ghu(dr.state_var,:);
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l_x = dr.ghx(data(i).other_endogenous,:);
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l_u = dr.ghu(data(i).other_endogenous,:);
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fu_complet = zeros(n, M_.exo_nbr);
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fu_complet(:,data(i).exogenous) = fu;
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ghu = -(fu_complet + fx_tp1 * l_x * l_u_sv + (fx_t) * l_u ) / jacob(: , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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exo = dr.exo_var;
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else
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ghu = - fu / jacob(: , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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end
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else
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if other_endo_nbr > 0
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l_u_sv = dr.ghu(dr.state_var,:);
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l_x = dr.ghx(data(i).other_endogenous,:);
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l_u = dr.ghu(data(i).other_endogenous,:);
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ghu = -(fx_tp1 * l_x * l_u_sv + (fx_t) * l_u ) / jacob(1 , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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exo = dr.exo_var;
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else
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ghu = [];
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end
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end
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end
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case 7
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%% ------------------------------------------------------------------
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%Solve Backward complete
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if maximum_lead > 0 && n_fwrd > 0
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data(i).eigval = eig(- jacob(: , n_pred + n - n_fwrd + 1: n_pred + n))/ ...
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jacob(: , n_pred + n + 1 : n_pred + n + n_fwrd);
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data(i).rank = sum(abs(data(i).eigval) > 0);
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full_rank = (rcond(jacob(: , n_pred + n + 1 : n_pred + n + ...
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n_fwrd)) > 1e-9);
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else
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data(i).eigval = [];
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data(i).rank = 0;
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full_rank = 1;
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end
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|
dr.full_rank = dr.full_rank && full_rank;
|
|
dr.eigval = [dr.eigval ; data(i).eigval];
|
|
case {5,8}
|
|
%% ------------------------------------------------------------------
|
|
%The lead_lag_incidence contains columns in the following order:
|
|
% static variables, backward variable, mixed variables and forward variables
|
|
%
|
|
%Proceeds to a QR decomposition on the jacobian matrix in order to reduce the problem size
|
|
index_c = lead_lag_incidence(2,:); % Index of all endogenous variables present at time=t
|
|
index_s = lead_lag_incidence(2,1:n_static); % Index of all static endogenous variables present at time=t
|
|
if n_static > 0
|
|
[Q, ~] = qr(jacob(:,index_s));
|
|
aa = Q'*jacob;
|
|
else
|
|
aa = jacob;
|
|
end
|
|
index_0m = (n_static+1:n_static+n_pred) + indexi_0 - 1;
|
|
index_0p = (n_static+n_pred+1:n) + indexi_0 - 1;
|
|
index_m = 1:(n_pred+n_both);
|
|
index_p = lead_lag_incidence(3,find(lead_lag_incidence(3,:)));
|
|
nyf = n_fwrd + n_both;
|
|
A = aa(:,index_m); % Jacobain matrix for lagged endogeneous variables
|
|
B = aa(:,index_c); % Jacobian matrix for contemporaneous endogeneous variables
|
|
C = aa(:,index_p); % Jacobain matrix for led endogeneous variables
|
|
|
|
row_indx = n_static+1:n;
|
|
|
|
if task ~= 1 && options_.dr_cycle_reduction
|
|
A1 = [aa(row_indx,index_m ) zeros(n_dynamic,n_fwrd)];
|
|
B1 = [aa(row_indx,index_0m) aa(row_indx,index_0p) ];
|
|
C1 = [zeros(n_dynamic,n_pred) aa(row_indx,index_p)];
|
|
[ghx, info] = cycle_reduction(A1, B1, C1, options_.dr_cycle_reduction_tol);
|
|
%ghx
|
|
ghx = ghx(:,index_m);
|
|
hx = ghx(1:n_pred+n_both,:);
|
|
gx = ghx(1+n_pred:end,:);
|
|
end
|
|
|
|
if (task ~= 1 && ((options_.dr_cycle_reduction && info ==1) || ~options_.dr_cycle_reduction)) || task == 1
|
|
D = [[aa(row_indx,index_0m) zeros(n_dynamic,n_both) aa(row_indx,index_p)] ; [zeros(n_both, n_pred) eye(n_both) zeros(n_both, n_both + n_fwrd)]];
|
|
E = [-aa(row_indx,[index_m index_0p]) ; [zeros(n_both, n_both + n_pred) eye(n_both, n_both + n_fwrd) ] ];
|
|
|
|
[ss, tt, w, sdim, data(i).eigval, info1] = mjdgges(E,D,options_.qz_criterium,options_.qz_zero_threshold);
|
|
|
|
if (verbose)
|
|
disp('eigval');
|
|
disp(data(i).eigval);
|
|
end
|
|
if info1
|
|
if info1 == -30
|
|
% one eigenvalue is close to 0/0
|
|
info(1) = 7;
|
|
else
|
|
info(1) = 2;
|
|
info(2) = info1;
|
|
info(3) = size(E,2);
|
|
end
|
|
return
|
|
end
|
|
nba = nd-sdim;
|
|
if task == 1
|
|
data(i).rank = rank(w(nd-nyf+1:end,nd-nyf+1:end));
|
|
dr.full_rank = dr.full_rank && (rcond(w(nd-nyf+1:end,nd- ...
|
|
nyf+1:end)) > 1e-9);
|
|
dr.eigval = [dr.eigval ; data(i).eigval];
|
|
end
|
|
if (verbose)
|
|
disp(['sum eigval > 1 = ' int2str(sum(abs(data(i).eigval) > 1.)) ' nyf=' int2str(nyf) ' and dr.rank=' int2str(data(i).rank)]);
|
|
disp(['data(' int2str(i) ').eigval']);
|
|
disp(data(i).eigval);
|
|
end
|
|
|
|
%First order approximation
|
|
if task ~= 1
|
|
if nba ~= nyf
|
|
if isfield(options_,'indeterminacy_continuity')
|
|
if options_.indeterminacy_msv == 1
|
|
[ss,tt,w,q] = qz(E',D');
|
|
[ss,tt,w,~] = reorder(ss,tt,w,q);
|
|
ss = ss';
|
|
tt = tt';
|
|
w = w';
|
|
nba = nyf;
|
|
end
|
|
else
|
|
sorted_roots = sort(abs(data(i).eigval));
|
|
if nba > nyf
|
|
temp = sorted_roots(nd-nba+1:nd-nyf)-1-options_.qz_criterium;
|
|
info(1) = 3;
|
|
elseif nba < nyf
|
|
temp = sorted_roots(nd-nyf+1:nd-nba)-1-options_.qz_criterium;
|
|
info(1) = 4;
|
|
end
|
|
info(2) = temp'*temp;
|
|
return
|
|
end
|
|
end
|
|
indx_stable_root = 1: (nd - nyf); %=> index of stable roots
|
|
indx_explosive_root = n_pred + n_both + 1:nd; %=> index of explosive roots
|
|
% derivatives with respect to dynamic state variables
|
|
% forward variables
|
|
Z = w';
|
|
Z11t = Z(indx_stable_root, indx_stable_root)';
|
|
Z21 = Z(indx_explosive_root, indx_stable_root);
|
|
Z22 = Z(indx_explosive_root, indx_explosive_root);
|
|
if ~isfloat(Z21) && (condest(Z21) > 1e9)
|
|
% condest() fails on a scalar under Octave
|
|
info(1) = 5;
|
|
info(2) = condest(Z21);
|
|
return
|
|
else
|
|
%gx = -inv(Z22) * Z21;
|
|
gx = - Z22 \ Z21;
|
|
end
|
|
|
|
% predetermined variables
|
|
hx = Z11t * inv(tt(indx_stable_root, indx_stable_root)) * ss(indx_stable_root, indx_stable_root) * inv(Z11t);
|
|
|
|
k1 = 1:(n_pred+n_both);
|
|
k2 = 1:(n_fwrd+n_both);
|
|
|
|
ghx = [hx(k1,:); gx(k2(n_both+1:end),:)];
|
|
end
|
|
end
|
|
|
|
if task~= 1
|
|
%lead variables actually present in the model
|
|
j4 = n_static+n_pred+1:n_static+n_pred+n_both+n_fwrd; % Index on the forward and both variables
|
|
j3 = nonzeros(lead_lag_incidence(2,j4)) - n_static - 2 * n_pred - n_both; % Index on the non-zeros forward and both variables
|
|
j4 = find(lead_lag_incidence(2,j4));
|
|
|
|
if n_static > 0
|
|
B_static = B(:,1:n_static); % submatrix containing the derivatives w.r. to static variables
|
|
else
|
|
B_static = [];
|
|
end
|
|
%static variables, backward variable, mixed variables and forward variables
|
|
B_pred = B(:,n_static+1:n_static+n_pred+n_both);
|
|
B_fyd = B(:,n_static+n_pred+n_both+1:end);
|
|
|
|
% static variables
|
|
if n_static > 0
|
|
temp = - C(1:n_static,j3)*gx(j4,:)*hx;
|
|
j5 = index_m;
|
|
b = aa(:,index_c);
|
|
b10 = b(1:n_static, 1:n_static);
|
|
b11 = b(1:n_static, n_static+1:n);
|
|
temp(:,j5) = temp(:,j5)-A(1:n_static,:);
|
|
temp = b10\(temp-b11*ghx);
|
|
ghx = [temp; ghx];
|
|
temp = [];
|
|
end
|
|
|
|
A_ = real([B_static C(:,j3)*gx+B_pred B_fyd]); % The state_variable of the block are located at [B_pred B_both]
|
|
|
|
if other_endo_nbr
|
|
if n_static > 0
|
|
fx = Q' * data(i).g1_o;
|
|
else
|
|
fx = data(i).g1_o;
|
|
end
|
|
% retrieves the derivatives with respect to endogenous
|
|
% variable belonging to previous blocks
|
|
fx_tm1 = zeros(n,other_endo_nbr);
|
|
fx_t = zeros(n,other_endo_nbr);
|
|
fx_tp1 = zeros(n,other_endo_nbr);
|
|
% stores in fx_tm1 the lagged values of fx
|
|
[r, c, lag] = find(data(i).lead_lag_incidence_other(1,:));
|
|
fx_tm1(:,c) = fx(:,lag);
|
|
% stores in fx the current values of fx
|
|
[r, c, curr] = find(data(i).lead_lag_incidence_other(2,:));
|
|
fx_t(:,c) = fx(:,curr);
|
|
% stores in fx_tp1 the leaded values of fx
|
|
[r, c, lead] = find(data(i).lead_lag_incidence_other(3,:));
|
|
fx_tp1(:,c) = fx(:,lead);
|
|
|
|
l_x = dr.ghx(data(i).other_endogenous,:);
|
|
|
|
l_x_sv = dr.ghx(dr.state_var, :);
|
|
|
|
selector_tm1 = M_.block_structure.block(i).tm1;
|
|
|
|
B_ = [zeros(size(B_static)) zeros(n,n_pred) C(:,j3) ];
|
|
C_ = l_x_sv;
|
|
D_ = (fx_t * l_x + fx_tp1 * l_x * l_x_sv + fx_tm1 * selector_tm1 );
|
|
% Solve the Sylvester equation:
|
|
% A_ * gx + B_ * gx * C_ + D_ = 0
|
|
if block_type == 5
|
|
vghx_other = - inv(kron(eye(size(D_,2)), A_) + kron(C_', B_)) * vec(D_);
|
|
ghx_other = reshape(vghx_other, size(D_,1), size(D_,2));
|
|
elseif options_.sylvester_fp
|
|
ghx_other = gensylv_fp(A_, B_, C_, D_, i, options_.sylvester_fixed_point_tol);
|
|
else
|
|
ghx_other = gensylv(1, A_, B_, C_, -D_);
|
|
end
|
|
if options_.aim_solver ~= 1
|
|
% Necessary when using Sims' routines for QZ
|
|
ghx_other = real(ghx_other);
|
|
end
|
|
|
|
dr.ghx(endo, :) = dr.ghx(endo, :) + ghx_other;
|
|
end
|
|
|
|
if exo_nbr
|
|
if n_static > 0
|
|
fu = Q' * data(i).g1_x;
|
|
else
|
|
fu = data(i).g1_x;
|
|
end
|
|
|
|
if other_endo_nbr > 0
|
|
l_u_sv = dr.ghu(dr.state_var,:);
|
|
l_x = dr.ghx(data(i).other_endogenous,:);
|
|
l_u = dr.ghu(data(i).other_endogenous,:);
|
|
fu_complet = zeros(n, M_.exo_nbr);
|
|
fu_complet(:,data(i).exogenous) = fu;
|
|
% Solve the equation in ghu:
|
|
% A_ * ghu + (fu_complet + fx_tp1 * l_x * l_u_sv + (fx_t + B_ * ghx_other) * l_u ) = 0
|
|
|
|
ghu = -A_\ (fu_complet + fx_tp1 * l_x * l_u_sv + fx_t * l_u + B_ * ghx_other * l_u_sv );
|
|
exo = dr.exo_var;
|
|
else
|
|
ghu = - A_ \ fu;
|
|
end
|
|
else
|
|
if other_endo_nbr > 0
|
|
l_u_sv = dr.ghu(dr.state_var,:);
|
|
l_x = dr.ghx(data(i).other_endogenous,:);
|
|
l_u = dr.ghu(data(i).other_endogenous,:);
|
|
% Solve the equation in ghu:
|
|
% A_ * ghu + (fx_tp1 * l_x * l_u_sv + (fx_t + B_ * ghx_other) * l_u ) = 0
|
|
ghu = -real(A_)\ (fx_tp1 * l_x * l_u_sv + (fx_t * l_u + B_ * ghx_other * l_u_sv) );
|
|
exo = dr.exo_var;
|
|
else
|
|
ghu = [];
|
|
end
|
|
end
|
|
|
|
|
|
|
|
if options_.loglinear
|
|
error('The loglinear option is not yet supported in first order approximation for a block decomposed model');
|
|
% k = find(dr.kstate(:,2) <= M_.maximum_endo_lag+1);
|
|
% klag = dr.kstate(k,[1 2]);
|
|
% k1 = dr.order_var;
|
|
%
|
|
% ghx = repmat(1./dr.ys(k1),1,size(ghx,2)).*ghx.* ...
|
|
% repmat(dr.ys(k1(klag(:,1)))',size(ghx,1),1);
|
|
% ghu = repmat(1./dr.ys(k1),1,size(ghu,2)).*ghu;
|
|
end
|
|
|
|
|
|
if options_.aim_solver ~= 1
|
|
% Necessary when using Sims' routines for QZ
|
|
ghx = real(ghx);
|
|
ghu = real(ghu);
|
|
end
|
|
|
|
%exogenous deterministic variables
|
|
if exo_det_nbr > 0
|
|
error('Deterministic exogenous variables are not yet implemented in first order approximation for a block decomposed model');
|
|
% f1 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+2:end,order_var))));
|
|
% f0 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var))));
|
|
% fudet = data(i).g1_xd;
|
|
% M1 = inv(f0+[zeros(n,n_static) f1*gx zeros(n,nyf-n_both)]);
|
|
% M2 = M1*f1;
|
|
% dr.ghud = cell(M_.exo_det_length,1);
|
|
% dr.ghud{1} = -M1*fudet;
|
|
% for i = 2:M_.exo_det_length
|
|
% dr.ghud{i} = -M2*dr.ghud{i-1}(end-nyf+1:end,:);
|
|
% end
|
|
end
|
|
end
|
|
end
|
|
if task ~=1
|
|
if (maximum_lag > 0 && (n_pred > 0 || n_both > 0))
|
|
sorted_col_dr_ghx = M_.block_structure.block(i).sorted_col_dr_ghx;
|
|
dr.ghx(endo, sorted_col_dr_ghx) = dr.ghx(endo, sorted_col_dr_ghx) + ghx;
|
|
data(i).ghx = ghx;
|
|
data(i).pol.i_ghx = sorted_col_dr_ghx;
|
|
else
|
|
data(i).pol.i_ghx = [];
|
|
end
|
|
data(i).ghu = ghu;
|
|
dr.ghu(endo, exo) = ghu;
|
|
data(i).pol.i_ghu = exo;
|
|
end
|
|
|
|
if (verbose)
|
|
disp('dr.ghx');
|
|
dr.ghx
|
|
disp('dr.ghu');
|
|
dr.ghu
|
|
end
|
|
|
|
end
|
|
M_.block_structure.block = data ;
|
|
if (verbose)
|
|
disp('dr.ghx');
|
|
disp(real(dr.ghx));
|
|
disp('dr.ghu');
|
|
disp(real(dr.ghu));
|
|
end
|
|
if (task == 1)
|
|
return
|
|
end
|