Select Git revision
dr_block.m 29.77 KiB
function [dr,info,M_,options_,oo_] = dr_block(dr,task,M_,options_,oo_)
% function [dr,info,M_,options_,oo_] = dr_block(dr,task,M_,options_,oo_)
% computes the reduced form solution of a rational expectation model (first
% approximation of the stochastic model around the deterministic steady state).
%
% INPUTS
% dr [matlab structure] Decision rules for stochastic simulations.
% task [integer] if task = 0 then dr1 computes decision rules.
% if task = 1 then dr1 computes eigenvalues.
% M_ [matlab structure] Definition of the model.
% options_ [matlab structure] Global options.
% oo_ [matlab structure] Results
%
% OUTPUTS
% dr [matlab structure] Decision rules for stochastic simulations.
% info [integer] info=1: the model doesn't define current variables uniquely
% info=2: problem in mjdgges.dll info(2) contains error code.
% info=3: BK order condition not satisfied info(2) contains "distance"
% absence of stable trajectory.
% info=4: BK order condition not satisfied info(2) contains "distance"
% indeterminacy.
% info=5: BK rank condition not satisfied.
% info=6: The jacobian matrix evaluated at the steady state is complex.
% M_ [matlab structure]
% options_ [matlab structure]
% oo_ [matlab structure]
%
% ALGORITHM
% first order block relaxation method applied to the model
% E[A Yt-1 + B Yt + C Yt+1 + ut] = 0
%
% SPECIAL REQUIREMENTS
% none.
%
% Copyright (C) 2010-2012 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 <http://www.gnu.org/licenses/>.
info = 0;
verbose = 0;
if options_.order > 1
error('2nd and 3rd order approximation not implemented with block option')
end
z = repmat(dr.ys,1,M_.maximum_lead + M_.maximum_lag + 1);
zx = repmat([oo_.exo_simul oo_.exo_det_simul],M_.maximum_lead + M_.maximum_lag + 1, 1);
if (isfield(M_,'block_structure'))
data = M_.block_structure.block;
Size = length(M_.block_structure.block);
else
data = M_;
Size = 1;
end;
if (options_.bytecode)
[chck, zz, data]= bytecode('dynamic','evaluate', z, zx, M_.params, dr.ys, 1, data);
else [r, data] = feval([M_.fname '_dynamic'], z', zx, M_.params, dr.ys, M_.maximum_lag+1, data);
chck = 0;
end;
mexErrCheck('bytecode', chck);
dr.full_rank = 1;
dr.eigval = [];
dr.nd = 0;
dr.ghx = [];
dr.ghu = [];
%Determine the global list of state variables:
dr.state_var = M_.state_var;
M_.block_structure.state_var = dr.state_var;
n_sv = size(dr.state_var, 2);
dr.ghx = zeros(M_.endo_nbr, length(dr.state_var));
dr.exo_var = 1:M_.exo_nbr;
dr.ghu = zeros(M_.endo_nbr, M_.exo_nbr);
for i = 1:Size;
ghx = [];
indexi_0 = 0;
if (verbose)
disp('======================================================================');
disp(['Block ' int2str(i)]);
disp('-----------');
data(i)
end;
n_pred = data(i).n_backward;
n_fwrd = data(i).n_forward;
n_both = data(i).n_mixed;
n_static = data(i).n_static;
nd = n_pred + n_fwrd + 2*n_both;
dr.nd = dr.nd + nd;
n_dynamic = n_pred + n_fwrd + n_both;
exo_nbr = M_.block_structure.block(i).exo_nbr;
exo_det_nbr = M_.block_structure.block(i).exo_det_nbr;
other_endo_nbr = M_.block_structure.block(i).other_endo_nbr;
jacob = full(data(i).g1);
lead_lag_incidence = data(i).lead_lag_incidence;
endo = data(i).variable;
exo = data(i).exogenous;
if (verbose)
disp('jacob');
disp(jacob);
disp('lead_lag_incidence');
disp(lead_lag_incidence);
end;
maximum_lag = data(i).maximum_endo_lag;
maximum_lead = data(i).maximum_endo_lead;
n = n_dynamic + n_static;
block_type = M_.block_structure.block(i).Simulation_Type;
if task ~= 1
if block_type == 2 || block_type == 4 || block_type == 7
block_type = 8;
end;
end;
if maximum_lag > 0 && (n_pred > 0 || n_both > 0) && block_type ~= 1
indexi_0 = min(lead_lag_incidence(2,:));
end;
switch block_type
case 1
%% ------------------------------------------------------------------
%Evaluate Forward
if maximum_lag > 0 && n_pred > 0
indx_r = find(M_.block_structure.block(i).lead_lag_incidence(1,:));
indx_c = M_.block_structure.block(i).lead_lag_incidence(1,indx_r);
data(i).eigval = diag(jacob(indx_r, indx_c));
data(i).rank = 0;
else
data(i).eigval = []; data(i).rank = 0;
end
dr.eigval = [dr.eigval ; data(i).eigval];
%First order approximation
if task ~= 1
[tmp1, tmp2, indx_c] = find(M_.block_structure.block(i).lead_lag_incidence(2,:));
B = jacob(:,indx_c);
if (maximum_lag > 0 && n_pred > 0)
[indx_r, tmp1, indx_r_v] = find(M_.block_structure.block(i).lead_lag_incidence(1,:));
ghx = - B \ jacob(:,indx_r_v);
end;
if other_endo_nbr
fx = data(i).g1_o;
% 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, 1:n_sv);
selector_tm1 = M_.block_structure.block(i).tm1;
ghx_other = - B \ (fx_t * l_x + (fx_tp1 * l_x * l_x_sv) + fx_tm1 * selector_tm1);
dr.ghx(endo, :) = dr.ghx(endo, :) + ghx_other;
end;
if exo_nbr
fu = data(i).g1_x;
exo = dr.exo_var;
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;
ghu = - B \ (fu_complet + fx_tp1 * l_x * l_u_sv + (fx_t) * l_u );
else
fu_complet = zeros(n, M_.exo_nbr);
fu_complet(:,data(i).exogenous) = fu;
ghu = - B \ fu_complet;
end;
else
exo = dr.exo_var;
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,:);
ghu = -B \ (fx_tp1 * l_x * l_u_sv + (fx_t) * l_u );
else
ghu = [];
end
end
end
case 2
%% ------------------------------------------------------------------
%Evaluate Backward
if maximum_lead > 0 && n_fwrd > 0
indx_r = find(M_.block_structure.block(i).lead_lag_incidence(3,:));
indx_c = M_.block_structure.block(i).lead_lag_incidence(3,indx_r); data(i).eigval = 1 ./ diag(jacob(indx_r, indx_c));
data(i).rank = sum(abs(data(i).eigval) > 0);
full_rank = (rcond(jacob(indx_r, indx_c)) > 1e-9);
else
data(i).eigval = [];
data(i).rank = 0;
full_rank = 1;
end
dr.eigval = [dr.eigval ; data(i).eigval];
dr.full_rank = dr.full_rank && full_rank;
%First order approximation
if task ~= 1
if (maximum_lag > 0)
indx_r = find(M_.block_structure.block(i).lead_lag_incidence(3,:));
indx_c = M_.block_structure.block(i).lead_lag_incidence(3,indx_r);
ghx = - inv(jacob(indx_r, indx_c));
end;
ghu = - inv(jacob(indx_r, indx_c)) * data(i).g1_x;
end
case 3
%% ------------------------------------------------------------------
%Solve Forward single equation
if maximum_lag > 0 && n_pred > 0
data(i).eigval = - jacob(1 , 1 : n_pred) / jacob(1 , n_pred + n_static + 1 : n_pred + n_static + n_pred + n_both);
data(i).rank = 0;
else
data(i).eigval = [];
data(i).rank = 0;
end;
dr.eigval = [dr.eigval ; data(i).eigval];
%First order approximation
if task ~= 1
if (maximum_lag > 0)
ghx = - jacob(1 , 1 : n_pred) / jacob(1 , n_pred + n_static + 1 : n_pred + n_static + n_pred + n_both);
else
ghx = 0;
end;
if other_endo_nbr
fx = data(i).g1_o;
% 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_tm1 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, 1:n_sv);
selector_tm1 = M_.block_structure.block(i).tm1;
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);
dr.ghx(endo, :) = dr.ghx(endo, :) + ghx_other;
end;
if exo_nbr
fu = data(i).g1_x;
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; 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);
exo = dr.exo_var;
else
ghu = - fu / jacob(1 , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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,:);
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);
exo = dr.exo_var;
else
ghu = [];
end
end
end
case 4
%% ------------------------------------------------------------------
%Solve Backward single equation
if maximum_lead > 0 && n_fwrd > 0
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) ;
data(i).rank = sum(abs(data(i).eigval) > 0);
full_rank = (abs(jacob(1,n_pred+n+1: n_pred+n+n_fwrd)) > 1e-9);
else
data(i).eigval = [];
data(i).rank = 0;
full_rank = 1;
end;
dr.full_rank = dr.full_rank && full_rank;
dr.eigval = [dr.eigval ; data(i).eigval];
case 6
%% ------------------------------------------------------------------
%Solve Forward complete
if maximum_lag > 0 && n_pred > 0
data(i).eigval = eig(- jacob(: , 1 : n_pred) / ...
jacob(: , (n_pred + n_static + 1 : n_pred + n_static + n_pred )));
data(i).rank = 0;
full_rank = (rcond(jacob(: , (n_pred + n_static + 1 : n_pred ...
+ n_static + n_pred ))) > 1e-9);
else
data(i).eigval = [];
data(i).rank = 0;
full_rank = 1;
end;
dr.eigval = [dr.eigval ; data(i).eigval];
dr.full_rank = dr.full_rank && full_rank;
if task ~= 1
if (maximum_lag > 0)
ghx = - jacob(: , 1 : n_pred) / jacob(: , n_pred + n_static + 1 : n_pred + n_static + n_pred + n_both);
else
ghx = 0;
end;
if other_endo_nbr
fx = data(i).g1_o;
% 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_tm1 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, 1:n_sv);
selector_tm1 = M_.block_structure.block(i).tm1;
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);
dr.ghx(endo, :) = dr.ghx(endo, :) + ghx_other;
end;
if exo_nbr
fu = data(i).g1_x;
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;
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);
exo = dr.exo_var;
else
ghu = - fu / jacob(: , n_pred + 1 : n_pred + n_static + n_pred + n_both);
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,:);
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);
exo = dr.exo_var;
else
ghu = [];
end
end
end
case 7
%% ------------------------------------------------------------------
%Solve Backward complete
if maximum_lead > 0 && n_fwrd > 0
data(i).eigval = eig(- jacob(: , n_pred + n - n_fwrd + 1: n_pred + n))/ ...
jacob(: , n_pred + n + 1 : n_pred + n + n_fwrd);
data(i).rank = sum(abs(data(i).eigval) > 0);
full_rank = (rcond(jacob(: , n_pred + n + 1 : n_pred + n + ...
n_fwrd)) > 1e-9);
else
data(i).eigval = [];
data(i).rank = 0;
full_rank = 1;
end;
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, junk] = 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 == 1
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 == 1 && info ==1) || options_.dr_cycle_reduction == 0)) || 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) ] ];
[err, 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
info(1) = 2;
info(2) = info1;
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
sorted_roots = sort(abs(dr.eigval));
if isfield(options_,'indeterminacy_continuity')
if options_.indeterminacy_msv == 1
[ss,tt,w,q] = qz(e',d');
[ss,tt,w,junk] = reorder(ss,tt,w,q);
ss = ss';
tt = tt';
w = w';
%nba = nyf;
end
else
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 == 1
ghx_other = gensylv_fp(A_, B_, C_, D_, i, options_.sylvester_fixed_point_tol);
else
[err, ghx_other] = gensylv(1, A_, B_, C_, -D_);
end;
if options_.aim_solver ~= 1 && options_.use_qzdiv
% 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 == 1
error('log linear option is for the moment not supported in first order approximation for a block decomposed mode');
% 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 && options_.use_qzdiv
% 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 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;