Commit 60feef4a authored by george's avatar george
Browse files

Prototype DR1 subset for running k_order_perturbation

git-svn-id: https://www.dynare.org/svn/dynare/trunk@2387 ac1d8469-bf42-47a9-8791-bf33cf982152
parent eb4b2a50
function [dr,info,M_,options_,oo_] = dr1(dr,task,M_,options_,oo_)
% Computes the reduced form solution of a rational expectation model (first or second order
% 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.
% M_ [matlab structure]
% options_ [matlab structure]
% oo_ [matlab structure]
%
% ALGORITHM
% ...
%
% SPECIAL REQUIREMENTS
% none.
%
% Copyright (C) 1996-2008 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;
options_ = set_default_option(options_,'loglinear',0);
options_ = set_default_option(options_,'noprint',0);
options_ = set_default_option(options_,'olr',0);
options_ = set_default_option(options_,'olr_beta',1);
options_ = set_default_option(options_,'qz_criterium',1.000001);
xlen = M_.maximum_endo_lead + M_.maximum_endo_lag + 1;
klen = M_.maximum_endo_lag + M_.maximum_endo_lead + 1;
iyv = M_.lead_lag_incidence';
iyv = iyv(:);
iyr0 = find(iyv) ;
it_ = M_.maximum_lag + 1 ;
if M_.exo_nbr == 0
oo_.exo_steady_state = [] ;
end
% expanding system for Optimal Linear Regulator
if options_.ramsey_policy
if isfield(M_,'orig_model')
orig_model = M_.orig_model;
M_.endo_nbr = orig_model.endo_nbr;
M_.endo_names = orig_model.endo_names;
M_.lead_lag_incidence = orig_model.lead_lag_incidence;
M_.maximum_lead = orig_model.maximum_lead;
M_.maximum_endo_lead = orig_model.maximum_endo_lead;
M_.maximum_lag = orig_model.maximum_lag;
M_.maximum_endo_lag = orig_model.maximum_endo_lag;
end
old_solve_algo = options_.solve_algo;
% options_.solve_algo = 1;
oo_.steady_state = dynare_solve('ramsey_static',oo_.steady_state,0,M_,options_,oo_,it_);
options_.solve_algo = old_solve_algo;
[junk,junk,multbar] = ramsey_static(oo_.steady_state,M_,options_,oo_,it_);
[jacobia_,M_] = ramsey_dynamic(oo_.steady_state,multbar,M_,options_,oo_,it_);
klen = M_.maximum_lag + M_.maximum_lead + 1;
dr.ys = [oo_.steady_state;zeros(M_.exo_nbr,1);multbar];
else
klen = M_.maximum_lag + M_.maximum_lead + 1;
iyv = M_.lead_lag_incidence';
iyv = iyv(:);
iyr0 = find(iyv) ;
it_ = M_.maximum_lag + 1 ;
if M_.exo_nbr == 0
oo_.exo_steady_state = [] ;
end
it_ = M_.maximum_lag + 1;
z = repmat(dr.ys,1,klen);
z = z(iyr0) ;
end
if options_.debug
save([M_.fname '_debug.mat'],'jacobia_')
end
dr=set_state_space(dr,M_);
kstate = dr.kstate;
kad = dr.kad;
kae = dr.kae;
nstatic = dr.nstatic;
nfwrd = dr.nfwrd;
npred = dr.npred;
nboth = dr.nboth;
order_var = dr.order_var;
nd = size(kstate,1);
nz = nnz(M_.lead_lag_incidence);
sdyn = M_.endo_nbr - nstatic;
k0 = M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var);
k1 = M_.lead_lag_incidence(find([1:klen] ~= M_.maximum_endo_lag+1),:);
if options_.order == 1
M_.var_order_endo_names=M_.endo_names(dr.order_var,:);
% z = repmat(dr.ys,1,klen);
% z = z(iyr0) ;
% oo_.dyn_ys=z; % extended ys
try
[ysteady, gx, gu]=k_order_perturbation(dr,task,M_,options_, oo_ );
load(M_.fname);
ghxu = eval([M_.fname '_g_1']);
sss= size(ghxu,2);
dr.ghx= ghxu(:,1:sss-M_.exo_nbr);
dr.ghu= ghxu(:,sss-M_.exo_nbr+1:end);
dr.ys=eval([M_.fname '_ss']);
catch
disp('*************************************************************************************');
% disp('Problem with using k_order perturbation solver - Using Dynare solver instead');
% warning('Problem with using k_order perturbation solver - Using Dynare solver instead');
error('Problem with using k_order perturbation solver ');
disp('*****************************************************************************');
options_.use_k_order=0; % and then try mjdgges instead
info(1) = 4;
info(2) = 1000;
return
end
elseif options_.order > 1
error(' can not use order > 1 with K-Order yet!')
% or ???
disp('********************************************************************');
disp(' can not use order > 1 with K-Order yet - Using Dynare solver instead');
disp('********************************************************************');
options_.use_k_order= 0; % and then try mjdgges instead
info(1) = 4;
info(2) = 1000;
return
end
if M_.maximum_endo_lead == 0; % backward models
% If required, try Gary Anderson and G Moore AIM solver if not
% check only and if 1st order (added by GP July'08)
dr.eigval = eig(transition_matrix(dr));
dr.rank = 0;
if any(abs(dr.eigval) > options_.qz_criterium)
temp = sort(abs(dr.eigval));
nba = nnz(abs(dr.eigval) > options_.qz_criterium);
temp = temp(nd-nba+1:nd)-1-options_.qz_criterium;
info(1) = 3;
info(2) = temp'*temp;
end
return;
end
%forward--looking models
[A,B] =transition_matrix(dr);
dr.eigval = eig(A);
% if any(abs(dr.eigval) > options_.qz_criterium)
% temp = sort(abs(dr.eigval));
% nba = nnz(abs(dr.eigval) > options_.qz_criterium);
% temp = temp(nd-nba+1:nd)-1-options_.qz_criterium;
% info(1) = 3;
% info(2) = temp'*temp;
% return
% end
sdim = sum( abs(dr.eigval) < options_.qz_criterium );
nba = nd-sdim;
nyf = sum(kstate(:,2) > M_.maximum_endo_lag+1);
if nba ~= nyf
temp = sort(abs(dr.eigval));
if nba > nyf
temp = temp(nd-nba+1:nd-nyf)-1-options_.qz_criterium;
info(1) = 3;
elseif nba < nyf;
temp = temp(nd-nyf+1:nd-nba)-1-options_.qz_criterium;
info(1) = 4;
end
info(2) = temp'*temp;
return
end
if options_.loglinear == 1
k = find(dr.kstate(:,2) <= M_.maximum_endo_lag+1);
klag = dr.kstate(k,[1 2]);
k1 = dr.order_var;
dr.ghx = repmat(1./dr.ys(k1),1,size(dr.ghx,2)).*dr.ghx.* ...
repmat(dr.ys(k1(klag(:,1)))',size(dr.ghx,1),1);
dr.ghu = repmat(1./dr.ys(k1),1,size(dr.ghu,2)).*dr.ghu;
end
dr.ghx = real(dr.ghx);
dr.ghu = real(dr.ghu);
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%exogenous deterministic variables
if M_.exo_det_nbr > 0
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 = sparse(jacobia_(:,nz+M_.exo_nbr+1:end));
M1 = inv(f0+[zeros(M_.endo_nbr,nstatic) f1*gx zeros(M_.endo_nbr,nyf-nboth)]);
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
if options_.order == 1
return
end
% Second order
%tempex = oo_.exo_simul ;
[junk,jacobia_,hessian] = feval([M_.fname '_dynamic'],z,...
[oo_.exo_simul ...
oo_.exo_det_simul], M_.params, it_);
%hessian = real(hessext('ff1_',[z; oo_.exo_steady_state]))' ;
kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
if M_.maximum_endo_lag > 0
kk = [cumsum(M_.lead_lag_incidence(1:M_.maximum_endo_lag,order_var),1); kk];
end
kk = kk';
kk = find(kk(:));
nk = size(kk,1) + M_.exo_nbr + M_.exo_det_nbr;
k1 = M_.lead_lag_incidence(:,order_var);
k1 = k1';
k1 = k1(:);
k1 = k1(kk);
k2 = find(k1);
kk1(k1(k2)) = k2;
kk1 = [kk1 length(k1)+1:length(k1)+M_.exo_nbr+M_.exo_det_nbr];
kk = reshape([1:nk^2],nk,nk);
kk1 = kk(kk1,kk1);
%[junk,junk,hessian] = feval([M_.fname '_dynamic'],z, oo_.exo_steady_state);
hessian(:,kk1(:)) = hessian;
%oo_.exo_simul = tempex ;
%clear tempex
n1 = 0;
n2 = np;
zx = zeros(np,np);
zu=zeros(np,M_.exo_nbr);
for i=2:M_.maximum_endo_lag+1
k1 = sum(kstate(:,2) == i);
zx(n1+1:n1+k1,n2-k1+1:n2)=eye(k1);
n1 = n1+k1;
n2 = n2-k1;
end
kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
k0 = [1:M_.endo_nbr];
gx1 = dr.ghx;
hu = dr.ghu(nstatic+[1:npred],:);
zx = [zx; gx1];
zu = [zu; dr.ghu];
for i=1:M_.maximum_endo_lead
k1 = find(kk(i+1,k0) > 0);
zu = [zu; gx1(k1,1:npred)*hu];
gx1 = gx1(k1,:)*hx;
zx = [zx; gx1];
kk = kk(:,k0);
k0 = k1;
end
zx=[zx; zeros(M_.exo_nbr,np);zeros(M_.exo_det_nbr,np)];
zu=[zu; eye(M_.exo_nbr);zeros(M_.exo_det_nbr,M_.exo_nbr)];
[nrzx,nczx] = size(zx);
rhs = -sparse_hessian_times_B_kronecker_C(hessian,zx);
%lhs
n = M_.endo_nbr+sum(kstate(:,2) > M_.maximum_endo_lag+1 & kstate(:,2) < M_.maximum_endo_lag+M_.maximum_endo_lead+1);
A = zeros(n,n);
B = zeros(n,n);
A(1:M_.endo_nbr,1:M_.endo_nbr) = jacobia_(:,M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var));
% variables with the highest lead
k1 = find(kstate(:,2) == M_.maximum_endo_lag+M_.maximum_endo_lead+1);
if M_.maximum_endo_lead > 1
k2 = find(kstate(:,2) == M_.maximum_endo_lag+M_.maximum_endo_lead);
[junk,junk,k3] = intersect(kstate(k1,1),kstate(k2,1));
else
k2 = [1:M_.endo_nbr];
k3 = kstate(k1,1);
end
% Jacobian with respect to the variables with the highest lead
B(1:M_.endo_nbr,end-length(k2)+k3) = jacobia_(:,kstate(k1,3)+M_.endo_nbr);
offset = M_.endo_nbr;
k0 = [1:M_.endo_nbr];
gx1 = dr.ghx;
for i=1:M_.maximum_endo_lead-1
k1 = find(kstate(:,2) == M_.maximum_endo_lag+i+1);
[k2,junk,k3] = find(kstate(k1,3));
A(1:M_.endo_nbr,offset+k2) = jacobia_(:,k3+M_.endo_nbr);
n1 = length(k1);
A(offset+[1:n1],nstatic+[1:npred]) = -gx1(kstate(k1,1),1:npred);
gx1 = gx1*hx;
A(offset+[1:n1],offset+[1:n1]) = eye(n1);
n0 = length(k0);
E = eye(n0);
if i == 1
[junk,junk,k4]=intersect(kstate(k1,1),[1:M_.endo_nbr]);
else
[junk,junk,k4]=intersect(kstate(k1,1),kstate(k0,1));
end
i1 = offset-n0+n1;
B(offset+[1:n1],offset-n0+[1:n0]) = -E(k4,:);
k0 = k1;
offset = offset + n1;
end
[junk,k1,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+M_.maximum_endo_lead+1,order_var));
A(1:M_.endo_nbr,nstatic+1:nstatic+npred)=...
A(1:M_.endo_nbr,nstatic+[1:npred])+jacobia_(:,k2)*gx1(k1,1:npred);
C = hx;
D = [rhs; zeros(n-M_.endo_nbr,size(rhs,2))];
dr.ghxx = gensylv(2,A,B,C,D);
%ghxu
%rhs
hu = dr.ghu(nstatic+1:nstatic+npred,:);
%kk = reshape([1:np*np],np,np);
%kk = kk(1:npred,1:npred);
%rhs = -hessian*kron(zx,zu)-f1*dr.ghxx(end-nyf+1:end,kk(:))*kron(hx(1:npred,:),hu(1:npred,:));
rhs = sparse_hessian_times_B_kronecker_C(hessian,zx,zu);
nyf1 = sum(kstate(:,2) == M_.maximum_endo_lag+2);
hu1 = [hu;zeros(np-npred,M_.exo_nbr)];
%B1 = [B(1:M_.endo_nbr,:);zeros(size(A,1)-M_.endo_nbr,size(B,2))];
[nrhx,nchx] = size(hx);
[nrhu1,nchu1] = size(hu1);
B1 = B*A_times_B_kronecker_C(dr.ghxx,hx,hu1);
rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
%lhs
dr.ghxu = A\rhs;
%ghuu
%rhs
kk = reshape([1:np*np],np,np);
kk = kk(1:npred,1:npred);
rhs = sparse_hessian_times_B_kronecker_C(hessian,zu);
B1 = A_times_B_kronecker_C(B*dr.ghxx,hu1);
rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
%lhs
dr.ghuu = A\rhs;
dr.ghxx = dr.ghxx(1:M_.endo_nbr,:);
dr.ghxu = dr.ghxu(1:M_.endo_nbr,:);
dr.ghuu = dr.ghuu(1:M_.endo_nbr,:);
% dr.ghs2
% derivatives of F with respect to forward variables
% reordering predetermined variables in diminishing lag order
O1 = zeros(M_.endo_nbr,nstatic);
O2 = zeros(M_.endo_nbr,M_.endo_nbr-nstatic-npred);
LHS = jacobia_(:,M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var));
RHS = zeros(M_.endo_nbr,M_.exo_nbr^2);
kk = find(kstate(:,2) == M_.maximum_endo_lag+2);
gu = dr.ghu;
guu = dr.ghuu;
Gu = [dr.ghu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr)];
Guu = [dr.ghuu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr*M_.exo_nbr)];
E = eye(M_.endo_nbr);
M_.lead_lag_incidenceordered = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
if M_.maximum_endo_lag > 0
M_.lead_lag_incidenceordered = [cumsum(M_.lead_lag_incidence(1:M_.maximum_endo_lag,order_var),1); M_.lead_lag_incidenceordered];
end
M_.lead_lag_incidenceordered = M_.lead_lag_incidenceordered';
M_.lead_lag_incidenceordered = M_.lead_lag_incidenceordered(:);
k1 = find(M_.lead_lag_incidenceordered);
M_.lead_lag_incidenceordered(k1) = [1:length(k1)]';
M_.lead_lag_incidenceordered =reshape(M_.lead_lag_incidenceordered,M_.endo_nbr,M_.maximum_endo_lag+M_.maximum_endo_lead+1)';
kh = reshape([1:nk^2],nk,nk);
kp = sum(kstate(:,2) <= M_.maximum_endo_lag+1);
E1 = [eye(npred); zeros(kp-npred,npred)];
H = E1;
hxx = dr.ghxx(nstatic+[1:npred],:);
for i=1:M_.maximum_endo_lead
for j=i:M_.maximum_endo_lead
[junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+j+1,order_var));
[junk,k3a,k3] = ...
find(M_.lead_lag_incidenceordered(M_.maximum_endo_lag+j+1,:));
nk3a = length(k3a);
B1 = sparse_hessian_times_B_kronecker_C(hessian(:,kh(k3,k3)),gu(k3a,:));
RHS = RHS + jacobia_(:,k2)*guu(k2a,:)+B1;
end
% LHS
[junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+i+1,order_var));
LHS = LHS + jacobia_(:,k2)*(E(k2a,:)+[O1(k2a,:) dr.ghx(k2a,:)*H O2(k2a,:)]);
if i == M_.maximum_endo_lead
break
end
kk = find(kstate(:,2) == M_.maximum_endo_lag+i+1);
gu = dr.ghx*Gu;
[nrGu,ncGu] = size(Gu);
G1 = A_times_B_kronecker_C(dr.ghxx,Gu);
G2 = A_times_B_kronecker_C(hxx,Gu);
guu = dr.ghx*Guu+G1;
Gu = hx*Gu;
Guu = hx*Guu;
Guu(end-npred+1:end,:) = Guu(end-npred+1:end,:) + G2;
H = E1 + hx*H;
end
RHS = RHS*M_.Sigma_e(:);
dr.fuu = RHS;
%RHS = -RHS-dr.fbias;
RHS = -RHS;
dr.ghs2 = LHS\RHS;
% deterministic exogenous variables
if M_.exo_det_nbr > 0
hud = dr.ghud{1}(nstatic+1:nstatic+npred,:);
zud=[zeros(np,M_.exo_det_nbr);dr.ghud{1};gx(:,1:npred)*hud;zeros(M_.exo_nbr,M_.exo_det_nbr);eye(M_.exo_det_nbr)];
R1 = hessian*kron(zx,zud);
dr.ghxud = cell(M_.exo_det_length,1);
kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
kp = nstatic+[1:npred];
dr.ghxud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{1}(kp,:)));
Eud = eye(M_.exo_det_nbr);
for i = 2:M_.exo_det_length
hudi = dr.ghud{i}(kp,:);
zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
R2 = hessian*kron(zx,zudi);
dr.ghxud{i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(hx,Eud)+dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{i}(kp,:)))-M1*R2;
end
R1 = hessian*kron(zu,zud);
dr.ghudud = cell(M_.exo_det_length,1);
kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
dr.ghuud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghu(kp,:),dr.ghud{1}(kp,:)));
Eud = eye(M_.exo_det_nbr);
for i = 2:M_.exo_det_length
hudi = dr.ghud{i}(kp,:);
zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
R2 = hessian*kron(zu,zudi);
dr.ghuud{i} = -M2*dr.ghxud{i-1}(kf,:)*kron(hu,Eud)-M1*R2;
end
R1 = hessian*kron(zud,zud);
dr.ghudud = cell(M_.exo_det_length,M_.exo_det_length);
dr.ghudud{1,1} = -M1*R1-M2*dr.ghxx(kf,:)*kron(hud,hud);
for i = 2:M_.exo_det_length
hudi = dr.ghud{i}(nstatic+1:nstatic+npred,:);
zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi+dr.ghud{i-1}(kf,:);zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
R2 = hessian*kron(zudi,zudi);
dr.ghudud{i,i} = -M2*(dr.ghudud{i-1,i-1}(kf,:)+...
2*dr.ghxud{i-1}(kf,:)*kron(hudi,Eud) ...
+dr.ghxx(kf,:)*kron(hudi,hudi))-M1*R2;
R2 = hessian*kron(zud,zudi);
dr.ghudud{1,i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(hud,Eud)+...
dr.ghxx(kf,:)*kron(hud,hudi))...
-M1*R2;
for j=2:i-1
hudj = dr.ghud{j}(kp,:);
zudj=[zeros(np,M_.exo_det_nbr);dr.ghud{j};gx(:,1:npred)*hudj;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
R2 = hessian*kron(zudj,zudi);
dr.ghudud{j,i} = -M2*(dr.ghudud{j-1,i-1}(kf,:)+dr.ghxud{j-1}(kf,:)* ...
kron(hudi,Eud)+dr.ghxud{i-1}(kf,:)* ...
kron(hudj,Eud)+dr.ghxx(kf,:)*kron(hudj,hudi))-M1*R2;
end
end
end
\ No newline at end of file
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