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Partial information: converted files to UNIX EOL convention

time-shift
Sébastien Villemot 2010-03-24 12:14:41 +01:00
parent 0af39dca5d
commit 45efcd61dd
6 changed files with 791 additions and 791 deletions
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324
matlab/partial_information/PCL_Part_info_irf.m
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@ -1,162 +1,162 @@
function [irfmat,irfst]=PCL_Part_info_irf( H, varobs, M_, dr, irfpers,ii)
% sets up parameters and calls part-info kalman filter
% developed by G Perendia, July 2006 for implementation from notes by Prof. Joe Pearlman to
% suit partial information RE solution in accordance with, and based on, the
% Pearlman, Currie and Levine 1986 solution.
% 22/10/06 - Version 2 for new Riccati with 4 params instead 5
% Copyright (C) 2001-20010 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/>.
% Recall that the state space is given by the
% predetermined variables s(t-1), x(t-1)
% and the jump variables x(t).
% The jump variables have dimension NETA
[junk,OBS] = ismember(varobs,M_.endo_names,'rows');
G1=dr.PI_ghx;
impact=dr.PI_ghu;
nmat=dr.PI_nmat;
CC=dr.PI_CC;
NX=M_.exo_nbr; % no of exogenous varexo shock variables.
FL_RANK=dr.PI_FL_RANK;
NY=M_.endo_nbr;
if isempty(OBS)
NOBS=NY;
LL=eye(NY,NY);
else %and if no obsevations specify OBS=[0] but this is not going to work properly
NOBS=length(OBS);
LL=zeros(NOBS,NY);
for i=1:NOBS
LL(i,OBS(i))=1;
end
end
if exist( 'irfpers')==1
if ~isempty(irfpers)
if irfpers<=0, irfpers=20, end;
else
irfpers=20;
end
else
irfpers=20;
end
ss=size(G1,1);
pd=ss-size(nmat,1);
SDX=M_.Sigma_e^0.5; % =SD,not V-COV, of Exog shocks or M_.Sigma_e^0.5 num_exog x num_exog matrix
if isempty(H)
H=M_.H;
end
VV=H; % V-COV of observation errors.
MM=impact*SDX; % R*(Q^0.5) in standard KF notation
% observation vector indices
% mapping to endogenous variables.
L1=LL*dr.PI_TT1;
L2=LL*dr.PI_TT2;
MM1=MM(1:ss-FL_RANK,:);
U11=MM1*MM1';
% SDX
U22=0;
% determine K1 and K2 observation mapping matrices
% This uses the fact that measurements are given by L1*s(t)+L2*x(t)
% and s(t) is expressed in the dynamics as
% H1*eps(t)+G11*s(t-1)+G12*x(t-1)+G13*x(t).
% Thus the observations o(t) can be written in the form
% o(t)=K1*[eps(t)' s(t-1)' x(t-1)']' + K2*x(t) where
% K1=[L1*H1 L1*G11 L1*G12] K2=L1*G13+L2
G12=G1(NX+1:ss-2*FL_RANK,:);
KK1=L1*G12;
K1=KK1(:,1:ss-FL_RANK);
K2=KK1(:,ss-FL_RANK+1:ss)+L2;
%pre calculate time-invariant factors
A11=G1(1:pd,1:pd);
A22=G1(pd+1:end, pd+1:end);
A12=G1(1:pd, pd+1:end);
A21=G1(pd+1:end,1:pd);
Lambda= nmat*A12+A22;
%A11_A12Nmat= A11-A12*nmat % test
I_L=inv(Lambda);
BB=A12*inv(A22);
FF=K2*inv(A22);
QQ=BB*U22*BB' + U11;
UFT=U22*FF';
% kf_param structure:
AA=A11-BB*A21;
CCCC=A11-A12*nmat; % F in new notation
DD=K1-FF*A21; % H in new notation
EE=K1-K2*nmat;
RR=FF*UFT+VV;
if ~any(RR)
% if zero add some dummy measurement err. variance-covariances
% with diagonals 0.000001. This would not be needed if we used
% the slow solver, or the generalised eigenvalue approach,
% but these are both slower.
RR=eye(size(RR,1))*1.0e-6;
end
SS=BB*UFT;
VKLUFT=VV+K2*I_L*UFT;
ALUFT=A12*I_L*UFT;
FULKV=FF*U22*I_L'*K2'+VV;
FUBT=FF*U22*BB';
nmat=nmat;
% initialise pshat
AQDS=AA*QQ*DD'+SS;
DQDR=DD*QQ*DD'+RR;
I_DQDR=inv(DQDR);
AQDQ=AQDS*I_DQDR;
ff=AA-AQDQ*DD;
hh=AA*QQ*AA'-AQDQ*AQDS';%*(DD*QQ*AA'+SS');
rr=DD*QQ*DD'+RR;
ZSIG0=disc_riccati_fast(ff,DD,rr,hh);
PP=ZSIG0 +QQ;
exo_names=M_.exo_names(M_.exo_names_orig_ord,:);
DPDR=DD*PP*DD'+RR;
I_DPDR=inv(DPDR);
PDIDPDRD=PP*DD'*I_DPDR*DD;
%GG=[CCCC (AA-CCCC)*(eye(ss-FL_RANK)-PP*DD'*I_DQDR*DD); zeros(ss-FL_RANK) AA*(eye(ss-FL_RANK)-PP*DD'*I_DQDR*DD)];
GG=[CCCC (AA-CCCC)*(eye(ss-FL_RANK)-PDIDPDRD); zeros(ss-FL_RANK) AA*(eye(ss-FL_RANK)-PDIDPDRD)];
imp=[impact(1:ss-FL_RANK,:); impact(1:ss-FL_RANK,:)];
% Calculate IRFs of observable series
%The extra term in leads to
%LL0=[EE (H-EE)(I-PH^T(HPH^T+V)^{-1}H)].
%Then in the case of observing all variables without noise (V=0), this
% leads to LL0=[EE 0].
I_PD=(eye(ss-FL_RANK)-PDIDPDRD);
LL0=[ EE (DD-EE)*I_PD];
%OVV = [ zeros( size(dr.PI_TT1,1), NX ) dr.PI_TT1 dr.PI_TT2];
VV = [ dr.PI_TT1 dr.PI_TT2];
stderr=diag(M_.Sigma_e^0.5);
irfmat=zeros(size(dr.PI_TT1 ,1),irfpers);
irfst=zeros(size(GG,1),irfpers);
irfst(:,1)=stderr(ii)*imp(:,ii);
for jj=2:irfpers;
irfst(:,jj)=GG*irfst(:,jj-1); % xjj=f irfstjj-2
irfmat(:,jj-1)=VV*irfst(NX+1:ss-FL_RANK,jj);
%irfmat(:,jj)=LL0*irfst(:,jj);
end
save ([M_.fname '_PCL_PtInfoIRFs_' num2str(ii) '_' deblank(exo_names(ii,:))], 'irfmat','irfst');
function [irfmat,irfst]=PCL_Part_info_irf( H, varobs, M_, dr, irfpers,ii)
% sets up parameters and calls part-info kalman filter
% developed by G Perendia, July 2006 for implementation from notes by Prof. Joe Pearlman to
% suit partial information RE solution in accordance with, and based on, the
% Pearlman, Currie and Levine 1986 solution.
% 22/10/06 - Version 2 for new Riccati with 4 params instead 5
% Copyright (C) 2001-20010 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/>.
% Recall that the state space is given by the
% predetermined variables s(t-1), x(t-1)
% and the jump variables x(t).
% The jump variables have dimension NETA
[junk,OBS] = ismember(varobs,M_.endo_names,'rows');
G1=dr.PI_ghx;
impact=dr.PI_ghu;
nmat=dr.PI_nmat;
CC=dr.PI_CC;
NX=M_.exo_nbr; % no of exogenous varexo shock variables.
FL_RANK=dr.PI_FL_RANK;
NY=M_.endo_nbr;
if isempty(OBS)
NOBS=NY;
LL=eye(NY,NY);
else %and if no obsevations specify OBS=[0] but this is not going to work properly
NOBS=length(OBS);
LL=zeros(NOBS,NY);
for i=1:NOBS
LL(i,OBS(i))=1;
end
end
if exist( 'irfpers')==1
if ~isempty(irfpers)
if irfpers<=0, irfpers=20, end;
else
irfpers=20;
end
else
irfpers=20;
end
ss=size(G1,1);
pd=ss-size(nmat,1);
SDX=M_.Sigma_e^0.5; % =SD,not V-COV, of Exog shocks or M_.Sigma_e^0.5 num_exog x num_exog matrix
if isempty(H)
H=M_.H;
end
VV=H; % V-COV of observation errors.
MM=impact*SDX; % R*(Q^0.5) in standard KF notation
% observation vector indices
% mapping to endogenous variables.
L1=LL*dr.PI_TT1;
L2=LL*dr.PI_TT2;
MM1=MM(1:ss-FL_RANK,:);
U11=MM1*MM1';
% SDX
U22=0;
% determine K1 and K2 observation mapping matrices
% This uses the fact that measurements are given by L1*s(t)+L2*x(t)
% and s(t) is expressed in the dynamics as
% H1*eps(t)+G11*s(t-1)+G12*x(t-1)+G13*x(t).
% Thus the observations o(t) can be written in the form
% o(t)=K1*[eps(t)' s(t-1)' x(t-1)']' + K2*x(t) where
% K1=[L1*H1 L1*G11 L1*G12] K2=L1*G13+L2
G12=G1(NX+1:ss-2*FL_RANK,:);
KK1=L1*G12;
K1=KK1(:,1:ss-FL_RANK);
K2=KK1(:,ss-FL_RANK+1:ss)+L2;
%pre calculate time-invariant factors
A11=G1(1:pd,1:pd);
A22=G1(pd+1:end, pd+1:end);
A12=G1(1:pd, pd+1:end);
A21=G1(pd+1:end,1:pd);
Lambda= nmat*A12+A22;
%A11_A12Nmat= A11-A12*nmat % test
I_L=inv(Lambda);
BB=A12*inv(A22);
FF=K2*inv(A22);
QQ=BB*U22*BB' + U11;
UFT=U22*FF';
% kf_param structure:
AA=A11-BB*A21;
CCCC=A11-A12*nmat; % F in new notation
DD=K1-FF*A21; % H in new notation
EE=K1-K2*nmat;
RR=FF*UFT+VV;
if ~any(RR)
% if zero add some dummy measurement err. variance-covariances
% with diagonals 0.000001. This would not be needed if we used
% the slow solver, or the generalised eigenvalue approach,
% but these are both slower.
RR=eye(size(RR,1))*1.0e-6;
end
SS=BB*UFT;
VKLUFT=VV+K2*I_L*UFT;
ALUFT=A12*I_L*UFT;
FULKV=FF*U22*I_L'*K2'+VV;
FUBT=FF*U22*BB';
nmat=nmat;
% initialise pshat
AQDS=AA*QQ*DD'+SS;
DQDR=DD*QQ*DD'+RR;
I_DQDR=inv(DQDR);
AQDQ=AQDS*I_DQDR;
ff=AA-AQDQ*DD;
hh=AA*QQ*AA'-AQDQ*AQDS';%*(DD*QQ*AA'+SS');
rr=DD*QQ*DD'+RR;
ZSIG0=disc_riccati_fast(ff,DD,rr,hh);
PP=ZSIG0 +QQ;
exo_names=M_.exo_names(M_.exo_names_orig_ord,:);
DPDR=DD*PP*DD'+RR;
I_DPDR=inv(DPDR);
PDIDPDRD=PP*DD'*I_DPDR*DD;
%GG=[CCCC (AA-CCCC)*(eye(ss-FL_RANK)-PP*DD'*I_DQDR*DD); zeros(ss-FL_RANK) AA*(eye(ss-FL_RANK)-PP*DD'*I_DQDR*DD)];
GG=[CCCC (AA-CCCC)*(eye(ss-FL_RANK)-PDIDPDRD); zeros(ss-FL_RANK) AA*(eye(ss-FL_RANK)-PDIDPDRD)];
imp=[impact(1:ss-FL_RANK,:); impact(1:ss-FL_RANK,:)];
% Calculate IRFs of observable series
%The extra term in leads to
%LL0=[EE (H-EE)(I-PH^T(HPH^T+V)^{-1}H)].
%Then in the case of observing all variables without noise (V=0), this
% leads to LL0=[EE 0].
I_PD=(eye(ss-FL_RANK)-PDIDPDRD);
LL0=[ EE (DD-EE)*I_PD];
%OVV = [ zeros( size(dr.PI_TT1,1), NX ) dr.PI_TT1 dr.PI_TT2];
VV = [ dr.PI_TT1 dr.PI_TT2];
stderr=diag(M_.Sigma_e^0.5);
irfmat=zeros(size(dr.PI_TT1 ,1),irfpers);
irfst=zeros(size(GG,1),irfpers);
irfst(:,1)=stderr(ii)*imp(:,ii);
for jj=2:irfpers;
irfst(:,jj)=GG*irfst(:,jj-1); % xjj=f irfstjj-2
irfmat(:,jj-1)=VV*irfst(NX+1:ss-FL_RANK,jj);
%irfmat(:,jj)=LL0*irfst(:,jj);
end
save ([M_.fname '_PCL_PtInfoIRFs_' num2str(ii) '_' deblank(exo_names(ii,:))], 'irfmat','irfst');

400
matlab/partial_information/PCL_Part_info_moments.m
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@ -1,200 +1,200 @@
function [irfmat,irfst]=PCL_Part_info_moments( H, varobs, dr,ivar)
% sets up parameters and calls part-info kalman filter
% developed by G Perendia, July 2006 for implementation from notes by Prof. Joe Pearlman to
% suit partial information RE solution in accordance with, and based on, the
% Pearlman, Currie and Levine 1986 solution.
% 22/10/06 - Version 2 for new Riccati with 4 params instead 5
% Copyright (C) 2001-20010 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/>.
% Recall that the state space is given by the
% predetermined variables s(t-1), x(t-1)
% and the jump variables x(t).
% The jump variables have dimension NETA
global M_ options_ oo_
warning_old_state = warning;
warning off
[junk,OBS] = ismember(varobs,M_.endo_names,'rows');
G1=dr.PI_ghx;
impact=dr.PI_ghu;
nmat=dr.PI_nmat;
CC=dr.PI_CC;
NX=M_.exo_nbr; % no of exogenous varexo shock variables.
% NETA=dr.nfwrd+dr.nboth; % total no of exp. errors set to no of forward looking equations
FL_RANK=dr.PI_FL_RANK;
NY=M_.endo_nbr;
if isempty(OBS)
NOBS=NY;
LL=eye(NY,NY);
else %and if no obsevations specify OBS=[0] but this is not going to work properly
NOBS=length(OBS);
LL=zeros(NOBS,NY);
for i=1:NOBS
LL(i,OBS(i))=1;
end
end
if exist( 'irfpers')==1
if ~isempty(irfpers)
if irfpers<=0, irfpers=20, end;
else
irfpers=20;
end
else
irfpers=20;
end
ss=size(G1,1);
pd=ss-size(nmat,1);
SDX=M_.Sigma_e^0.5; % =SD,not V-COV, of Exog shocks or M_.Sigma_e^0.5 num_exog x num_exog matrix
if isempty(H)
H=M_.H;
end
VV=H; % V-COV of observation errors.
MM=impact*SDX; % R*(Q^0.5) in standard KF notation
% observation vector indices
% mapping to endogenous variables.
L1=LL*dr.PI_TT1;
L2=LL*dr.PI_TT2;
MM1=MM(1:ss-FL_RANK,:);
U11=MM1*MM1';
% SDX
U22=0;
% determine K1 and K2 observation mapping matrices
% This uses the fact that measurements are given by L1*s(t)+L2*x(t)
% and s(t) is expressed in the dynamics as
% H1*eps(t)+G11*s(t-1)+G12*x(t-1)+G13*x(t).
% Thus the observations o(t) can be written in the form
% o(t)=K1*[eps(t)' s(t-1)' x(t-1)']' + K2*x(t) where
% K1=[L1*H1 L1*G11 L1*G12] K2=L1*G13+L2
G12=G1(NX+1:ss-2*FL_RANK,:);
KK1=L1*G12;
K1=KK1(:,1:ss-FL_RANK);
K2=KK1(:,ss-FL_RANK+1:ss)+L2;
%pre calculate time-invariant factors
A11=G1(1:pd,1:pd);
A22=G1(pd+1:end, pd+1:end);
A12=G1(1:pd, pd+1:end);
A21=G1(pd+1:end,1:pd);
Lambda= nmat*A12+A22;
%A11_A12Nmat= A11-A12*nmat % test
I_L=inv(Lambda);
BB=A12*inv(A22);
FF=K2*inv(A22);
QQ=BB*U22*BB' + U11;
UFT=U22*FF';
% kf_param structure:
AA=A11-BB*A21;
CCCC=A11-A12*nmat; % F in new notation
DD=K1-FF*A21; % H in new notation
EE=K1-K2*nmat;
RR=FF*UFT+VV;
if ~any(RR)
% if zero add some dummy measurement err. variance-covariances
% with diagonals 0.000001. This would not be needed if we used
% the slow solver, or the generalised eigenvalue approach,
% but these are both slower.
RR=eye(size(RR,1))*1.0e-6;
end
SS=BB*UFT;
VKLUFT=VV+K2*I_L*UFT;
ALUFT=A12*I_L*UFT;
FULKV=FF*U22*I_L'*K2'+VV;
FUBT=FF*U22*BB';
nmat=nmat;
% initialise pshat
AQDS=AA*QQ*DD'+SS;
DQDR=DD*QQ*DD'+RR;
I_DQDR=inv(DQDR);
AQDQ=AQDS*I_DQDR;
ff=AA-AQDQ*DD;
hh=AA*QQ*AA'-AQDQ*AQDS';%*(DD*QQ*AA'+SS');
rr=DD*QQ*DD'+RR;
ZSIG0=disc_riccati_fast(ff,DD,rr,hh);
PP=ZSIG0 +QQ;
exo_names=M_.exo_names(M_.exo_names_orig_ord,:);
DPDR=DD*PP*DD'+RR;
I_DPDR=inv(DPDR);
%GG=[ CCCC, zeros(pd,NETA); -nmat*CCCC, zeros(NETA,NETA)];
PDIDPDRD=PP*DD'*I_DPDR*DD;
MSIG=disclyap_fast(CCCC, CCCC*PDIDPDRD*PP*CCCC');
COV_P=[ PP, PP; PP, PP+MSIG]; % P0
dr.PI_GG=[CCCC (AA-CCCC)*(eye(ss-FL_RANK)-PDIDPDRD); zeros(ss-FL_RANK) AA*(eye(ss-FL_RANK)-PDIDPDRD)];
GAM= [ AA*(eye(ss-FL_RANK)-PDIDPDRD) zeros(ss-FL_RANK); (AA-CCCC)*(eye(ss-FL_RANK)-PDIDPDRD), CCCC];
VV = [ dr.PI_TT1 dr.PI_TT2];
nn=size(VV,1);
COV_OMEGA= COV_P( end-nn+1:end, end-nn+1:end);
COV_YR0= VV*COV_OMEGA*VV';
diagCovYR0=diag(COV_YR0);
labels = deblank(M_.endo_names(ivar,:));
if options_.nomoments == 0
z = [ sqrt(diagCovYR0(ivar)) diagCovYR0(ivar) ];
title='MOMENTS OF SIMULATED VARIABLES';
headers=strvcat('VARIABLE','STD. DEV.','VARIANCE');
dyntable(title,headers,labels,z,size(labels,2)+2,16,10);
end
if options_.nocorr == 0
diagSqrtCovYR0=sqrt(diagCovYR0);
%COR_Y= diag(diagSqrtCovYR0)*COV_YR0*diag(diagSqrtCovYR0);
DELTA=inv(diag(diagSqrtCovYR0));
COR_Y= DELTA*COV_YR0*DELTA;
title = 'CORRELATION OF SIMULATED VARIABLES';
headers = strvcat('VARIABLE',M_.endo_names(ivar,:));
dyntable(title,headers,labels,COR_Y(ivar,ivar),size(labels,2)+2,8,4);
else
COR_Y=[];
end
ar = options_.ar;
options_ = set_default_option(options_,'ar',5);
ar = options_.ar;
if ar > 0
COV_YRk= zeros(nn,ar);
AutoCOR_YRk= zeros(nn,ar);
for k=1:ar;
COV_P=GAM*COV_P;
COV_OMEGA= COV_P( end-nn+1:end, end-nn+1:end);
COV_YRk = VV*COV_OMEGA*VV';
AutoCOR_YRkMAT=DELTA*COV_YRk*DELTA;
oo_.autocorr{k}=AutoCOR_YRkMAT(ivar,ivar);
AutoCOR_YRk(:,k)= diag(COV_YRk)./diagCovYR0;
end
title = 'AUTOCORRELATION OF SIMULATED VARIABLES';
headers = strvcat('VARIABLE',int2str([1:ar]'));
dyntable(title,headers,labels,AutoCOR_YRk(ivar,:),size(labels,2)+2,8,4);
else
AutoCOR_YRk=[];
end
save ([M_.fname '_PCL_moments'], 'COV_YR0','AutoCOR_YRk', 'COR_Y');
warning(warning_old_state);
function [irfmat,irfst]=PCL_Part_info_moments( H, varobs, dr,ivar)
% sets up parameters and calls part-info kalman filter
% developed by G Perendia, July 2006 for implementation from notes by Prof. Joe Pearlman to
% suit partial information RE solution in accordance with, and based on, the
% Pearlman, Currie and Levine 1986 solution.
% 22/10/06 - Version 2 for new Riccati with 4 params instead 5
% Copyright (C) 2001-20010 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/>.
% Recall that the state space is given by the
% predetermined variables s(t-1), x(t-1)
% and the jump variables x(t).
% The jump variables have dimension NETA
global M_ options_ oo_
warning_old_state = warning;
warning off
[junk,OBS] = ismember(varobs,M_.endo_names,'rows');
G1=dr.PI_ghx;
impact=dr.PI_ghu;
nmat=dr.PI_nmat;
CC=dr.PI_CC;
NX=M_.exo_nbr; % no of exogenous varexo shock variables.
% NETA=dr.nfwrd+dr.nboth; % total no of exp. errors set to no of forward looking equations
FL_RANK=dr.PI_FL_RANK;
NY=M_.endo_nbr;
if isempty(OBS)
NOBS=NY;
LL=eye(NY,NY);
else %and if no obsevations specify OBS=[0] but this is not going to work properly
NOBS=length(OBS);
LL=zeros(NOBS,NY);
for i=1:NOBS
LL(i,OBS(i))=1;
end
end
if exist( 'irfpers')==1
if ~isempty(irfpers)
if irfpers<=0, irfpers=20, end;
else
irfpers=20;
end
else
irfpers=20;
end
ss=size(G1,1);
pd=ss-size(nmat,1);
SDX=M_.Sigma_e^0.5; % =SD,not V-COV, of Exog shocks or M_.Sigma_e^0.5 num_exog x num_exog matrix
if isempty(H)
H=M_.H;
end
VV=H; % V-COV of observation errors.
MM=impact*SDX; % R*(Q^0.5) in standard KF notation
% observation vector indices
% mapping to endogenous variables.
L1=LL*dr.PI_TT1;
L2=LL*dr.PI_TT2;
MM1=MM(1:ss-FL_RANK,:);
U11=MM1*MM1';
% SDX
U22=0;
% determine K1 and K2 observation mapping matrices
% This uses the fact that measurements are given by L1*s(t)+L2*x(t)
% and s(t) is expressed in the dynamics as
% H1*eps(t)+G11*s(t-1)+G12*x(t-1)+G13*x(t).
% Thus the observations o(t) can be written in the form
% o(t)=K1*[eps(t)' s(t-1)' x(t-1)']' + K2*x(t) where
% K1=[L1*H1 L1*G11 L1*G12] K2=L1*G13+L2
G12=G1(NX+1:ss-2*FL_RANK,:);
KK1=L1*G12;
K1=KK1(:,1:ss-FL_RANK);
K2=KK1(:,ss-FL_RANK+1:ss)+L2;
%pre calculate time-invariant factors
A11=G1(1:pd,1:pd);
A22=G1(pd+1:end, pd+1:end);
A12=G1(1:pd, pd+1:end);
A21=G1(pd+1:end,1:pd);
Lambda= nmat*A12+A22;
%A11_A12Nmat= A11-A12*nmat % test
I_L=inv(Lambda);
BB=A12*inv(A22);
FF=K2*inv(A22);
QQ=BB*U22*BB' + U11;
UFT=U22*FF';
% kf_param structure:
AA=A11-BB*A21;
CCCC=A11-A12*nmat; % F in new notation
DD=K1-FF*A21; % H in new notation
EE=K1-K2*nmat;
RR=FF*UFT+VV;
if ~any(RR)
% if zero add some dummy measurement err. variance-covariances
% with diagonals 0.000001. This would not be needed if we used
% the slow solver, or the generalised eigenvalue approach,
% but these are both slower.
RR=eye(size(RR,1))*1.0e-6;
end
SS=BB*UFT;
VKLUFT=VV+K2*I_L*UFT;
ALUFT=A12*I_L*UFT;
FULKV=FF*U22*I_L'*K2'+VV;
FUBT=FF*U22*BB';
nmat=nmat;
% initialise pshat
AQDS=AA*QQ*DD'+SS;
DQDR=DD*QQ*DD'+RR;
I_DQDR=inv(DQDR);
AQDQ=AQDS*I_DQDR;
ff=AA-AQDQ*DD;
hh=AA*QQ*AA'-AQDQ*AQDS';%*(DD*QQ*AA'+SS');
rr=DD*QQ*DD'+RR;
ZSIG0=disc_riccati_fast(ff,DD,rr,hh);
PP=ZSIG0 +QQ;
exo_names=M_.exo_names(M_.exo_names_orig_ord,:);
DPDR=DD*PP*DD'+RR;
I_DPDR=inv(DPDR);
%GG=[ CCCC, zeros(pd,NETA); -nmat*CCCC, zeros(NETA,NETA)];
PDIDPDRD=PP*DD'*I_DPDR*DD;
MSIG=disclyap_fast(CCCC, CCCC*PDIDPDRD*PP*CCCC');
COV_P=[ PP, PP; PP, PP+MSIG]; % P0
dr.PI_GG=[CCCC (AA-CCCC)*(eye(ss-FL_RANK)-PDIDPDRD); zeros(ss-FL_RANK) AA*(eye(ss-FL_RANK)-PDIDPDRD)];
GAM= [ AA*(eye(ss-FL_RANK)-PDIDPDRD) zeros(ss-FL_RANK); (AA-CCCC)*(eye(ss-FL_RANK)-PDIDPDRD), CCCC];
VV = [ dr.PI_TT1 dr.PI_TT2];
nn=size(VV,1);
COV_OMEGA= COV_P( end-nn+1:end, end-nn+1:end);
COV_YR0= VV*COV_OMEGA*VV';
diagCovYR0=diag(COV_YR0);
labels = deblank(M_.endo_names(ivar,:));
if options_.nomoments == 0
z = [ sqrt(diagCovYR0(ivar)) diagCovYR0(ivar) ];
title='MOMENTS OF SIMULATED VARIABLES';
headers=strvcat('VARIABLE','STD. DEV.','VARIANCE');
dyntable(title,headers,labels,z,size(labels,2)+2,16,10);
end
if options_.nocorr == 0
diagSqrtCovYR0=sqrt(diagCovYR0);
%COR_Y= diag(diagSqrtCovYR0)*COV_YR0*diag(diagSqrtCovYR0);
DELTA=inv(diag(diagSqrtCovYR0));
COR_Y= DELTA*COV_YR0*DELTA;
title = 'CORRELATION OF SIMULATED VARIABLES';
headers = strvcat('VARIABLE',M_.endo_names(ivar,:));
dyntable(title,headers,labels,COR_Y(ivar,ivar),size(labels,2)+2,8,4);
else
COR_Y=[];
end
ar = options_.ar;
options_ = set_default_option(options_,'ar',5);
ar = options_.ar;
if ar > 0
COV_YRk= zeros(nn,ar);
AutoCOR_YRk= zeros(nn,ar);
for k=1:ar;
COV_P=GAM*COV_P;
COV_OMEGA= COV_P( end-nn+1:end, end-nn+1:end);
COV_YRk = VV*COV_OMEGA*VV';
AutoCOR_YRkMAT=DELTA*COV_YRk*DELTA;
oo_.autocorr{k}=AutoCOR_YRkMAT(ivar,ivar);
AutoCOR_YRk(:,k)= diag(COV_YRk)./diagCovYR0;
end
title = 'AUTOCORRELATION OF SIMULATED VARIABLES';
headers = strvcat('VARIABLE',int2str([1:ar]'));
dyntable(title,headers,labels,AutoCOR_YRk(ivar,:),size(labels,2)+2,8,4);
else
AutoCOR_YRk=[];
end
save ([M_.fname '_PCL_moments'], 'COV_YR0','AutoCOR_YRk', 'COR_Y');
warning(warning_old_state);

488
matlab/partial_information/PI_gensys.m
View File

@ -1,244 +1,244 @@
function [G1pi,C,impact,nmat,TT1,TT2,gev,eu, DD, E3, E5]=PI_gensys(a0,a1,a2,a3,c,PSI,NX,NETA,FL_RANK,M_,options_)
% System given as
% a0*E_t[y(t+1])+a1*y(t)=a2*y(t-1)+c+psi*eps(t)
% with z an exogenous variable process.
% Returned system is
% [s(t)' x(t)' E_t x(t+1)']'=G1pi [s(t-1)' x(t-1)' x(t)]'+C+impact*eps(t),
% and (a) the matrix nmat satisfying nmat*E_t z(t)+ E_t x(t+1)=0
% (b) matrices TT1, TT2 that relate y(t) to these states: y(t)=[TT1 TT2][s(t)' x(t)']'.
% Note that the dimension of the state vector = dim(a0)+NO_FL_EQS
%
% If div is omitted from argument list, a div>1 is calculated.
% eu(1)=1 for existence, eu(2)=1 for uniqueness. eu(1)=-1 for
% existence only with not-s.c. z; eu=[-2,-2] for coincident zeros.
% Based on
% Christopher A. Sims
% Corrected 10/28/96 by CAS
% Copyright (C) 1996-2010 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/>.
global lq_instruments;
eu=[0;0];C=c;
realsmall=1e-6;
fixdiv=(nargin==6);
n=size(a0,1);
DD=[];E3=[]; E5=0;%[];
%
% Find SVD of a0, and create partitions of U, S and V
%
[U0,S0,V0] = svd(a0);
FL_RANK=rank(S0);
U01=U0(1:n,1:FL_RANK);
U02=U0(1:n,FL_RANK+1:n);
V01=V0(1:n,1:FL_RANK);
V02=V0(1:n,FL_RANK+1:n);
S01=S0(1:FL_RANK,1:FL_RANK);
%
% Define TT1, TT2
%
TT1=V02;
TT2=V01;
%
%Invert S01
%
Sinv=eye(FL_RANK);
for i=1:FL_RANK
Sinv(i,i)=1/S01(i,i);
end
%
%Set up the system matrix for the variables s(t)=V02*Y(t), x(t)=V01*Y(t) and E_t x(t+1)
% and define z(t)'=[s(t)' x(t)]
%
FF=Sinv*U01'*a1*V02;
UAVinv=inv(U02'*a1*V02);
G11=UAVinv*U02'*a2*V02;
G12=UAVinv*U02'*a2*V01;
G13=-UAVinv*U02'*a1*V01;
G31=-FF*G11+Sinv*U01'*a2*V02;
G32=-FF*G12+Sinv*U01'*a2*V01;
G33=-FF*G13-Sinv*U01'*a1*V01;
H1=UAVinv*U02'*PSI;
H3=-FF*H1+Sinv*U01'*PSI; % This should equal 0
G21=zeros(FL_RANK,n-FL_RANK);
G22=zeros(FL_RANK,FL_RANK);
G23=eye(FL_RANK);
%H2=zeros(FL_RANK,NX);
num_inst=0;
P1=H1;
P3=H3;
if(options_.ACES_solver==1 & isfield(lq_instruments,'names'))
num_inst=size(lq_instruments.names,1);
if ~isfield(lq_instruments,'inst_varexo_indices') & num_inst>0
for i=1:num_inst
i_tmp = strmatch(deblank(lq_instruments.names(i,:)),M_.exo_names,'exact');
if isempty(i_tmp)
error (['One of the specified instrument variables does not exist']) ;
else
i_var(i) = i_tmp;
end
end
lq_instruments.inst_varexo_indices=i_var;
elseif size(lq_instruments.inst_varexo_indices)>0
i_var=lq_instruments.inst_varexo_indices;
if ~num_inst
num_inst=size(lq_instruments.inst_varexo_indices);
end
else
i_var=[];
num_inst=0;
end
if size(i_var,2)>0 & size(i_var,2)==num_inst
N1=H1(:,i_var);
N3=H3(:,i_var);
x_var=zeros(NX,1);
for i=1:NX
if isempty(find(i_var==i))
x_var(i)=i;
end
end
x_var=nonzeros(x_var);
P1=H1(:,x_var);
P3=H3(:,x_var);
NX=NX-num_inst;
else
error('WARNING: There are no instrumnets for ACES!');
end
lq_instruments.N1=N1;
lq_instruments.N3=N3;
elseif(options_.ACES_solver==1)
error('WARNING: There are no instrumnets for ACES!');
end
% New Definitions
Ze11=zeros(NX,NX);
Ze12=zeros(NX,n-FL_RANK);
Ze134=zeros(NX,FL_RANK);
Ze31=zeros(FL_RANK,NX);
% End of New Definitions
%
% System matrix is called 'G1pi'; Shock matrix is called 'impact'
%
G1pi=[Ze11 Ze12 Ze134 Ze134; P1 G11 G12 G13; Ze31 G21 G22 G23; P3 G31 G32 G33];
impact=[eye(NX,NX); zeros(n+FL_RANK,NX)];
if(options_.ACES_solver==1)
E3=V02*[P1 G11 G12 G13];
E3=E3+ [zeros(size(V01,1),size(E3,2)-size(V01,2)) V01];
E5=-V02*N1;
DD=[zeros(NX,size(N1,2));N1; zeros(FL_RANK,size(N1,2));N3];
eu =[1; 1], nmat=[], gev=[];
return; % do not check B&K compliancy
end
G0pi=eye(n+FL_RANK+NX);
try
[a b q z v]=qz(G0pi,G1pi);
catch
try
lerror=lasterror;
disp(['PI_Gensys: ' lerror.message]);
if 0==strcmp('MATLAB:qz:matrixWithNaNInf',lerror.identifier)
disp '** Unexpected Error PI_Gensys:qz: ** :';
button=questdlg('Continue Y/N?','Unexpected Error in qz','No','Yes','Yes');
switch button
case 'No'
error ('Terminated')
%case 'Yes'
end
end
G1pi=[];impact=[];nmat=[]; gev=[];
eu=[-2;-2];
return
catch
disp '** Unexpected Error in qz ** :';
disp lerror.message;
button=questdlg('Continue Y/N?','Unexpected Error in qz','No','Yes','Yes');
switch button
case 'No'
error ('Terminated')
case 'Yes'
G1pi=[];impact=[];nmat=[]; gev=[];
eu=[-2;-2];
return
end
end
end
if ~fixdiv, div=1.01; end
nunstab=0;
zxz=0;
nn=size(a,1);
for i=1:nn
% ------------------div calc------------
if ~fixdiv
if abs(a(i,i)) > 0
divhat=abs(b(i,i))/abs(a(i,i));
% bug detected by Vasco Curdia and Daria Finocchiaro, 2/25/2004 A root of
% exactly 1.01 and no root between 1 and 1.02, led to div being stuck at 1.01
% and the 1.01 root being misclassified as stable. Changing < to <= below fixes this.
if 1+realsmall<divhat & divhat<=div
div=.5*(1+divhat);
end
end
end
% ----------------------------------------
nunstab=nunstab+(abs(b(i,i))>div*abs(a(i,i)));
if abs(a(i,i))<realsmall & abs(b(i,i))<realsmall
zxz=1;
end
end
div ;
if ~zxz
[a b q z]=qzdiv(div,a,b,q,z);
end
gev=[diag(a) diag(b)];
if zxz
disp('Coincident zeros. Indeterminacy and/or nonexistence.')
eu=[-2;-2];
% correction added 7/29/2003. Otherwise the failure to set output
% arguments leads to an error message and no output (including eu).
nmat=[]; %;gev=[]
return
end
if (FL_RANK ~= nunstab & options_.ACES_solver~=1)
disp(['Number of unstable variables ' num2str(nunstab)]);
disp( ['does not match number of expectational equations ' num2str(FL_RANK)]);
nmat=[];% gev=[];
eu=[-2;-2];
return
end
% New Definitions
z1=z(:,1:n+NX)';
z2=z(:,n+NX+1:n+NX+FL_RANK)';
% New N Matrix by J Pearlman
z12=z2(:,1:n+NX);
z22=z2(:,n+NX+1:n+NX+FL_RANK);
% End of New Definitions
% modified by GP:
nmat=real(inv(z22)*z12);
eu=[1;1];
function [G1pi,C,impact,nmat,TT1,TT2,gev,eu, DD, E3, E5]=PI_gensys(a0,a1,a2,a3,c,PSI,NX,NETA,FL_RANK,M_,options_)
% System given as
% a0*E_t[y(t+1])+a1*y(t)=a2*y(t-1)+c+psi*eps(t)
% with z an exogenous variable process.
% Returned system is
% [s(t)' x(t)' E_t x(t+1)']'=G1pi [s(t-1)' x(t-1)' x(t)]'+C+impact*eps(t),
% and (a) the matrix nmat satisfying nmat*E_t z(t)+ E_t x(t+1)=0
% (b) matrices TT1, TT2 that relate y(t) to these states: y(t)=[TT1 TT2][s(t)' x(t)']'.
% Note that the dimension of the state vector = dim(a0)+NO_FL_EQS
%
% If div is omitted from argument list, a div>1 is calculated.
% eu(1)=1 for existence, eu(2)=1 for uniqueness. eu(1)=-1 for
% existence only with not-s.c. z; eu=[-2,-2] for coincident zeros.
% Based on
% Christopher A. Sims
% Corrected 10/28/96 by CAS
% Copyright (C) 1996-2010 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/>.
global lq_instruments;
eu=[0;0];C=c;
realsmall=1e-6;
fixdiv=(nargin==6);
n=size(a0,1);
DD=[];E3=[]; E5=0;%[];
%
% Find SVD of a0, and create partitions of U, S and V
%
[U0,S0,V0] = svd(a0);
FL_RANK=rank(S0);
U01=U0(1:n,1:FL_RANK);
U02=U0(1:n,FL_RANK+1:n);
V01=V0(1:n,1:FL_RANK);
V02=V0(1:n,FL_RANK+1:n);
S01=S0(1:FL_RANK,1:FL_RANK);
%
% Define TT1, TT2
%
TT1=V02;
TT2=V01;
%
%Invert S01
%
Sinv=eye(FL_RANK);
for i=1:FL_RANK
Sinv(i,i)=1/S01(i,i);
end
%
%Set up the system matrix for the variables s(t)=V02*Y(t), x(t)=V01*Y(t) and E_t x(t+1)
% and define z(t)'=[s(t)' x(t)]
%
FF=Sinv*U01'*a1*V02;
UAVinv=inv(U02'*a1*V02);
G11=UAVinv*U02'*a2*V02;
G12=UAVinv*U02'*a2*V01;
G13=-UAVinv*U02'*a1*V01;
G31=-FF*G11+Sinv*U01'*a2*V02;
G32=-FF*G12+Sinv*U01'*a2*V01;
G33=-FF*G13-Sinv*U01'*a1*V01;
H1=UAVinv*U02'*PSI;
H3=-FF*H1+Sinv*U01'*PSI; % This should equal 0
G21=zeros(FL_RANK,n-FL_RANK);
G22=zeros(FL_RANK,FL_RANK);
G23=eye(FL_RANK);
%H2=zeros(FL_RANK,NX);
num_inst=0;
P1=H1;
P3=H3;
if(options_.ACES_solver==1 & isfield(lq_instruments,'names'))
num_inst=size(lq_instruments.names,1);
if ~isfield(lq_instruments,'inst_varexo_indices') & num_inst>0
for i=1:num_inst
i_tmp = strmatch(deblank(lq_instruments.names(i,:)),M_.exo_names,'exact');
if isempty(i_tmp)
error (['One of the specified instrument variables does not exist']) ;
else
i_var(i) = i_tmp;
end
end
lq_instruments.inst_varexo_indices=i_var;
elseif size(lq_instruments.inst_varexo_indices)>0
i_var=lq_instruments.inst_varexo_indices;
if ~num_inst
num_inst=size(lq_instruments.inst_varexo_indices);
end
else
i_var=[];
num_inst=0;
end
if size(i_var,2)>0 & size(i_var,2)==num_inst
N1=H1(:,i_var);
N3=H3(:,i_var);
x_var=zeros(NX,1);
for i=1:NX
if isempty(find(i_var==i))
x_var(i)=i;
end
end
x_var=nonzeros(x_var);
P1=H1(:,x_var);
P3=H3(:,x_var);
NX=NX-num_inst;
else
error('WARNING: There are no instrumnets for ACES!');
end
lq_instruments.N1=N1;
lq_instruments.N3=N3;
elseif(options_.ACES_solver==1)
error('WARNING: There are no instrumnets for ACES!');
end
% New Definitions
Ze11=zeros(NX,NX);
Ze12=zeros(NX,n-FL_RANK);
Ze134=zeros(NX,FL_RANK);
Ze31=zeros(FL_RANK,NX);
% End of New Definitions
%
% System matrix is called 'G1pi'; Shock matrix is called 'impact'
%
G1pi=[Ze11 Ze12 Ze134 Ze134; P1 G11 G12 G13; Ze31 G21 G22 G23; P3 G31 G32 G33];
impact=[eye(NX,NX); zeros(n+FL_RANK,NX)];
if(options_.ACES_solver==1)
E3=V02*[P1 G11 G12 G13];
E3=E3+ [zeros(size(V01,1),size(E3,2)-size(V01,2)) V01];
E5=-V02*N1;
DD=[zeros(NX,size(N1,2));N1; zeros(FL_RANK,size(N1,2));N3];
eu =[1; 1], nmat=[], gev=[];
return; % do not check B&K compliancy
end
G0pi=eye(n+FL_RANK+NX);
try
[a b q z v]=qz(G0pi,G1pi);
catch
try
lerror=lasterror;
disp(['PI_Gensys: ' lerror.message]);
if 0==strcmp('MATLAB:qz:matrixWithNaNInf',lerror.identifier)
disp '** Unexpected Error PI_Gensys:qz: ** :';
button=questdlg('Continue Y/N?','Unexpected Error in qz','No','Yes','Yes');
switch button
case 'No'
error ('Terminated')
%case 'Yes'
end
end
G1pi=[];impact=[];nmat=[]; gev=[];
eu=[-2;-2];
return
catch
disp '** Unexpected Error in qz ** :';
disp lerror.message;
button=questdlg('Continue Y/N?','Unexpected Error in qz','No','Yes','Yes');
switch button
case 'No'
error ('Terminated')
case 'Yes'
G1pi=[];impact=[];nmat=[]; gev=[];
eu=[-2;-2];
return
end
end
end
if ~fixdiv, div=1.01; end
nunstab=0;
zxz=0;
nn=size(a,1);
for i=1:nn
% ------------------div calc------------
if ~fixdiv
if abs(a(i,i)) > 0
divhat=abs(b(i,i))/abs(a(i,i));
% bug detected by Vasco Curdia and Daria Finocchiaro, 2/25/2004 A root of
% exactly 1.01 and no root between 1 and 1.02, led to div being stuck at 1.01
% and the 1.01 root being misclassified as stable. Changing < to <= below fixes this.
if 1+realsmall<divhat & divhat<=div
div=.5*(1+divhat);
end
end
end
% ----------------------------------------
nunstab=nunstab+(abs(b(i,i))>div*abs(a(i,i)));
if abs(a(i,i))<realsmall & abs(b(i,i))<realsmall
zxz=1;
end
end
div ;
if ~zxz
[a b q z]=qzdiv(div,a,b,q,z);
end
gev=[diag(a) diag(b)];
if zxz
disp('Coincident zeros. Indeterminacy and/or nonexistence.')
eu=[-2;-2];
% correction added 7/29/2003. Otherwise the failure to set output
% arguments leads to an error message and no output (including eu).
nmat=[]; %;gev=[]
return
end
if (FL_RANK ~= nunstab & options_.ACES_solver~=1)
disp(['Number of unstable variables ' num2str(nunstab)]);
disp( ['does not match number of expectational equations ' num2str(FL_RANK)]);
nmat=[];% gev=[];
eu=[-2;-2];
return
end
% New Definitions
z1=z(:,1:n+NX)';
z2=z(:,n+NX+1:n+NX+FL_RANK)';
% New N Matrix by J Pearlman
z12=z2(:,1:n+NX);
z22=z2(:,n+NX+1:n+NX+FL_RANK);
% End of New Definitions
% modified by GP:
nmat=real(inv(z22)*z12);
eu=[1;1];

182
matlab/partial_information/disc_riccati_fast.m
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@ -1,91 +1,91 @@
function Z=disc_riccati_fast(F,D,R,H,ch)
% function Z=disc_riccati_fast(F,D,R,H,ch)
%
% Solves discrete Riccati Equation:
% Z=FZF' - FZD'inv(DZD'+R)DZF' + H
% Using the Doubling Algorithm
%
% George Perendia: based on the doubling algorithm for Riccati
% and the disclyap_fast function provided by Prof. Joe Pearlman
% V.1 19/5/2006
% V.2 22/10/06
% =================================================================
% Copyright (C) 1996-2010 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/>.
if nargin == 4 | isempty( ch ) == 1
flag_ch = 0;
else
flag_ch = 1;
end
% intialisation
tol = 1e-10; % iteration convergence threshold
P0=H;
X0=F;
if ~any(R) % i.e. ==0
warning('Dangerously evading inversion of zero matrix!');
Y0=zeros(size(R));
else
Y0=D'*inv(R)*D;
end
POYO=P0*Y0;
I=eye(size(POYO));
clear POYO;
% iterate Riccati equation solution
matd=1;
count=0;
while matd > tol && count < 100
INVPY=inv(I+P0*Y0);
P1=X0*INVPY*P0*X0'+ P0;
Y1=X0'*Y0*INVPY*X0+ Y0;
X1=X0*INVPY*X0;
matd=sum( sum(abs( P1 - P0 )));
% P0=(P1+P1')/2
P0=P1;
X0=X1;
Y0=Y1;
count=count+1;
% matd;
end
Z=(P0+P0')/2;
%Z=P0
% check if the convergence took place
if count==100
matd
error('Riccati not converged fast enough!');
% error.identifier='Riccati not converged!'
% error
end
%if count >5
% disp('Riccati count= ');
% count
%end
clear X0 X1 Y0 Y1 P1 I INVPY;
% Check that X is positive definite
if flag_ch==1
[C,p]=chol(Z);
if p ~= 0
error('Z is not positive definite')
end
end
function Z=disc_riccati_fast(F,D,R,H,ch)
% function Z=disc_riccati_fast(F,D,R,H,ch)
%
% Solves discrete Riccati Equation:
% Z=FZF' - FZD'inv(DZD'+R)DZF' + H
% Using the Doubling Algorithm
%
% George Perendia: based on the doubling algorithm for Riccati
% and the disclyap_fast function provided by Prof. Joe Pearlman
% V.1 19/5/2006
% V.2 22/10/06
% =================================================================
% Copyright (C) 1996-2010 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/>.
if nargin == 4 | isempty( ch ) == 1
flag_ch = 0;
else
flag_ch = 1;
end
% intialisation
tol = 1e-10; % iteration convergence threshold
P0=H;
X0=F;
if ~any(R) % i.e. ==0
warning('Dangerously evading inversion of zero matrix!');
Y0=zeros(size(R));
else
Y0=D'*inv(R)*D;
end
POYO=P0*Y0;
I=eye(size(POYO));
clear POYO;
% iterate Riccati equation solution
matd=1;
count=0;
while matd > tol && count < 100
INVPY=inv(I+P0*Y0);
P1=X0*INVPY*P0*X0'+ P0;
Y1=X0'*Y0*INVPY*X0+ Y0;
X1=X0*INVPY*X0;
matd=sum( sum(abs( P1 - P0 )));
% P0=(P1+P1')/2
P0=P1;
X0=X1;
Y0=Y1;
count=count+1;
% matd;
end
Z=(P0+P0')/2;
%Z=P0
% check if the convergence took place
if count==100
matd
error('Riccati not converged fast enough!');
% error.identifier='Riccati not converged!'
% error
end
%if count >5
% disp('Riccati count= ');
% count
%end
clear X0 X1 Y0 Y1 P1 I INVPY;
% Check that X is positive definite
if flag_ch==1
[C,p]=chol(Z);
if p ~= 0
error('Z is not positive definite')
end
end

94
tests/partial_information/PItest3aHc0PCLsimModPiYrVarobsAll.mod
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@ -1,47 +1,47 @@
% inflation target (pitarg) modelled as AR1
% cy = 0.614479/0.769365 - obtained from the computed steady state from the nonlinear counterpart
var pi mc mun muc c y n r g a pitarg ;
varexo eps_g eps_a eps_e eps_m eps_targ;
parameters beta xi hc wd sigma gamma rho_g rho_a rho_r rho_targ thetap cy varrho;
beta = 0.99;
xi = 0.5034;
hc = 0.0;
wd = 0.40;
gamma = 0.5868;
sigma = 4.0897;
cy = 0.614479/0.769365;
rho_g = 0.8325;
rho_a = 0.9827;
rho_r = 0.3529;
thetap = 2.2161;
varrho = 0.3853;
rho_targ = 0.6133;
model(linear);
pi = (beta/(1+beta*gamma))*pi(+1)+(gamma/(1+beta*gamma))*pi(-1)+(((1-beta*xi)*(1-xi))/((1+beta*gamma)*xi))*(mc+eps_m);
mc = mun-muc-a;
mun = (c-hc*c(-1))/(1-hc)+wd*n/(1-wd)+muc;
muc = ((1-varrho)*(1-sigma)-1)*(c-hc*c(-1))/(1-hc)-wd*varrho*(1-sigma)*n/(1-wd);
muc(+1) = muc-(r-pi(+1));
y = cy*c+(1-cy)*g;
n = y-a;
r = rho_r*r(-1)+thetap*(1-rho_r)*(pi(+1)-rho_targ*pitarg)+eps_e;
g = rho_g*g(-1)+eps_g;
a = rho_a*a(-1)+eps_a;
pitarg = rho_targ*pitarg(-1)+eps_targ;
end;
shocks;
var eps_g; stderr 3.8505;
var eps_a; stderr 0.7573;
var eps_e; stderr 0.2409;
var eps_m; stderr 0.8329;
var eps_targ; stderr 0.3978;
end;
varobs pi mc mun muc c y n r g a pitarg;
stoch_simul(partial_information,irf=30)pi y r;//pi n c y r;
% inflation target (pitarg) modelled as AR1
% cy = 0.614479/0.769365 - obtained from the computed steady state from the nonlinear counterpart
var pi mc mun muc c y n r g a pitarg ;
varexo eps_g eps_a eps_e eps_m eps_targ;
parameters beta xi hc wd sigma gamma rho_g rho_a rho_r rho_targ thetap cy varrho;
beta = 0.99;
xi = 0.5034;
hc = 0.0;
wd = 0.40;
gamma = 0.5868;
sigma = 4.0897;
cy = 0.614479/0.769365;
rho_g = 0.8325;
rho_a = 0.9827;
rho_r = 0.3529;
thetap = 2.2161;
varrho = 0.3853;
rho_targ = 0.6133;
model(linear);
pi = (beta/(1+beta*gamma))*pi(+1)+(gamma/(1+beta*gamma))*pi(-1)+(((1-beta*xi)*(1-xi))/((1+beta*gamma)*xi))*(mc+eps_m);
mc = mun-muc-a;
mun = (c-hc*c(-1))/(1-hc)+wd*n/(1-wd)+muc;
muc = ((1-varrho)*(1-sigma)-1)*(c-hc*c(-1))/(1-hc)-wd*varrho*(1-sigma)*n/(1-wd);
muc(+1) = muc-(r-pi(+1));
y = cy*c+(1-cy)*g;
n = y-a;
r = rho_r*r(-1)+thetap*(1-rho_r)*(pi(+1)-rho_targ*pitarg)+eps_e;
g = rho_g*g(-1)+eps_g;
a = rho_a*a(-1)+eps_a;
pitarg = rho_targ*pitarg(-1)+eps_targ;
end;
shocks;
var eps_g; stderr 3.8505;
var eps_a; stderr 0.7573;
var eps_e; stderr 0.2409;
var eps_m; stderr 0.8329;
var eps_targ; stderr 0.3978;
end;
varobs pi mc mun muc c y n r g a pitarg;
stoch_simul(partial_information,irf=30)pi y r;//pi n c y r;

94
tests/partial_information/PItest3aHc0PCLsimModPiYrVarobsCNR.mod
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@ -1,47 +1,47 @@
% inflation target (pitarg) modelled as AR1
% cy = 0.614479/0.769365 - obtained from the computed steady state from the nonlinear counterpart
var pi mc mun muc c y n r g a pitarg;
varexo eps_g eps_a eps_e eps_m eps_targ;
parameters beta xi hc wd sigma gamma rho_g rho_a rho_r rho_targ thetap cy varrho;
beta = 0.99;
xi = 0.5034;
hc = 0.0;
wd = 0.40;
gamma = 0.5868;
sigma = 4.0897;
cy = 0.614479/0.769365;
rho_g = 0.8325;
rho_a = 0.9827;
rho_r = 0.3529;
thetap = 2.2161;
varrho = 0.3853;
rho_targ = 0.6133;
model(linear);
pi = (beta/(1+beta*gamma))*pi(+1)+(gamma/(1+beta*gamma))*pi(-1)+(((1-beta*xi)*(1-xi))/((1+beta*gamma)*xi))*(mc+eps_m);
mc = mun-muc-a;
mun = (c-hc*c(-1))/(1-hc)+wd*n/(1-wd)+muc;
muc = ((1-varrho)*(1-sigma)-1)*(c-hc*c(-1))/(1-hc)-wd*varrho*(1-sigma)*n/(1-wd);
muc(+1) = muc-(r-pi(+1));
y = cy*c+(1-cy)*g;
n = y-a;
r = rho_r*r(-1)+thetap*(1-rho_r)*(pi(+1)-rho_targ*pitarg)+eps_e;
g = rho_g*g(-1)+eps_g;
a = rho_a*a(-1)+eps_a;
pitarg = rho_targ*pitarg(-1)+eps_targ;
end;
shocks;
var eps_g; stderr 3.8505;
var eps_a; stderr 0.7573;
var eps_e; stderr 0.2409;
var eps_m; stderr 0.8329;
var eps_targ; stderr 0.3978;
end;
varobs c n r ;
stoch_simul(partial_information,irf=30)pi y r;//pi n c y r;
% inflation target (pitarg) modelled as AR1
% cy = 0.614479/0.769365 - obtained from the computed steady state from the nonlinear counterpart
var pi mc mun muc c y n r g a pitarg;
varexo eps_g eps_a eps_e eps_m eps_targ;
parameters beta xi hc wd sigma gamma rho_g rho_a rho_r rho_targ thetap cy varrho;
beta = 0.99;
xi = 0.5034;
hc = 0.0;
wd = 0.40;
gamma = 0.5868;
sigma = 4.0897;
cy = 0.614479/0.769365;
rho_g = 0.8325;
rho_a = 0.9827;
rho_r = 0.3529;
thetap = 2.2161;
varrho = 0.3853;
rho_targ = 0.6133;
model(linear);
pi = (beta/(1+beta*gamma))*pi(+1)+(gamma/(1+beta*gamma))*pi(-1)+(((1-beta*xi)*(1-xi))/((1+beta*gamma)*xi))*(mc+eps_m);
mc = mun-muc-a;
mun = (c-hc*c(-1))/(1-hc)+wd*n/(1-wd)+muc;
muc = ((1-varrho)*(1-sigma)-1)*(c-hc*c(-1))/(1-hc)-wd*varrho*(1-sigma)*n/(1-wd);
muc(+1) = muc-(r-pi(+1));
y = cy*c+(1-cy)*g;
n = y-a;
r = rho_r*r(-1)+thetap*(1-rho_r)*(pi(+1)-rho_targ*pitarg)+eps_e;
g = rho_g*g(-1)+eps_g;
a = rho_a*a(-1)+eps_a;
pitarg = rho_targ*pitarg(-1)+eps_targ;
end;
shocks;
var eps_g; stderr 3.8505;
var eps_a; stderr 0.7573;
var eps_e; stderr 0.2409;
var eps_m; stderr 0.8329;
var eps_targ; stderr 0.3978;
end;
varobs c n r ;
stoch_simul(partial_information,irf=30)pi y r;//pi n c y r;