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function y=PCL_Part_info_irf( H, varobs, ivar, 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) 2006-2017 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
OBS = [];
for i=1:rows(varobs)
OBS = [OBS find(strcmp(deblank(varobs(i,:)), cellstr(M_.endo_names))) ];
end
NOBS = length(OBS);
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;
LL = sparse(1:NOBS,OBS,ones(NOBS,1),NY,NY);
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;
I_L=inv(Lambda);
BB=A12*inv(A22);
FF=K2*inv(A22);
QQ=BB*U22*BB' + U11;
UFT=U22*FF';
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)-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
I_PD=(eye(ss-FL_RANK)-PDIDPDRD);
LL0=[ EE (DD-EE)*I_PD];
VV = [ dr.PI_TT1 dr.PI_TT2];
stderr=diag(M_.Sigma_e^0.5);
irfmat=zeros(size(dr.PI_TT1 ,1),irfpers+1);
irfst=zeros(size(GG,1),irfpers+1);
irfst(:,1)=stderr(ii)*imp(:,ii);
for jj=2:irfpers+1
irfst(:,jj)=GG*irfst(:,jj-1);
irfmat(:,jj-1)=VV*irfst(NX+1:ss-FL_RANK,jj);
end
y = irfmat(:,1:irfpers);
save ([M_.fname '_PCL_PtInfoIRFs_' num2str(ii) '_' deblank(exo_names(ii,:))], 'irfmat','irfst');
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