142 lines
4.0 KiB
Matlab
142 lines
4.0 KiB
Matlab
function y=PCL_Part_info_irf( H, varobs, ivar, M_, dr, irfpers,ii)
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% sets up parameters and calls part-info kalman filter
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% developed by G Perendia, July 2006 for implementation from notes by Prof. Joe Pearlman to
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% suit partial information RE solution in accordance with, and based on, the
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% Pearlman, Currie and Levine 1986 solution.
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% 22/10/06 - Version 2 for new Riccati with 4 params instead 5
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% Copyright © 2006-2018 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 <https://www.gnu.org/licenses/>.
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% Recall that the state space is given by the
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% predetermined variables s(t-1), x(t-1)
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% and the jump variables x(t).
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% The jump variables have dimension NETA
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OBS = [];
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for i=1:rows(varobs)
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OBS = [OBS find(strcmp(varobs{i}, M_.endo_names)) ];
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end
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NOBS = length(OBS);
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G1=dr.PI_ghx;
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impact=dr.PI_ghu;
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nmat=dr.PI_nmat;
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CC=dr.PI_CC;
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NX=M_.exo_nbr; % no of exogenous varexo shock variables.
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FL_RANK=dr.PI_FL_RANK;
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NY=M_.endo_nbr;
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LL = sparse(1:NOBS,OBS,ones(NOBS,1),NY,NY);
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ss=size(G1,1);
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pd=ss-size(nmat,1);
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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
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if isempty(H)
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H=M_.H;
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end
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VV=H; % V-COV of observation errors.
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MM=impact*SDX; % R*(Q^0.5) in standard KF notation
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% observation vector indices
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% mapping to endogenous variables.
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L1=LL*dr.PI_TT1;
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L2=LL*dr.PI_TT2;
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MM1=MM(1:ss-FL_RANK,:);
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U11=MM1*MM1';
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% SDX
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U22=0;
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% determine K1 and K2 observation mapping matrices
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% This uses the fact that measurements are given by L1*s(t)+L2*x(t)
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% and s(t) is expressed in the dynamics as
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% H1*eps(t)+G11*s(t-1)+G12*x(t-1)+G13*x(t).
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% Thus the observations o(t) can be written in the form
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% o(t)=K1*[eps(t)' s(t-1)' x(t-1)']' + K2*x(t) where
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% K1=[L1*H1 L1*G11 L1*G12] K2=L1*G13+L2
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G12=G1(NX+1:ss-2*FL_RANK,:);
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KK1=L1*G12;
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K1=KK1(:,1:ss-FL_RANK);
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K2=KK1(:,ss-FL_RANK+1:ss)+L2;
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%pre calculate time-invariant factors
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A11=G1(1:pd,1:pd);
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A22=G1(pd+1:end, pd+1:end);
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A12=G1(1:pd, pd+1:end);
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A21=G1(pd+1:end,1:pd);
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Lambda= nmat*A12+A22;
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I_L=inv(Lambda);
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BB=A12*inv(A22);
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FF=K2*inv(A22);
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QQ=BB*U22*BB' + U11;
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UFT=U22*FF';
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AA=A11-BB*A21;
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CCCC=A11-A12*nmat; % F in new notation
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DD=K1-FF*A21; % H in new notation
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EE=K1-K2*nmat;
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RR=FF*UFT+VV;
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if ~any(RR)
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% if zero add some dummy measurement err. variance-covariances
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% with diagonals 0.000001. This would not be needed if we used
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% the slow solver, or the generalised eigenvalue approach,
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% but these are both slower.
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RR=eye(size(RR,1))*1.0e-6;
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end
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SS=BB*UFT;
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VKLUFT=VV+K2*I_L*UFT;
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ALUFT=A12*I_L*UFT;
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FULKV=FF*U22*I_L'*K2'+VV;
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FUBT=FF*U22*BB';
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nmat=nmat;
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% initialise pshat
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AQDS=AA*QQ*DD'+SS;
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DQDR=DD*QQ*DD'+RR;
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I_DQDR=inv(DQDR);
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AQDQ=AQDS*I_DQDR;
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ff=AA-AQDQ*DD;
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hh=AA*QQ*AA'-AQDQ*AQDS';%*(DD*QQ*AA'+SS');
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rr=DD*QQ*DD'+RR;
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ZSIG0=disc_riccati_fast(ff,DD,rr,hh);
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PP=ZSIG0 +QQ;
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exo_names=M_.exo_names;
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DPDR=DD*PP*DD'+RR;
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I_DPDR=inv(DPDR);
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PDIDPDRD=PP*DD'*I_DPDR*DD;
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GG=[CCCC (AA-CCCC)*(eye(ss-FL_RANK)-PDIDPDRD); zeros(ss-FL_RANK) AA*(eye(ss-FL_RANK)-PDIDPDRD)];
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imp=[impact(1:ss-FL_RANK,:); impact(1:ss-FL_RANK,:)];
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% Calculate IRFs of observable series
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I_PD=(eye(ss-FL_RANK)-PDIDPDRD);
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LL0=[ EE (DD-EE)*I_PD];
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VV = [ dr.PI_TT1 dr.PI_TT2];
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stderr=diag(M_.Sigma_e^0.5);
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irfmat=zeros(size(dr.PI_TT1 ,1),irfpers+1);
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irfst=zeros(size(GG,1),irfpers+1);
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irfst(:,1)=stderr(ii)*imp(:,ii);
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for jj=2:irfpers+1
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irfst(:,jj)=GG*irfst(:,jj-1);
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irfmat(:,jj-1)=VV*irfst(NX+1:ss-FL_RANK,jj);
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end
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y = irfmat(:,1:irfpers);
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save ([M_.fname '_PCL_PtInfoIRFs_' num2str(ii) '_' exo_names{ii}], 'irfmat','irfst');
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