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dynare/matlab/partial_information/dr1_PI.m

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function [dr,info,M_,options_,oo_] = dr1_PI(dr,task,M_,options_,oo_)
% function [dr,info,M_,options_,oo_] = dr1_PI(dr,task,M_,options_,oo_)
% Computes the reduced form solution of a rational expectation model first
% order
% approximation of the Partial Information stochastic model solver around the deterministic steady state).
% Prepares System as
% A0*E_t[y(t+1])+A1*y(t)=A2*y(t-1)+c+psi*eps(t)
% with z an exogenous variable process.
% and calls PI_Gensys.m solver
% based on Pearlman et al 1986 paper and derived from
% C.Sims' gensys linear solver.
% to return solution in format
% [s(t)' x(t)' E_t x(t+1)']'=G1pi [s(t-1)' x(t-1)' x(t)]'+C+impact*eps(t),
%
% 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) 1996-2010 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/>.
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;
if (options_.aim_solver == 1)
options_.aim_solver == 0;
warning('You can not use AIM with Part Info solver. AIM ignored');
end
if (options_.order > 1)
warning('You can not use order higher than 1 with Part Info solver. Order 1 assumed');
options_.order =1;
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
z = repmat(dr.ys,1,klen);
z = z(iyr0) ;
[junk,jacobia_] = feval([M_.fname '_dynamic'],z,[oo_.exo_simul ...
oo_.exo_det_simul], M_.params, it_);
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),:);
b = jacobia_(:,k0);
if (options_.aim_solver == 1)
error('Anderson and Moore AIM solver is not compatible with Partial Information models');
end % end if useAIM and...
%forward--looking models
if nstatic > 0
[Q,R] = qr(b(:,1:nstatic));
aa = Q'*jacobia_;
else
aa = jacobia_;
end
% If required, try PCL86 solver, that is, if not the check being
% performed only and if it is 1st order
% create sparse, extended jacobia AA:
nendo=M_.endo_nbr; % = size(aa,1)
%%% OLD: aax=zeros(size(aa,1),size(aa,1)*klen);
% partition jacobian:
jlen=dr.nspred+dr.nsfwrd+M_.endo_nbr+M_.exo_nbr; % length of jacobian
% find size xlen of the state vector Y and of A0, A1 and A2 transition matrices:
% it is the sum the all i variables's lag/lead representations,
% for each variable i representation being defined as:
% Max (i_lags-1,0)+ Max (i_leads-1,0)+1
% so that if variable x appears with 2 lags and 1 lead, and z
% with 2 lags and 3 leads, the size of the state space is:
% 1+0+1 + 1+2+1 =6
% e.g. E_t Y(t+1)=
% E_t x(t)
% E_t x(t+1)
% E_t z(t)
% E_t z(t+1)
% E_t z(t+2)
% E_t z(t+3)
% first transpose M_.lead_lag_incidence';
lead_lag=M_.lead_lag_incidence';
max_lead_lag=zeros(nendo,2); % lead/lag representation in Y for each endogenous variable i
if ( M_.maximum_lag <= 1) && (M_.maximum_lead <= 1)
xlen=nendo; %%=0;
AA0=zeros(xlen,xlen); % empty A0
AA2=AA0; % empty A2 and A3
AA3=AA0;
AA1=jacobia_(:,npred+1:npred+nendo);
fnd = find(lead_lag(:,3));
AA0(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,3))); %forwd jacobian
fnd = find(lead_lag(:,1));
AA2(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,1))); %backward
if M_.orig_endo_nbr<nendo
exp_0= strmatch('AUX_EXPECT_LEAD_0_', M_.endo_names);
num_exp_0=size(exp_0,1);
if num_exp_0>0
AA3(:,exp_0)=AA1(:,exp_0);
XX0=zeros(nendo,num_exp_0);
AA1(:,exp_0)=XX0(:,[1:num_exp_0])
end
end
else
xlen=0;
for i=1:nendo
llmask=find(lead_lag(i,:)); % mask of leads and lags for var i
nlag = max((M_.maximum_lag+1-min(llmask)), 0); % reduced no of lags and
nlead = max((max(llmask)-(M_.maximum_lag+1)), 0); % reduced no of leads for var i
max_lead_lag(i,:)=[nlag nlead]; % store for future reference
%xlen=xlen+(nlag+nlead+1); % size as the sum over all the i variables
xlen=xlen+(max(nlag-1,0)+max(nlead-1,0)+1); % size as the sum over all the i variables
end
AA0=zeros(xlen,xlen); % empty A0
AA2=AA0; % empty A2 and A3
AA3=AA0;
end
if (xlen>nendo )||( M_.maximum_lag >1) || (M_.maximum_lead >1) % we could not use shortcut above
start=xlen -nendo+1;
offset=0;
for i=1:nendo
llmask=find(lead_lag(i,:)); % mask of leads and lags for var i
nlag=max_lead_lag(i,1); % size for the i'th variable lags
nlead=max_lead_lag(i,2); % size for the i'th variable lead
ilen=max(nlag-1,0)+max(nlead-1,0)+1; % size for the i'th variable
if lead_lag(i,M_.maximum_lag-nlag+1) && nlag>0 %(j0==1 )&& lead_lag(i,j0) % !=0 %(ilen - iLagLen) %<=max(nlag,1)
AA2( start:end, offset+1)=aa(:,lead_lag(i,M_.maximum_lag-nlag+1));
else
AA2( start+i-1, offset+1)=Inf;
end
if lead_lag(i,klen-M_.maximum_lead+nlead) && nlead>0 %(j0==1 )&& lead_lag(i,j0) % !=0 %(ilen - iLagLen) %<=max(nlag,1)
AA0( start:end, offset+ilen)=aa(:,lead_lag(i,klen-M_.maximum_lead+nlead));
else
AA0( start+i-1, offset+ilen)=Inf;
end
for j0= 1:ilen % M_.maximum_lag
if (j0<max(nlag-1,0)+1) && (ilen>nlag)&& lead_lag(i,j0+1) % !=0 %(ilen - iLagLen) %
AA1( start:end, offset+j0)=aa(:,lead_lag(i,(j0+1)));
elseif (j0==max(nlag-1,0)+1) && lead_lag(i,(M_.maximum_lag+1)) %&& (j0<=ilen-max(nlead-1,0) ) ...
%AA1( start+i-1, offset+j0)=Inf; // jacobian at t
AA1( start:end, offset+j0)=aa(:,lead_lag(i,(M_.maximum_lag+1)));
elseif (j0>max(nlag-1,0)+1)&& (ilen>nlead)&& lead_lag(i,M_.maximum_lag+j0+1)
AA1( start:end, offset+j0)=aa(:,lead_lag(i,(M_.maximum_lag+1+j0)));
end
end
offset=offset+ilen;
if offset>xlen
error(' dr1_PI: offset exceeds max xlen!');
end
end
end
PSI=-[[zeros(xlen-nendo,M_.exo_nbr)];[jacobia_(:, jlen-M_.exo_nbr+1:end)]]; % exog
cc=0;
NX=M_.exo_nbr; % no of exogenous varexo shock variables.
NETA=nfwrd+nboth; % total no of exp. errors set to no of forward looking equations
FL_RANK=rank(AA0); % nfwrd+nboth; % min total no of forward looking equations and vars
try
% call [G1pi,C,impact,nmat,TT1,TT2,gev,eu]=PI_gensys(a0,a1,a2,c,PSI,NX,NETA,NO_FL_EQS)
% System given as
% a0*E_t[y(t+1])+a1*y(t)=a2*y(t-1)+c+psi*eps(t)
% with eps 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)']'.
if(options_.ACES_solver==1)
SSbar= diag(dr.ys);%(oo_.steady_state);
AA0=AA0*SSbar;
AA1=AA1*SSbar;
AA2=AA2*SSbar;
AA3=AA3*SSbar;
end
%%if any(AA3) % for expectational models when complete
%% [G1pi,CC,impact,nmat,TT1,TT2,gev,eu, DD, E3,E5]=PI_gensysEXP(AA0,AA1,-AA2,AA3,cc,PSI,NX,NETA,FL_RANK, M_, options_);
%%else
[G1pi,CC,impact,nmat,TT1,TT2,gev,eu, DD, E3,E5]=PI_gensys(AA0,AA1,-AA2,AA3,cc,PSI,NX,NETA,FL_RANK, M_, options_);
%%end
% reuse some of the bypassed code and tests that may be needed
if eu ~=[1; 1]
info(1) = abs(eu(1)+eu(2));
info(2) = 1.0e+8;
% return
end
dr.PI_ghx=G1pi;
dr.PI_ghu=impact;
dr.PI_TT1=TT1;
dr.PI_TT2=TT2;
dr.PI_nmat=nmat;
dr.PI_CC=CC;
dr.PI_gev=gev;
dr.PI_eu=eu;
dr.PI_FL_RANK=FL_RANK;
%dr.ys=zeros(nendo); % zero steady state
dr.ghx=G1pi;
dr.ghu=impact;
dr.eigval = eig(G1pi);
dr.rank=FL_RANK;
if options_.ACES_solver==1
ACES.A=G1pi;
ACES.C=impact; % (:,1);
ACES.D=DD; %=impact (:,20);
ACES.E3=E3;
ACES.E5=E5;
save ACES ;%ACES_A ACES_C ACES_D ACES_E2 ACES_E5
%save([M_.fname '_ACES_IN'], 'ACES')
save ([M_.fname '_ACES_A.txt'], 'G1pi', '-ascii', '-double', '-tabs');
save ([M_.fname '_ACES_C.txt'], 'impact','-ascii', '-double', '-tabs');
save ([M_.fname '_ACES_D.txt'], 'DD', '-ascii', '-double', '-tabs');
save ([M_.fname '_ACES_E3.txt'], 'E3', '-ascii', '-double', '-tabs');
save ([M_.fname '_ACES_E5.txt'], 'E5', '-ascii', '-double', '-tabs');
end
catch
disp('Problem with using Part Info solver - Using Dynare solver instead');
lerror=lasterror;
disp (lerror);
options_.PartInfo = 0; % and then try mjdgges instead
end
% TODO:
% if options_.loglinear == 1
% if exogenous deterministic variables
return;
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