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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) 1996-2018 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 <https://www.gnu.org/licenses/>.
global lq_instruments;
info = 0;
options_ = set_default_option(options_,'qz_criterium',1.000001);
xlen = M_.maximum_endo_lead + M_.maximum_endo_lag + 1;
if options_.aim_solver
options_.aim_solver = false;
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 && ~options_.ACES_solver
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;
opt = options_;
opt.jacobian_flag = false;
oo_.steady_state = dynare_solve('ramsey_static',oo_.steady_state,opt,M_,options_,oo_,it_);
options_.solve_algo = old_solve_algo;
[~,~,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
if options_.ACES_solver
sim_ruleids=[];
tct_ruleids=[];
if size(M_.equations_tags,1)>0 % there are tagged equations, check if they are aceslq rules
for teq=1:size(M_.equations_tags,1)
if strcmp(M_.equations_tags(teq,3),'aceslq_sim_rule')
sim_ruleids=[sim_ruleids cell2mat(M_.equations_tags(teq,1))]
end
if strcmp(M_.equations_tags(teq,3),'aceslq_tct_rule')
tct_ruleids=[tct_ruleids cell2mat(M_.equations_tags(teq,1))]
end
end
end
lq_instruments.sim_ruleids=sim_ruleids;
lq_instruments.tct_ruleids=tct_ruleids;
%if isfield(lq_instruments,'xsopt_SS') %% changed by BY
[~, lq_instruments.xsopt_SS,lq_instruments.lmopt_SS,s2,check] = opt_steady_get;%% changed by BY
[qc, DYN_Q] = QPsolve(lq_instruments, s2, check); %% added by BY
z = repmat(lq_instruments.xsopt_SS,1,klen);
else
z = repmat(dr.ys,1,klen);
end
z = z(iyr0) ;
[~,jacobia_] = feval([M_.fname '.dynamic'],z,[oo_.exo_simul ...
oo_.exo_det_simul], M_.params, dr.ys, it_);
if options_.ACES_solver && (length(sim_ruleids)>0 || length(tct_ruleids)>0 )
if length(sim_ruleids)>0
sim_rule=jacobia_(sim_ruleids,:);
% uses the subdirectory - BY
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_sim_rule.txt'], 'sim_rule', '-ascii', '-double', '-tabs');
end
if length(tct_ruleids)>0
tct_rule=jacobia_(tct_ruleids,:);
% uses the subdirectory - BY
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_tct_rule.txt'], 'tct_rule', '-ascii', '-double', '-tabs');
end
aces_ruleids=union(tct_ruleids,sim_ruleids);
j_size=size(jacobia_,1);
j_rows=1:j_size;
j_rows = setxor(j_rows,aces_ruleids);
jacobia_=jacobia_(j_rows ,:);
end
end
if options_.debug
save([M_.dname filesep 'Output' filesep M_.fname '_debug.mat'],'jacobia_')
end
dr=set_state_space(dr,M_,options_);
kstate = dr.kstate;
nstatic = M_.nstatic;
nfwrd = M_.nfwrd;
nspred = M_.nspred;
nboth = M_.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_.aim_solver
error('Anderson and Moore AIM solver is not compatible with Partial Information models');
end % end if useAIM and...
% 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)
if(options_.ACES_solver)
%if ~isfield(lq_instruments,'names')
if isfield(options_,'instruments')
lq_instruments.names=options_.instruments;
end
%end
if isfield(lq_instruments,'names')
num_inst=size(lq_instruments.names,1);
if ~isfield(lq_instruments,'inst_var_indices') && num_inst>0
for i=1:num_inst
i_tmp = strmatch(deblank(lq_instruments.names(i,:)), M_.endo_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_var_indices=i_var;
elseif size(lq_instruments.inst_var_indices)>0
i_var=lq_instruments.inst_var_indices;
if ~num_inst
num_inst=size(lq_instruments.inst_var_indices);
end
else
i_var=[];
num_inst=0;
end
if size(i_var,2)>0 && size(i_var,2)==num_inst
m_var=zeros(nendo,1);
for i=1:nendo
if isempty(find(i_var==i))
m_var(i)=i;
end
end
m_var=nonzeros(m_var);
lq_instruments.m_var=m_var;
else
error('WARNING: There are no instrumnets for ACES!');
end
else %if(options_.ACES_solver==1)
error('WARNING: There are no instrumnets for ACES!');
end
end
% 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)
% partition jacobian:
jlen=M_.nspred+M_.nsfwrd+M_.endo_nbr+M_.exo_nbr; % length of jacobian
PSI=-jacobia_(:, jlen-M_.exo_nbr+1:end); % exog
% 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=size(jacobia_,1);%nendo;
AA0=zeros(xlen,xlen); % empty A0
AA2=AA0; % empty A2 and A3
AA3=AA0;
if xlen==nendo % && M_.maximum_lag <=1 && M_.maximum_lead <=1 % apply a shortcut
AA1=jacobia_(:,nspred+1:nspred+nendo);
if M_.maximum_lead ==1
fnd = find(lead_lag(:,M_.maximum_lag+2));
AA0(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,M_.maximum_lag+2))); %forwd jacobian
end
if nspred>0 && M_.maximum_lag ==1
fnd = find(lead_lag(:,1));
AA2(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,1))); %backward
end
elseif options_.ACES_solver % more endo vars than equations in jacobia_
if nendo-xlen==num_inst
PSI=[PSI;zeros(num_inst, M_.exo_nbr)];
% AA1 contemporary
AA_all=jacobia_(:,nspred+1:nspred+nendo);
AA1=AA_all(:,lq_instruments.m_var); % endo without instruments
lq_instruments.ij1=AA_all(:,lq_instruments.inst_var_indices); % instruments only
lq_instruments.B1=-[lq_instruments.ij1; eye(num_inst)];
AA1=[AA1, zeros(xlen,num_inst); zeros(num_inst,xlen), eye(num_inst)];
%PSI=[PSI; zeros(num_inst,M_.exo_nbr)];
if M_.maximum_lead ==1 % AA0 forward looking
AA_all(:,:)=0.0;
fnd = find(lead_lag(:,M_.maximum_lag+2));
AA_all(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,M_.maximum_lag+2))); %forwd jacobian
AA0=AA_all(:,lq_instruments.m_var);
lq_instruments.ij0=AA_all(:,lq_instruments.inst_var_indices); % instruments only
lq_instruments.B0=[lq_instruments.ij0; eye(num_inst)];
AA0=[AA0, zeros(xlen,num_inst); zeros(num_inst,xlen+num_inst)];
end
if nspred>0 && M_.maximum_lag ==1
AA_all(:,:)=0.0;
fnd = find(lead_lag(:,1));
AA_all(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,1))); %backward
AA2=AA_all(:,lq_instruments.m_var);
lq_instruments.ij2=AA_all(:,lq_instruments.inst_var_indices); % instruments only
lq_instruments.B2=[lq_instruments.ij2; eye(num_inst)];
AA2=[AA2, lq_instruments.ij2 ; zeros(num_inst,xlen+num_inst)];
end
else
error('ACES number of instruments does match');
end
else
error('More than one lead or lag in the jabian');
end
if M_.orig_endo_nbr<nendo
% findif there are any expecatations at time t
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
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)
if isfield(lq_instruments,'xsopt_SS')
SSbar= diag([lq_instruments.xsopt_SS(m_var)]);% lq_instruments.xsopt_SS(lq_instruments.inst_var_indices)]);
insSSbar=repmat(lq_instruments.xsopt_SS(lq_instruments.inst_var_indices)',nendo-num_inst,1);
else
SSbar= diag([dr.ys(m_var)]);%; dr.ys(lq_instruments.inst_var_indices)]);%(oo_.steady_state);
insSSbar=repmat(dr.ys(lq_instruments.inst_var_indices)',nendo-num_inst,1);
end
SSbar=diag([diag(SSbar);diag(eye(num_inst))]);
insSSbar=[insSSbar;diag(eye(num_inst))];
AA0=AA0*SSbar;
AA1=AA1*SSbar;
AA2=AA2*SSbar;
lq_instruments.B1=(lq_instruments.B1).*insSSbar;
end
%% for expectational models when complete
if any(AA3)
AA3=AA3*SSbar;
[G1pi,CC,impact,nmat,TT1,TT2,gev,eu, DD, E2,E5, GAMMA, FL_RANK]=PI_gensysEXP(AA0,AA1,-AA2,AA3,cc,PSI,NX,NETA,FL_RANK, M_, options_);
else
[G1pi,CC,impact,nmat,TT1,TT2,gev,eu, DD, E2,E5, GAMMA, FL_RANK]=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 || eu(2) ~= 1) && ~options_.ACES_solver
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
betap=options_.planner_discount;
sigma_cov=M_.Sigma_e;
% get W - BY
W=(1-betap)*GAMMA'*DYN_Q*GAMMA;
%W=[0]
ACES.A=G1pi;
ACES.C=impact; % (:,1);
ACES.D=DD; %=impact (:,20);
ACES.E2=E2;
ACES.E5=E5;
ACES.GAMMA=GAMMA;
ACES_M=size(G1pi,2)-FL_RANK;
ACES_NM=FL_RANK;
ACES.M=ACES_M;
ACES.NM=FL_RANK;
% added by BY
ACES.Q=DYN_Q;
ACES.W=W;
NY=nendo-num_inst;
% save the followings in a subdirectory - BY
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_Matrices'], 'ACES');
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_GAMMA'], 'GAMMA');
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_A.txt'], 'G1pi', '-ascii', '-double', '-tabs');
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_C.txt'], 'impact','-ascii', '-double', '-tabs');
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_D.txt'], 'DD', '-ascii', '-double', '-tabs');
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_E2.txt'], 'E2', '-ascii', '-double', '-tabs');
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_E5.txt'], 'E5', '-ascii', '-double', '-tabs');
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_GAMMA.txt'], 'GAMMA', '-ascii', '-double', '-tabs');
%save ([M_.fname '_ACESLQ_M.txt'], 'ACES_M', '-ascii', '-tabs');
%save ([M_.fname '_ACESLQ_NM.txt'], 'ACES_NM', '-ascii', '-tabs');
%save ([M_.fname '_ACESLQ_betap.txt'], 'betap', '-ascii', '-tabs');
%save ([M_.fname '_ACESLQ_NI.txt'], 'num_inst', '-ascii', '-tabs');
%save ([M_.fname '_ACESLQ_ND.txt'], 'NX', '-ascii', '-tabs');
%save ([M_.fname '_ACESLQ_NY.txt'], 'NY', '-ascii', '-tabs');
ACES_VARS=char(M_.endo_names);
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_VARS.txt'], 'ACES_VARS', '-ascii', '-tabs');
% added by BY
% save the char array ACES_VARS into .txt as it is
fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_VARnames.txt'),'wt');
ACES_VARS =[ACES_VARS repmat(sprintf('\n'),size(ACES_VARS,1),1)];
fwrite(fid,ACES_VARS.');
fclose(fid);
% save as integers
fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_M.txt'),'wt');
fprintf(fid,'%d\n',ACES_M);
fclose(fid);
fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_NM.txt'),'wt');
fprintf(fid,'%d\n',ACES_NM);
fclose(fid);
fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_betap.txt'),'wt');
fprintf(fid,'%d\n',betap);
fclose(fid);
fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_NI.txt'),'wt');
fprintf(fid,'%d\n',num_inst);
fclose(fid);
fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_ND.txt'),'wt');
fprintf(fid,'%d\n',NX);
fclose(fid);
fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_NY.txt'),'wt');
fprintf(fid,'%d\n',NY);
fclose(fid);
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_Q.txt'], 'DYN_Q', '-ascii', '-double', '-tabs');
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_W.txt'], 'W', '-ascii', '-double', '-tabs');
save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_SIGMAE.txt'], 'sigma_cov', '-ascii', '-double', '-tabs');
end
catch
lerror=lasterror;
if options_.ACES_solver
disp('Problem with using Part Info ACES solver:');
error(lerror.message);
else
disp('Problem with using Part Info solver');
error(lerror.message);
end
end
% TODO:
% if options_.loglinear == 1
% if exogenous deterministic variables
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