630 lines
19 KiB
Matlab
630 lines
19 KiB
Matlab
% Copyright (C) 2001 Michel Juillard
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%
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function [dr,info]=dr1(dr,task)
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global M_ options_ oo_
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global olr_state
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% info = 1: the model doesn't define current variables uniquely
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% info = 2: problem in mjdgges.dll info(2) contains error code
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% info = 3: BK order condition not satisfied info(2) contains "distance"
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% absence of stable trajectory
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% info = 4: BK order condition not satisfied info(2) contains "distance"
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% indeterminacy
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% info = 5: BK rank condition not satisfied
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info = 0;
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options_ = set_default_option(options_,'loglinear',0);
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options_ = set_default_option(options_,'noprint',0);
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options_ = set_default_option(options_,'olr',0);
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options_ = set_default_option(options_,'olr_beta',1);
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options_ = set_default_option(options_,'qz_criterium',1.000001);
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xlen = M_.maximum_lead + M_.maximum_lag + 1;
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klen = M_.maximum_lag + M_.maximum_lead + 1;
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iyv = M_.lead_lag_incidence';
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iyv = iyv(:);
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iyr0 = find(iyv) ;
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it_ = M_.maximum_lag + 1 ;
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if M_.exo_nbr == 0
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oo_.exo_steady_state = [] ;
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end
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tempex = oo_.exo_simul;
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it_ = M_.maximum_lag + 1;
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if options_.olr
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z = repmat(zeros(M_.endo_nbr,1),1,klen);
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else
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z = repmat(dr.ys,1,klen);
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end
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z = z(iyr0) ;
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if options_.order == 1
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[junk,jacobia_] = feval([M_.fname '_dynamic'],z,tempex);
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elseif options_.order == 2
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[junk,jacobia_,hessian] = feval([M_.fname '_dynamic'],z,tempex);
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end
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oo_.exo_simul = tempex ;
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tempex = [];
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% expanding system for Optimal Linear Regulator
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if options_.olr
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bet = options_.olr_beta;
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jacobia1 = [];
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n_inst = size(options_.olr_inst,1);
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if ~isfield(olr_state_,'done')
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olr_state_.done = 1;
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olr_state_.old_M_.maximum_lag = M_.maximum_lag;
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olr_state_.old_M_.maximum_lead = M_.maximum_lead;
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olr_state_.old_M_.endo_nbr = M_.endo_nbr;
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olr_state_.old_M_.lead_lag_incidence = M_.lead_lag_incidence;
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for i=1:M_.endo_nbr
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temp = ['mult_' int2str(i)];
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lgoo_.endo_simul = strvcat(lgoo_.endo_simul,temp);
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end
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M_.endo_nbr = 2*M_.endo_nbr-n_inst;
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M_.maximum_lag = max(M_.maximum_lag,M_.maximum_lead);
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M_.maximum_lead = M_.maximum_lag;
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end
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nj = olr_state_.old_M_.endo_nbr-n_inst;
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offset_min = M_.maximum_lag - olr_state_.old_M_.maximum_lag;
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offset_max = M_.maximum_lead - olr_state_.old_M_.maximum_lead;
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newiy = zeros(2*M_.maximum_lag+1,nj+olr_state_.old_M_.endo_nbr);
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jacobia_ = jacobia_(1:nj,:);
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for i=1:2*M_.maximum_lag+1
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if i > offset_min & i <= 2*M_.maximum_lag+1-offset_max
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[junk,k1,k2] = find(olr_state_.old_M_.lead_lag_incidence(i-offset_min,:));
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if i == M_.maximum_lag+1
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jacobia1 = [jacobia1 [jacobia_(:,k2); 2*options_.olr_w]];
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else
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jacobia1 = [jacobia1 [jacobia_(:,k2); ...
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zeros(olr_state_.old_M_.endo_nbr,length(k1))]];
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end
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newiy(i,k1) = ones(1,length(k1));
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end
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i1 = 2*M_.maximum_lag+2-i;
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if i1 <= 2*M_.maximum_lag+1-offset_max & i1 > offset_min
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[junk,k1,k2] = find(olr_state_.old_M_.lead_lag_incidence(i1-offset_min,:));
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k3 = find(any(jacobia_(:,k2),2));
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x = zeros(olr_state_.old_M_.endo_nbr,length(k3));
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x(k1,:) = bet^(-i1+M_.maximum_lag+1)*jacobia_(k3,k2)';
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jacobia1 = [jacobia1 [zeros(nj,length(k3)); x]];
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newiy(i,k3+olr_state_.old_M_.endo_nbr) = ones(1,length(k3));
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end
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end
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jacobia1 = [jacobia1 [jacobia_(:,end-M_.exo_nbr+1:end); ...
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zeros(olr_state_.old_M_.endo_nbr, M_.exo_nbr)]];
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newiy = newiy';
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newiy = find(newiy(:));
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M_.lead_lag_incidence = zeros(M_.endo_nbr*(M_.maximum_lag+M_.maximum_lead+1),1);
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M_.lead_lag_incidence(newiy) = [1:length(newiy)]';
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M_.lead_lag_incidence =reshape(M_.lead_lag_incidence,M_.endo_nbr,M_.maximum_lag+M_.maximum_lead+1)';
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jacobia_ = jacobia1;
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clear jacobia1
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% computes steady state
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resid = feval([M_.fname '_steady'],zeros(olr_state_.old_M_.endo_nbr,1));
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if resid'*resid < 1e-12
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dr.ys =[dr.ys; zeros(nj,1)];
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else
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AA = zeros(M_.endo_nbr,M_.endo_nbr);
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for i=1:M_.maximum_lag+M_.maximum_lead+1
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[junk,k1,k2] = find(M_.lead_lag_incidence(i,:));
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AA(:,k1) = AA(:,k1)+jacobia_(:,k2);
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end
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dr.ys = -AA\[resid; zeros(nj,1)];
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end
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end
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% end of code section for Optimal Linear Regulator
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klen = M_.maximum_lag + M_.maximum_lead + 1;
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dr=set_state_space(dr);
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kstate = dr.kstate;
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kad = dr.kad;
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kae = dr.kae;
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nstatic = dr.nstatic;
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nfwrd = dr.nfwrd;
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npred = dr.npred;
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nboth = dr.nboth;
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order_var = dr.order_var;
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nd = size(kstate,1);
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sdyn = M_.endo_nbr - nstatic;
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k1 = M_.lead_lag_incidence(find([1:klen] ~= M_.maximum_lag+1),:);
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b = jacobia_(:,M_.lead_lag_incidence(M_.maximum_lag+1,order_var));
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a = b\jacobia_(:,nonzeros(k1'));
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nz = nnz(M_.lead_lag_incidence);
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if any(isinf(a(:)))
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info = 1;
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return
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end
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if M_.exo_nbr
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fu = b\jacobia_(:,nz+1:end);
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end
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if M_.maximum_lead == 0; % backward model
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dr.ghx = zeros(size(a));
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m = 0;
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for i=M_.maximum_lag:-1:1
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k = nonzeros(M_.lead_lag_incidence(i,order_var));
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dr.ghx(:,m+[1:length(k)]) = -a(:,k);
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m = m+length(k);
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end
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if M_.exo_nbr
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dr.ghu = -fu;
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end
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dr.eigval = eig(transition_matrix(dr));
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dr.rank = 0;
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if any(abs(dr.eigval) > options_.qz_criterium)
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temp = sort(abs(dr.eigval));
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nba = nnz(abs(dr.eigval) > options_.qz_criterium);
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temp = temp(nd-nba+1:nd)-1-options_.qz_criterium;
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info(1) = 3;
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info(2) = temp'*temp;
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end
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return;
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end
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% buildind D and E
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d = zeros(nd,nd) ;
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e = d ;
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k = find(kstate(:,2) >= M_.maximum_lag+2 & kstate(:,3));
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d(1:sdyn,k) = a(nstatic+1:end,kstate(k,3)) ;
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k1 = find(kstate(:,2) == M_.maximum_lag+2);
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a1 = eye(sdyn);
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e(1:sdyn,k1) = -a1(:,kstate(k1,1)-nstatic);
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k = find(kstate(:,2) <= M_.maximum_lag+1 & kstate(:,4));
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e(1:sdyn,k) = -a(nstatic+1:end,kstate(k,4)) ;
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k2 = find(kstate(:,2) == M_.maximum_lag+1);
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k2 = k2(~ismember(kstate(k2,1),kstate(k1,1)));
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d(1:sdyn,k2) = a1(:,kstate(k2,1)-nstatic);
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if ~isempty(kad)
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for j = 1:size(kad,1)
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d(sdyn+j,kad(j)) = 1 ;
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e(sdyn+j,kae(j)) = 1 ;
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end
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end
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if ~exist('mjdgges')
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% using Chris Sim's routines
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use_qzdiv = 1;
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[ss,tt,qq,w] = qz(e,d);
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[tt,ss,qq,w] = qzdiv(options_.qz_criterium,tt,ss,qq,w);
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ss1=diag(ss);
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tt1=diag(tt);
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warning_state = warning;
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warning off;
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dr.eigval = ss1./tt1 ;
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warning warning_state;
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nba = nnz(abs(dr.eigval) > options_.qz_criterium);
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else
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use_qzdiv = 0;
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[ss,tt,w,sdim,dr.eigval,info1] = mjdgges(e,d,options_.qz_criterium);
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if info1
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info(1) = 2;
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info(2) = info1;
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return
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end
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nba = nd-sdim;
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end
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nyf = sum(kstate(:,2) > M_.maximum_lag+1);
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if task == 1
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dr.rank = rank(w(1:nyf,nd-nyf+1:end));
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dr.eigval = eig(e,d);
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return
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end
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if nba ~= nyf
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temp = sort(abs(dr.eigval));
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if nba > nyf
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temp = temp(nd-nba+1:nd-nyf)-1-options_.qz_criterium;
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info(1) = 3
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elseif nba < nyf;
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temp = temp(nd-nyf+1:nd-nba)-1-options_.qz_criterium
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info(1) = 4;
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end
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info(2) = temp'*temp;
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return
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end
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np = nd - nyf;
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n2 = np + 1;
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n3 = nyf;
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n4 = n3 + 1;
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% derivatives with respect to dynamic state variables
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% forward variables
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w1 =w(1:n3,n2:nd);
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if condest(w1) > 1e9;
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info(1) = 5;
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info(2) = condest(w1);
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return;
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else
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gx = -w1'\w(n4:nd,n2:nd)';
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end
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% predetermined variables
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hx = w(1:n3,1:np)'*gx+w(n4:nd,1:np)';
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hx = (tt(1:np,1:np)*hx)\(ss(1:np,1:np)*hx);
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k1 = find(kstate(n4:nd,2) == M_.maximum_lag+1);
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k2 = find(kstate(1:n3,2) == M_.maximum_lag+2);
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dr.ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
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%lead variables actually present in the model
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j3 = nonzeros(kstate(:,3));
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j4 = find(kstate(:,3));
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% derivatives with respect to exogenous variables
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if M_.exo_nbr
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a1 = eye(M_.endo_nbr);
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aa1 = [];
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if nstatic > 0
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aa1 = a1(:,1:nstatic);
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end
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dr.ghu = -[aa1 a(:,j3)*gx(j4,1:npred)+a1(:,nstatic+1:nstatic+ ...
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npred) a1(:,nstatic+npred+1:end)]\fu;
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end
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% static variables
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if nstatic > 0
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temp = -a(1:nstatic,j3)*gx(j4,:)*hx;
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j5 = find(kstate(n4:nd,4));
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temp(:,j5) = temp(:,j5)-a(1:nstatic,nonzeros(kstate(:,4)));
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dr.ghx = [temp; dr.ghx];
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temp = [];
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end
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if options_.loglinear == 1
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k = find(dr.kstate(:,2) <= M_.maximum_lag+1);
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klag = dr.kstate(k,[1 2]);
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k1 = dr.order_var;
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dr.ghx = repmat(1./dr.ys(k1),1,size(dr.ghx,2)).*dr.ghx.* ...
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repmat(dr.ys(k1(klag(:,1)))',size(dr.ghx,1),1);
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dr.ghu = repmat(1./dr.ys(k1),1,size(dr.ghu,2)).*dr.ghu;
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end
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%necessary when using Sims' routines
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if use_qzdiv
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gx = real(gx);
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hx = real(hx);
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dr.ghx = real(dr.ghx);
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dr.ghu = real(dr.ghu);
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end
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%exogenous deterministic variables
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if M_.exo_det_nbr > 1
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f1 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_lag+2:end,order_var))));
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f0 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_lag+1,order_var))));
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fudet = sparse(jacobia_(:,nz+M_.exo_nbr+1:end));
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M1 = inv(f0+[zeros(M_.endo_nbr,nstatic) f1*gx zeros(M_.endo_nbr,nyf-nboth)]);
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M2 = M1*f1;
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dr.ghud = cell(M_.oo_.exo_simuldet_length,1);
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dr.ghud{1} = -M1*fudet;
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for i = 2:M_.oo_.exo_simuldet_length
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dr.ghud{i} = -M2*dr.ghud{i-1}(end-nyf+1:end,:);
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end
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end
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if options_.order == 1
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return
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end
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% Second order
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%tempex = oo_.exo_simul ;
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%hessian = real(hessext('ff1_',[z; oo_.exo_steady_state]))' ;
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kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_lag+1:end,order_var)),1));
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if M_.maximum_lag > 0
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kk = [cumsum(M_.lead_lag_incidence(1:M_.maximum_lag,order_var),1); kk];
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end
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kk = kk';
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kk = find(kk(:));
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nk = size(kk,1)+M_.exo_nbr;
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k1 = M_.lead_lag_incidence(:,order_var);
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k1 = k1';
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k1 = k1(:);
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k1 = k1(kk);
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k2 = find(k1);
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kk1(k1(k2)) = k2;
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kk1 = [kk1 length(k1)+1:length(k1)+M_.exo_nbr];
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kk = reshape([1:nk^2],nk,nk);
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kk1 = kk(kk1,kk1);
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%[junk,junk,hessian] = feval([M_.fname '_dynamic'],z, oo_.exo_steady_state);
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hessian(:,kk1(:)) = hessian;
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%oo_.exo_simul = tempex ;
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%clear tempex
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n1 = 0;
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n2 = np;
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zx = zeros(np,np);
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zu=zeros(np,M_.exo_nbr);
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for i=2:M_.maximum_lag+1
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k1 = sum(kstate(:,2) == i);
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zx(n1+1:n1+k1,n2-k1+1:n2)=eye(k1);
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n1 = n1+k1;
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n2 = n2-k1;
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end
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kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_lag+1:end,order_var)),1));
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k0 = [1:M_.endo_nbr];
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gx1 = dr.ghx;
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hu = dr.ghu(nstatic+[1:npred],:);
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zx = [zx; gx1];
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zu = [zu; dr.ghu];
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for i=1:M_.maximum_lead
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k1 = find(kk(i+1,k0) > 0);
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zu = [zu; gx1(k1,1:npred)*hu];
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gx1 = gx1(k1,:)*hx;
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zx = [zx; gx1];
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kk = kk(:,k0);
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k0 = k1;
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end
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zx=[zx; zeros(M_.exo_nbr,np)];
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zu=[zu; eye(M_.exo_nbr)];
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[n1,n2] = size(zx);
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if n1*n1*n2*n2 > 1e7
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rhs = zeros(M_.endo_nbr,n2*n2);
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k1 = 1;
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for i1 = 1:n2
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for i2 = 1:n2
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rhs(:,k1) = hessian*kron(zx(:,i1),zx(:,i2));
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k1 = k1 + 1;
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end
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end
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else
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rhs = hessian*kron(zx,zx);
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end
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rhs = -rhs;
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%lhs
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n = M_.endo_nbr+sum(kstate(:,2) > M_.maximum_lag+1 & kstate(:,2) < M_.maximum_lag+M_.maximum_lead+1);
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A = zeros(n,n);
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B = zeros(n,n);
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[junk,k1,k2] = find(M_.lead_lag_incidence(M_.maximum_lag+M_.maximum_lead+1,order_var));
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gx2 = dr.ghx(k1,:);
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A(1:M_.endo_nbr,1:M_.endo_nbr) = jacobia_(:,M_.lead_lag_incidence(M_.maximum_lag+1,order_var));
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A(1:M_.endo_nbr,nstatic+1:nstatic+npred)=...
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A(1:M_.endo_nbr,nstatic+[1:npred])+jacobia_(:,k2)*gx2(:,1:npred);
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% variables with the highest lead
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k1 = find(kstate(:,2) == M_.maximum_lag+M_.maximum_lead+1);
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if M_.maximum_lead > 1
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k2 = find(kstate(:,2) == M_.maximum_lag+M_.maximum_lead);
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[junk,junk,k3] = intersect(kstate(k1,1),kstate(k2,1));
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else
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k2 = [1:M_.endo_nbr];
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k3 = kstate(k1,1);
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end
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% Jacobian with respect to the variables with the highest lead
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B(1:M_.endo_nbr,end-length(k2)+k3) = jacobia_(:,kstate(k1,3)+M_.endo_nbr);
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offset = M_.endo_nbr;
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k0 = [1:M_.endo_nbr];
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for i=1:M_.maximum_lead-1
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k1 = find(kstate(:,2) == M_.maximum_lag+i+1);
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[k2,junk,k3] = find(kstate(k1,3));
|
|
A(1:M_.endo_nbr,offset+k2) = jacobia_(:,k3+M_.endo_nbr);
|
|
n1 = length(k1);
|
|
A(offset+[1:n1],nstatic+[1:npred]) = -gx(k1,1:npred);
|
|
A(offset+[1:n1],offset+[1:n1]) = eye(n1);
|
|
n0 = length(k0);
|
|
E = eye(n0);
|
|
if i == 1
|
|
[junk,junk,k4]=intersect(kstate(k1,1),[1:M_.endo_nbr]);
|
|
else
|
|
[junk,junk,k4]=intersect(kstate(k1,1),kstate(k0,1));
|
|
end
|
|
i1 = offset-n0+n1;
|
|
B(offset+[1:n1],offset-n0+[1:n0]) = -E(k4,:);
|
|
k0 = k1;
|
|
offset = offset + n1;
|
|
end
|
|
%C = kron(hx,hx);
|
|
C = hx;
|
|
D = [rhs; zeros(n-M_.endo_nbr,size(rhs,2))];
|
|
%x0 = sylvester3(A,B,C,D);
|
|
%dr.ghxx = sylvester3a(x0,A,B,C,D);
|
|
dr.ghxx = gensylv(2,A,B,C,D);
|
|
|
|
%ghxu
|
|
%rhs
|
|
hu = dr.ghu(nstatic+1:nstatic+npred,:);
|
|
%kk = reshape([1:np*np],np,np);
|
|
%kk = kk(1:npred,1:npred);
|
|
%rhs = -hessian*kron(zx,zu)-f1*dr.ghxx(end-nyf+1:end,kk(:))*kron(hx(1:npred,:),hu(1:npred,:));
|
|
if n1*n1*n2*M_.exo_nbr > 1e7
|
|
rhs = zeros(M_.endo_nbr,n2*M_.exo_nbr);
|
|
k1 = 1;
|
|
for i1 = 1:n2
|
|
for i2 = 1:M_.exo_nbr
|
|
rhs(:,k1) = hessian*kron(zx(:,i1),zu(:,i2));
|
|
k1 = k1 + 1;
|
|
end
|
|
end
|
|
else
|
|
rhs = hessian*kron(zx,zu);
|
|
end
|
|
nyf1 = sum(kstate(:,2) == M_.maximum_lag+2);
|
|
hu1 = [hu;zeros(np-npred,M_.exo_nbr)];
|
|
B1 = [B(1:M_.endo_nbr,:);zeros(size(A,1)-M_.endo_nbr,size(B,2))];
|
|
rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1*dr.ghxx*kron(hx,hu1);
|
|
|
|
%lhs
|
|
dr.ghxu = A\rhs;
|
|
|
|
%ghuu
|
|
%rhs
|
|
kk = reshape([1:np*np],np,np);
|
|
kk = kk(1:npred,1:npred);
|
|
if n1*n1*M_.exo_nbr*M_.exo_nbr > 1e7
|
|
rhs = zeros(M_.endo_nbr,M_.exo_nbr*M_.exo_nbr);
|
|
k1 = 1;
|
|
for i1 = 1:M_.exo_nbr
|
|
for i2 = 1:M_.exo_nbr
|
|
rhs(:,k1) = hessian*kron(zu(:,i1),zu(:,i2));
|
|
k1 = k1 + 1;
|
|
end
|
|
end
|
|
else
|
|
rhs = hessian*kron(zu,zu);
|
|
end
|
|
|
|
rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B*dr.ghxx*kron(hu1,hu1);
|
|
|
|
%lhs
|
|
dr.ghuu = A\rhs;
|
|
|
|
dr.ghxx = dr.ghxx(1:M_.endo_nbr,:);
|
|
dr.ghxu = dr.ghxu(1:M_.endo_nbr,:);
|
|
dr.ghuu = dr.ghuu(1:M_.endo_nbr,:);
|
|
|
|
|
|
% dr.ghs2
|
|
% derivatives of F with respect to forward variables
|
|
% reordering predetermined variables in diminishing lag order
|
|
O1 = zeros(M_.endo_nbr,nstatic);
|
|
O2 = zeros(M_.endo_nbr,M_.endo_nbr-nstatic-npred);
|
|
LHS = jacobia_(:,M_.lead_lag_incidence(M_.maximum_lag+1,order_var));
|
|
RHS = zeros(M_.endo_nbr,M_.exo_nbr^2);
|
|
kk = find(kstate(:,2) == M_.maximum_lag+2);
|
|
gu = dr.ghu;
|
|
guu = dr.ghuu;
|
|
Gu = [dr.ghu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr)];
|
|
Guu = [dr.ghuu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr*M_.exo_nbr)];
|
|
E = eye(M_.endo_nbr);
|
|
M_.lead_lag_incidenceordered = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_lag+1:end,order_var)),1));
|
|
if M_.maximum_lag > 0
|
|
M_.lead_lag_incidenceordered = [cumsum(M_.lead_lag_incidence(1:M_.maximum_lag,order_var),1); M_.lead_lag_incidenceordered];
|
|
end
|
|
M_.lead_lag_incidenceordered = M_.lead_lag_incidenceordered';
|
|
M_.lead_lag_incidenceordered = M_.lead_lag_incidenceordered(:);
|
|
k1 = find(M_.lead_lag_incidenceordered);
|
|
M_.lead_lag_incidenceordered(k1) = [1:length(k1)]';
|
|
M_.lead_lag_incidenceordered =reshape(M_.lead_lag_incidenceordered,M_.endo_nbr,M_.maximum_lag+M_.maximum_lead+1)';
|
|
kh = reshape([1:nk^2],nk,nk);
|
|
kp = sum(kstate(:,2) <= M_.maximum_lag+1);
|
|
E1 = [eye(npred); zeros(kp-npred,npred)];
|
|
H = E1;
|
|
hxx = dr.ghxx(nstatic+[1:npred],:);
|
|
for i=1:M_.maximum_lead
|
|
for j=i:M_.maximum_lead
|
|
[junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_lag+j+1,order_var));
|
|
[junk,k3a,k3] = find(M_.lead_lag_incidenceordered(M_.maximum_lag+j+1,:));
|
|
RHS = RHS + jacobia_(:,k2)*guu(k2a,:)+hessian(:,kh(k3,k3))* ...
|
|
kron(gu(k3a,:),gu(k3a,:));
|
|
end
|
|
|
|
% LHS
|
|
[junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_lag+i+1,order_var));
|
|
LHS = LHS + jacobia_(:,k2)*(E(k2a,:)+[O1(k2a,:) dr.ghx(k2a,:)*H O2(k2a,:)]);
|
|
|
|
if i == M_.maximum_lead
|
|
break
|
|
end
|
|
|
|
kk = find(kstate(:,2) == M_.maximum_lag+i+1);
|
|
gu = dr.ghx*Gu;
|
|
GuGu = kron(Gu,Gu);
|
|
guu = dr.ghx*Guu+dr.ghxx*GuGu;
|
|
Gu = hx*Gu;
|
|
Guu = hx*Guu;
|
|
Guu(end-npred+1:end,:) = Guu(end-npred+1:end,:) + hxx*GuGu;
|
|
|
|
H = E1 + hx*H;
|
|
end
|
|
RHS = RHS*M_.Sigma_e(:);
|
|
dr.fuu = RHS;
|
|
RHS = -RHS-dr.fbias;
|
|
dr.ghs2 = LHS\RHS;
|
|
|
|
% deterministic exogenous variables
|
|
if M_.exo_det_nbr > 0
|
|
hud = dr.ghud{1}(nstatic+1:nstatic+npred,:);
|
|
zud=[zeros(np,M_.exo_det_nbr);dr.ghud{1};gx(:,1:npred)*hud;zeros(M_.exo_nbr,M_.exo_det_nbr);eye(M_.exo_det_nbr)];
|
|
R1 = hessian*kron(zx,zud);
|
|
dr.ghxud = cell(M_.oo_.exo_simuldet_length,1);
|
|
kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
|
|
kp = nstatic+[1:npred];
|
|
dr.ghxud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{1}(kp,:)));
|
|
Eud = eye(M_.exo_det_nbr);
|
|
for i = 2:M_.oo_.exo_simuldet_length
|
|
hudi = dr.ghud{i}(kp,:);
|
|
zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
|
|
R2 = hessian*kron(zx,zudi);
|
|
dr.ghxud{i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(hx,Eud)+dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{i}(kp,:)))-M1*R2;
|
|
end
|
|
R1 = hessian*kron(zu,zud);
|
|
dr.ghudud = cell(M_.oo_.exo_simuldet_length,1);
|
|
kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
|
|
|
|
dr.ghuud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghu(kp,:),dr.ghud{1}(kp,:)));
|
|
Eud = eye(M_.exo_det_nbr);
|
|
for i = 2:M_.oo_.exo_simuldet_length
|
|
hudi = dr.ghud{i}(kp,:);
|
|
zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
|
|
R2 = hessian*kron(zu,zudi);
|
|
dr.ghuud{i} = -M2*dr.ghxud{i-1}(kf,:)*kron(hu,Eud)-M1*R2;
|
|
end
|
|
R1 = hessian*kron(zud,zud);
|
|
dr.ghudud = cell(M_.oo_.exo_simuldet_length,M_.oo_.exo_simuldet_length);
|
|
dr.ghudud{1,1} = -M1*R1-M2*dr.ghxx(kf,:)*kron(hud,hud);
|
|
for i = 2:M_.oo_.exo_simuldet_length
|
|
hudi = dr.ghud{i}(nstatic+1:nstatic+npred,:);
|
|
zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi+dr.ghud{i-1}(kf,:);zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
|
|
R2 = hessian*kron(zudi,zudi);
|
|
dr.ghudud{i,i} = -M2*(dr.ghudud{i-1,i-1}(kf,:)+...
|
|
2*dr.ghxud{i-1}(kf,:)*kron(hudi,Eud) ...
|
|
+dr.ghxx(kf,:)*kron(hudi,hudi))-M1*R2;
|
|
R2 = hessian*kron(zud,zudi);
|
|
dr.ghudud{1,i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(hud,Eud)+...
|
|
dr.ghxx(kf,:)*kron(hud,hudi))...
|
|
-M1*R2;
|
|
for j=2:i-1
|
|
hudj = dr.ghud{j}(kp,:);
|
|
zudj=[zeros(np,M_.exo_det_nbr);dr.ghud{j};gx(:,1:npred)*hudj;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
|
|
R2 = hessian*kron(zudj,zudi);
|
|
dr.ghudud{j,i} = -M2*(dr.ghudud{j-1,i-1}(kf,:)+dr.ghxud{j-1}(kf,:)* ...
|
|
kron(hudi,Eud)+dr.ghxud{i-1}(kf,:)* ...
|
|
kron(hudj,Eud)+dr.ghxx(kf,:)*kron(hudj,hudi))-M1*R2;
|
|
end
|
|
|
|
end
|
|
end
|
|
% 01/08/2001 MJ put return on iorder == 1 after defining dr.kstate and dr.kdyn
|
|
% 01/17/2001 MJ added dr.delta_s: correction factor for order = 2
|
|
% 01/21/2001 FC correction of delta_s for more than 1 shock
|
|
% 01/23/2001 MJ suppression of redundant sum() in delta_s formula
|
|
% 02/22/2001 MJ stderr_ replaced by Sigma_e_
|
|
% 08/24/2001 MJ changed the order of the variables, separates static
|
|
% variables and handles only one instance of variables both
|
|
% in lead and lag
|
|
% 08/24/2001 MJ added sigma to state variables as in Schmitt-Grohe and
|
|
% Uribe (2001)
|
|
% 10/20/2002 MJ corrected lags on several periods bug
|
|
% 10/30/2002 MJ corrected lags on several periods bug on static when some
|
|
% intermediary lags are missing
|
|
% 12/08/2002 MJ uses sylvester3 to solve for dr.ghxx
|
|
% 01/01/2003 MJ added dr.fbias for iterative for dr_algo == 1
|
|
% 02/21/2003 MJ corrected bug for models without lagged variables
|
|
% 03/02/2003 MJ fixed second order for lag on several periods
|
|
% 05/21/2003 MJ add check call argument and make computation for CHECK
|
|
% 06/01/2003 MJ added a test for M_.maximum_lead > 1 and order > 1
|
|
% 08/28/2003 MJ corrected bug in computation of 2nd order (ordering of
|
|
% forward variable in LHS)
|
|
% 08/29/2003 MJ use Sims routine if mjdgges isn't available
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|