2005-09-11 16:15:35 +02:00
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function [dr,info]=dr1(dr,task)
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2006-10-29 18:28:57 +01:00
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% function dr = dr1(dr,task)
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% finds the state vector for structural state space representation
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% sets many fields of dr
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%
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% INPUTS
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% dr: structure of decision rules for stochastic simulations
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% task = 0: computes decision rules
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% task = 1: computes eigenvalues
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%
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% OUTPUTS
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% dr: structure of decision rules for stochastic simulations
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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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%
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% ALGORITHM
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% ...
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% SPECIAL REQUIREMENTS
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% none
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%
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%
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% part of DYNARE, copyright S. Adjemian, M. Juillard (1996-2006)
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% Gnu Public License.
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global M_ options_ oo_ olr_state
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2005-02-18 20:54:39 +01:00
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2005-09-11 16:15:35 +02:00
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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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2005-02-18 20:54:39 +01:00
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2006-10-29 18:28:57 +01:00
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xlen = M_.maximum_endo_lead + M_.maximum_endo_lag + 1;
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klen = M_.maximum_endo_lag + M_.maximum_endo_lead + 1;
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2005-02-18 20:54:39 +01:00
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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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2006-12-17 16:01:20 +01:00
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% expanding system for Optimal Linear Regulator
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2007-01-04 15:42:27 +01:00
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if options_.ramsey_policy
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2006-12-17 16:01:20 +01:00
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if isfield(M_,'orig_model')
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orig_model = M_.orig_model;
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M_.endo_nbr = orig_model.endo_nbr;
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M_.endo_names = orig_model.endo_names;
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M_.lead_lag_incidence = orig_model.lead_lag_incidence;
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M_.maximum_lead = orig_model.maximum_lead;
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M_.maximum_endo_lead = orig_model.maximum_endo_lead;
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M_.maximum_lag = orig_model.maximum_lag;
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M_.maximum_endo_lag = orig_model.maximum_endo_lag;
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end
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2007-01-04 15:42:27 +01:00
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old_solve_algo = options_.solve_algo;
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2007-10-31 15:52:11 +01:00
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% options_.solve_algo = 1;
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2006-12-17 16:01:20 +01:00
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oo_.steady_state = dynare_solve('ramsey_static',oo_.steady_state,0);
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2007-01-04 15:42:27 +01:00
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options_.solve_algo = old_solve_algo;
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2006-12-17 16:01:20 +01:00
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[junk,junk,multbar] = ramsey_static(oo_.steady_state);
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jacobia_=ramsey_dynamic(oo_.steady_state,multbar);
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klen = M_.maximum_lag + M_.maximum_lead + 1;
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dr.ys = [oo_.steady_state;zeros(M_.exo_nbr,1);multbar];
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2007-10-31 15:52:11 +01:00
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if options_.ramsey_policy == 2
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mask = M_.orig_model.lead_lag_incidence ~= 0;
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incidence_submatrix = M_.lead_lag_incidence(M_.orig_model.maximum_lead+(1:size(mask,1)),1:M_.orig_model.endo_nbr);
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k = nonzeros((incidence_submatrix.*mask)');
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nl = nnz(M_.lead_lag_incidence);
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k = [k; nl+(1:M_.exo_nbr)'];
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kk = reshape(1:(nl+M_.exo_nbr)^2,nl+M_.exo_nbr,nl+M_.exo_nbr);
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kk2 = kk(k,k);
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k1 = find(M_.orig_model.lead_lag_incidence');
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y = repmat(oo_.dr.ys(1:M_.orig_model.endo_nbr),1,M_.orig_model.maximum_lag+M_.orig_model.maximum_lead+1);
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[f,fJ,fh] = feval([M_.fname '_dynamic'],y(k1),zeros(1,M_.exo_nbr));
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% looking for dynamic variables that are both in the original model
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% and in the optimal policy model
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k1 = k1+nnz(M_.lead_lag_incidence(1:M_.orig_model.maximum_lead,1:M_.orig_model.endo_nbr));
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hessian = sparse([],[],[],size(jacobia_,1),(nl+M_.exo_nbr)^2,nnz(fh));
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hessian(M_.orig_model.endo_nbr+(1:size(fh,1)),kk2) = fh;
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options_.order = 2;
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elseif options_.ramsey_policy == 3
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maxlag1 = M_.orig_model.maximum_lag;
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maxlead1 = M_.orig_model.maximum_lead;
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endo_nbr1 = M_.orig_model.endo_nbr;
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lead_lag_incidence1 = M_.orig_model.lead_lag_incidence;
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y = repmat(oo_.dr.ys(1:M_.orig_model.endo_nbr),1,M_.orig_model.maximum_lag+M_.orig_model.maximum_lead+1);
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k1 = find(M_.orig_model.lead_lag_incidence');
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[f,fj,fh] = feval([M_.fname '_dynamic'],y(k1),zeros(1,M_.exo_nbr));
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nrj = size(fj,1);
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iy = M_.lead_lag_incidence;
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kstate = oo_.dr.kstate;
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inv_order_var = oo_.dr.inv_order_var;
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offset = 0;
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i3 = zeros(0,1);
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i4 = find(kstate(:,2) <= M_.maximum_lag+1);
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kstate1 = kstate(i4,:);
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kk2 = zeros(0,1);
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% lagged variables
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for i=2:M_.maximum_lag + 1
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i1 = find(kstate(:,2) == i);
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k1 = kstate(i1,:);
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i2 = find(oo_.dr.order_var(k1(:,1)) <= M_.orig_model.endo_nbr);
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i3 = [i3; i2+offset];
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offset = offset + size(k1,1);
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i4 = find(kstate1(:,2) == i);
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kk2 = [kk2; i4];
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end
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i2 = find(oo_.dr.order_var(k1(:,1)) > M_.orig_model.endo_nbr);
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j2 = k1(i2,1);
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nj2 = length(j2);
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k2 = offset+(1:nj2)';
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offset = offset + length(i2);
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i3 = [i3; ...
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find(M_.orig_model.lead_lag_incidence(M_.orig_model.maximum_lag+1:end,:)')+offset];
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i3 = [i3; (1:M_.exo_nbr)'+length(i3)];
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ni3 = length(i3);
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nrfj = size(fj,1);
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jacobia_ = zeros(nrfj+length(j2),ni3);
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jacobia_(1:nrfj,i3) = fj;
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jacobia_(nrfj+(1:nj2),1:size(oo_.dr.ghx,2)) = oo_.dr.ghx(j2,:);
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jacobia_(nrfj+(1:nj2),k2) = eye(nj2);
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kk1 = reshape(1:ni3^2,ni3,ni3);
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hessian = zeros(nrfj+length(j2),ni3^2);
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hessian(1:nrfj,kk1(i3,i3)) = fh;
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k = find(any(M_.lead_lag_incidence(1:M_.maximum_lag, ...
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M_.orig_model.endo_nbr+1:end)));
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if maxlead1 > maxlag1
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M_.lead_lag_incidence = [ [zeros(maxlead1-maxlag1,endo_nbr1); ...
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lead_lag_incidence1] ...
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[M_.lead_lag_incidence(M_.maximum_lag+(1:maxlead1), ...
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k); zeros(maxlead1,length(k))]];
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elseif maxlag1 > maxlead1
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M_.lead_lag_incidence = [ [lead_lag_incidence1; zeros(maxlag1- ...
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maxlead1,endo_nbr1);] ...
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[M_.lead_lag_incidence(M_.maximum_lag+(1:maxlead1), ...
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k); zeros(maxlead1,length(k))]];
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else % maxlag1 == maxlead1
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M_.lead_lag_incidence = [ lead_lag_incidence1
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[M_.lead_lag_incidence(M_.maximum_lag+(1:maxlead1), ...
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k); zeros(maxlead1,length(k))]];
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end
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M_.maximum_lag = max(maxlead1,maxlag1);
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M_.maximum_endo_lag = M_.maximum_lag;
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M_.maximum_lead = M_.maximum_lag;
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M_.maximum_endo_lead = M_.maximum_lag;
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M_.endo_names = strvcat(M_.orig_model.endo_names, M_.endo_names(endo_nbr1+k,:));
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M_.endo_nbr = endo_nbr1+length(k);
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end
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2005-09-11 16:15:35 +02:00
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else
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2006-12-17 16:01:20 +01:00
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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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it_ = M_.maximum_lag + 1;
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2005-09-11 16:15:35 +02:00
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z = repmat(dr.ys,1,klen);
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2006-12-17 16:01:20 +01:00
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z = z(iyr0) ;
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if options_.order == 1
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2007-12-11 16:41:48 +01:00
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[junk,jacobia_] = feval([M_.fname '_dynamic'],z,[oo_.exo_simul ...
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oo_.exo_det_simul]);
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2006-12-17 16:01:20 +01:00
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elseif options_.order == 2
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2006-06-02 09:42:00 +02:00
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[junk,jacobia_,hessian] = feval([M_.fname '_dynamic'],z,...
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[oo_.exo_simul ...
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2006-12-17 16:01:20 +01:00
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oo_.exo_det_simul]);
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2005-09-11 16:15:35 +02:00
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end
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2005-02-18 20:54:39 +01:00
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end
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2007-01-30 16:50:22 +01:00
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if options_.debug
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save([M_.fname '_debug'],'jacobia_')
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end
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2005-02-18 20:54:39 +01:00
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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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2006-01-13 16:50:32 +01:00
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nz = nnz(M_.lead_lag_incidence);
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2005-02-18 20:54:39 +01:00
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sdyn = M_.endo_nbr - nstatic;
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2006-10-29 18:28:57 +01:00
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k0 = M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var);
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k1 = M_.lead_lag_incidence(find([1:klen] ~= M_.maximum_endo_lag+1),:);
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2005-09-30 17:02:43 +02:00
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b = jacobia_(:,k0);
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2005-02-18 20:54:39 +01:00
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2006-10-29 18:28:57 +01:00
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if M_.maximum_endo_lead == 0; % backward models
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2006-01-08 09:39:00 +01:00
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a = jacobia_(:,nonzeros(k1'));
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2005-09-11 16:15:35 +02:00
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dr.ghx = zeros(size(a));
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m = 0;
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2006-10-29 18:28:57 +01:00
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for i=M_.maximum_endo_lag:-1:1
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2005-09-11 16:15:35 +02:00
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k = nonzeros(M_.lead_lag_incidence(i,order_var));
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2006-01-06 16:12:00 +01:00
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dr.ghx(:,m+[1:length(k)]) = -b\a(:,k);
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2005-09-11 16:15:35 +02:00
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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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2006-01-13 16:50:32 +01:00
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dr.ghu = -b\jacobia_(:,nz+1:end);
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2005-02-20 19:25:09 +01:00
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end
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2005-09-11 16:15:35 +02:00
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dr.eigval = eig(transition_matrix(dr));
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2005-02-18 20:54:39 +01:00
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dr.rank = 0;
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2005-09-11 16:15:35 +02:00
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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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2005-02-18 20:54:39 +01:00
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return;
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end
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2006-01-08 09:39:00 +01:00
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%forward--looking models
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if nstatic > 0
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[Q,R] = qr(b(:,1:nstatic));
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aa = Q'*jacobia_;
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else
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aa = jacobia_;
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end
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a = aa(:,nonzeros(k1'));
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b = aa(:,k0);
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b10 = b(1:nstatic,1:nstatic);
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b11 = b(1:nstatic,nstatic+1:end);
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b2 = b(nstatic+1:end,nstatic+1:end);
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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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2005-02-18 20:54:39 +01:00
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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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2006-10-29 18:28:57 +01:00
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k = find(kstate(:,2) >= M_.maximum_endo_lag+2 & kstate(:,3));
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2005-02-18 20:54:39 +01:00
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d(1:sdyn,k) = a(nstatic+1:end,kstate(k,3)) ;
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2006-10-29 18:28:57 +01:00
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k1 = find(kstate(:,2) == M_.maximum_endo_lag+2);
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2005-09-27 22:22:05 +02:00
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e(1:sdyn,k1) = -b2(:,kstate(k1,1)-nstatic);
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2006-10-29 18:28:57 +01:00
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k = find(kstate(:,2) <= M_.maximum_endo_lag+1 & kstate(:,4));
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2005-02-18 20:54:39 +01:00
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e(1:sdyn,k) = -a(nstatic+1:end,kstate(k,4)) ;
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2006-10-29 18:28:57 +01:00
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k2 = find(kstate(:,2) == M_.maximum_endo_lag+1);
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2005-02-18 20:54:39 +01:00
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k2 = k2(~ismember(kstate(k2,1),kstate(k1,1)));
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2005-09-27 22:22:05 +02:00
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d(1:sdyn,k2) = b2(:,kstate(k2,1)-nstatic);
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2005-02-18 20:54:39 +01:00
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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;
|
|
|
|
warning off;
|
2005-09-11 16:15:35 +02:00
|
|
|
dr.eigval = ss1./tt1 ;
|
2005-02-18 20:54:39 +01:00
|
|
|
warning warning_state;
|
2005-09-11 16:15:35 +02:00
|
|
|
nba = nnz(abs(dr.eigval) > options_.qz_criterium);
|
2005-02-18 20:54:39 +01:00
|
|
|
else
|
|
|
|
use_qzdiv = 0;
|
2005-09-11 16:15:35 +02:00
|
|
|
[ss,tt,w,sdim,dr.eigval,info1] = mjdgges(e,d,options_.qz_criterium);
|
|
|
|
if info1
|
|
|
|
info(1) = 2;
|
|
|
|
info(2) = info1;
|
|
|
|
return
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
|
|
|
nba = nd-sdim;
|
|
|
|
end
|
|
|
|
|
2006-10-29 18:28:57 +01:00
|
|
|
nyf = sum(kstate(:,2) > M_.maximum_endo_lag+1);
|
2005-02-18 20:54:39 +01:00
|
|
|
|
2005-09-11 16:15:35 +02:00
|
|
|
if task == 1
|
2005-02-18 20:54:39 +01:00
|
|
|
dr.rank = rank(w(1:nyf,nd-nyf+1:end));
|
2005-09-11 16:15:35 +02:00
|
|
|
dr.eigval = eig(e,d);
|
2005-02-18 20:54:39 +01:00
|
|
|
return
|
|
|
|
end
|
|
|
|
|
2005-09-11 16:15:35 +02:00
|
|
|
if nba ~= nyf
|
|
|
|
temp = sort(abs(dr.eigval));
|
|
|
|
if nba > nyf
|
|
|
|
temp = temp(nd-nba+1:nd-nyf)-1-options_.qz_criterium;
|
2005-09-26 14:40:14 +02:00
|
|
|
info(1) = 3;
|
2005-09-11 16:15:35 +02:00
|
|
|
elseif nba < nyf;
|
2006-05-23 21:42:56 +02:00
|
|
|
temp = temp(nd-nyf+1:nd-nba)-1-options_.qz_criterium;
|
2005-09-11 16:15:35 +02:00
|
|
|
info(1) = 4;
|
|
|
|
end
|
|
|
|
info(2) = temp'*temp;
|
|
|
|
return
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
|
|
|
|
|
|
|
np = nd - nyf;
|
|
|
|
n2 = np + 1;
|
|
|
|
n3 = nyf;
|
|
|
|
n4 = n3 + 1;
|
|
|
|
% derivatives with respect to dynamic state variables
|
|
|
|
% forward variables
|
2005-09-11 16:15:35 +02:00
|
|
|
w1 =w(1:n3,n2:nd);
|
|
|
|
if condest(w1) > 1e9;
|
|
|
|
info(1) = 5;
|
|
|
|
info(2) = condest(w1);
|
|
|
|
return;
|
|
|
|
else
|
|
|
|
gx = -w1'\w(n4:nd,n2:nd)';
|
|
|
|
end
|
|
|
|
|
2005-02-18 20:54:39 +01:00
|
|
|
% predetermined variables
|
|
|
|
hx = w(1:n3,1:np)'*gx+w(n4:nd,1:np)';
|
|
|
|
hx = (tt(1:np,1:np)*hx)\(ss(1:np,1:np)*hx);
|
|
|
|
|
2006-10-29 18:28:57 +01:00
|
|
|
k1 = find(kstate(n4:nd,2) == M_.maximum_endo_lag+1);
|
|
|
|
k2 = find(kstate(1:n3,2) == M_.maximum_endo_lag+2);
|
2005-02-18 20:54:39 +01:00
|
|
|
dr.ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
|
|
|
|
|
|
|
|
%lead variables actually present in the model
|
|
|
|
j3 = nonzeros(kstate(:,3));
|
|
|
|
j4 = find(kstate(:,3));
|
|
|
|
% derivatives with respect to exogenous variables
|
|
|
|
if M_.exo_nbr
|
2006-12-16 09:59:09 +01:00
|
|
|
fu = aa(:,nz+(1:M_.exo_nbr));
|
2005-09-30 17:02:43 +02:00
|
|
|
a1 = b;
|
2005-02-18 20:54:39 +01:00
|
|
|
aa1 = [];
|
|
|
|
if nstatic > 0
|
|
|
|
aa1 = a1(:,1:nstatic);
|
|
|
|
end
|
|
|
|
dr.ghu = -[aa1 a(:,j3)*gx(j4,1:npred)+a1(:,nstatic+1:nstatic+ ...
|
|
|
|
npred) a1(:,nstatic+npred+1:end)]\fu;
|
2006-12-16 09:59:09 +01:00
|
|
|
else
|
|
|
|
dr.ghu = [];
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
|
|
|
|
|
|
|
% static variables
|
|
|
|
if nstatic > 0
|
|
|
|
temp = -a(1:nstatic,j3)*gx(j4,:)*hx;
|
|
|
|
j5 = find(kstate(n4:nd,4));
|
|
|
|
temp(:,j5) = temp(:,j5)-a(1:nstatic,nonzeros(kstate(:,4)));
|
2005-09-30 17:02:43 +02:00
|
|
|
temp = b10\(temp-b11*dr.ghx);
|
2005-02-18 20:54:39 +01:00
|
|
|
dr.ghx = [temp; dr.ghx];
|
|
|
|
temp = [];
|
|
|
|
end
|
|
|
|
|
|
|
|
if options_.loglinear == 1
|
2006-10-29 18:28:57 +01:00
|
|
|
k = find(dr.kstate(:,2) <= M_.maximum_endo_lag+1);
|
2005-02-18 20:54:39 +01:00
|
|
|
klag = dr.kstate(k,[1 2]);
|
|
|
|
k1 = dr.order_var;
|
|
|
|
|
|
|
|
dr.ghx = repmat(1./dr.ys(k1),1,size(dr.ghx,2)).*dr.ghx.* ...
|
|
|
|
repmat(dr.ys(k1(klag(:,1)))',size(dr.ghx,1),1);
|
|
|
|
dr.ghu = repmat(1./dr.ys(k1),1,size(dr.ghu,2)).*dr.ghu;
|
|
|
|
end
|
|
|
|
|
|
|
|
%necessary when using Sims' routines
|
|
|
|
if use_qzdiv
|
|
|
|
gx = real(gx);
|
|
|
|
hx = real(hx);
|
|
|
|
dr.ghx = real(dr.ghx);
|
|
|
|
dr.ghu = real(dr.ghu);
|
|
|
|
end
|
|
|
|
|
|
|
|
%exogenous deterministic variables
|
2006-06-02 09:42:00 +02:00
|
|
|
if M_.exo_det_nbr > 0
|
2006-10-29 18:28:57 +01:00
|
|
|
f1 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+2:end,order_var))));
|
|
|
|
f0 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var))));
|
2005-09-11 16:15:35 +02:00
|
|
|
fudet = sparse(jacobia_(:,nz+M_.exo_nbr+1:end));
|
2005-02-18 20:54:39 +01:00
|
|
|
M1 = inv(f0+[zeros(M_.endo_nbr,nstatic) f1*gx zeros(M_.endo_nbr,nyf-nboth)]);
|
|
|
|
M2 = M1*f1;
|
2006-06-02 09:42:00 +02:00
|
|
|
dr.ghud = cell(M_.exo_det_length,1);
|
2005-02-18 20:54:39 +01:00
|
|
|
dr.ghud{1} = -M1*fudet;
|
2006-06-02 09:42:00 +02:00
|
|
|
for i = 2:M_.exo_det_length
|
2005-02-18 20:54:39 +01:00
|
|
|
dr.ghud{i} = -M2*dr.ghud{i-1}(end-nyf+1:end,:);
|
|
|
|
end
|
|
|
|
end
|
|
|
|
|
2005-09-11 16:15:35 +02:00
|
|
|
if options_.order == 1
|
2005-02-18 20:54:39 +01:00
|
|
|
return
|
|
|
|
end
|
|
|
|
|
|
|
|
% Second order
|
2005-09-22 16:28:25 +02:00
|
|
|
%tempex = oo_.exo_simul ;
|
2005-02-18 20:54:39 +01:00
|
|
|
|
|
|
|
%hessian = real(hessext('ff1_',[z; oo_.exo_steady_state]))' ;
|
2006-10-29 18:28:57 +01:00
|
|
|
kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
|
|
|
|
if M_.maximum_endo_lag > 0
|
|
|
|
kk = [cumsum(M_.lead_lag_incidence(1:M_.maximum_endo_lag,order_var),1); kk];
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
|
|
|
kk = kk';
|
|
|
|
kk = find(kk(:));
|
2006-06-02 09:42:00 +02:00
|
|
|
nk = size(kk,1) + M_.exo_nbr + M_.exo_det_nbr;
|
2005-02-18 20:54:39 +01:00
|
|
|
k1 = M_.lead_lag_incidence(:,order_var);
|
|
|
|
k1 = k1';
|
|
|
|
k1 = k1(:);
|
|
|
|
k1 = k1(kk);
|
|
|
|
k2 = find(k1);
|
|
|
|
kk1(k1(k2)) = k2;
|
2006-06-02 09:42:00 +02:00
|
|
|
kk1 = [kk1 length(k1)+1:length(k1)+M_.exo_nbr+M_.exo_det_nbr];
|
2005-02-18 20:54:39 +01:00
|
|
|
kk = reshape([1:nk^2],nk,nk);
|
|
|
|
kk1 = kk(kk1,kk1);
|
2005-09-22 16:28:25 +02:00
|
|
|
%[junk,junk,hessian] = feval([M_.fname '_dynamic'],z, oo_.exo_steady_state);
|
|
|
|
hessian(:,kk1(:)) = hessian;
|
2005-02-18 20:54:39 +01:00
|
|
|
|
2005-09-22 16:28:25 +02:00
|
|
|
%oo_.exo_simul = tempex ;
|
|
|
|
%clear tempex
|
2005-02-18 20:54:39 +01:00
|
|
|
|
|
|
|
n1 = 0;
|
|
|
|
n2 = np;
|
|
|
|
zx = zeros(np,np);
|
2005-09-11 16:15:35 +02:00
|
|
|
zu=zeros(np,M_.exo_nbr);
|
2006-10-29 18:28:57 +01:00
|
|
|
for i=2:M_.maximum_endo_lag+1
|
2005-02-18 20:54:39 +01:00
|
|
|
k1 = sum(kstate(:,2) == i);
|
|
|
|
zx(n1+1:n1+k1,n2-k1+1:n2)=eye(k1);
|
|
|
|
n1 = n1+k1;
|
|
|
|
n2 = n2-k1;
|
|
|
|
end
|
2006-10-29 18:28:57 +01:00
|
|
|
kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
|
2005-02-18 20:54:39 +01:00
|
|
|
k0 = [1:M_.endo_nbr];
|
|
|
|
gx1 = dr.ghx;
|
2005-09-11 16:15:35 +02:00
|
|
|
hu = dr.ghu(nstatic+[1:npred],:);
|
2005-02-18 20:54:39 +01:00
|
|
|
zx = [zx; gx1];
|
2005-09-11 16:15:35 +02:00
|
|
|
zu = [zu; dr.ghu];
|
2006-10-29 18:28:57 +01:00
|
|
|
for i=1:M_.maximum_endo_lead
|
2005-02-18 20:54:39 +01:00
|
|
|
k1 = find(kk(i+1,k0) > 0);
|
2005-09-11 16:15:35 +02:00
|
|
|
zu = [zu; gx1(k1,1:npred)*hu];
|
2005-02-18 20:54:39 +01:00
|
|
|
gx1 = gx1(k1,:)*hx;
|
|
|
|
zx = [zx; gx1];
|
|
|
|
kk = kk(:,k0);
|
|
|
|
k0 = k1;
|
|
|
|
end
|
2006-06-02 09:42:00 +02:00
|
|
|
zx=[zx; zeros(M_.exo_nbr,np);zeros(M_.exo_det_nbr,np)];
|
|
|
|
zu=[zu; eye(M_.exo_nbr);zeros(M_.exo_det_nbr,M_.exo_nbr)];
|
2006-11-01 10:09:44 +01:00
|
|
|
[nrzx,nczx] = size(zx);
|
2007-12-02 22:18:10 +01:00
|
|
|
|
2007-12-06 21:12:20 +01:00
|
|
|
if ~exist('sparse_hessian_times_B_kronecker_C') | ((strcmp(version('-release'),'2007b') ...
|
2007-12-07 14:23:57 +01:00
|
|
|
~= 1) & strcmpi(computer,'PCWIN'))
|
2007-12-02 22:18:10 +01:00
|
|
|
if nrzx*nrzx*nczx*nczx > 1e7
|
|
|
|
rhs = zeros(M_.endo_nbr,nczx*nczx);
|
|
|
|
k1 = 1;
|
|
|
|
for i1 = 1:nczx
|
|
|
|
for i2 = 1:nczx
|
|
|
|
rhs(:,k1) = hessian*kron(zx(:,i1),zx(:,i2));
|
|
|
|
k1 = k1 + 1;
|
|
|
|
end
|
|
|
|
end
|
|
|
|
else
|
|
|
|
rhs = hessian*kron(zx,zx);
|
|
|
|
end
|
2005-02-18 20:54:39 +01:00
|
|
|
else
|
2007-12-02 22:18:10 +01:00
|
|
|
rhs = sparse_hessian_times_B_kronecker_C(hessian,zx);
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
|
|
|
rhs = -rhs;
|
|
|
|
|
|
|
|
%lhs
|
2006-10-29 18:28:57 +01:00
|
|
|
n = M_.endo_nbr+sum(kstate(:,2) > M_.maximum_endo_lag+1 & kstate(:,2) < M_.maximum_endo_lag+M_.maximum_endo_lead+1);
|
2005-02-18 20:54:39 +01:00
|
|
|
A = zeros(n,n);
|
|
|
|
B = zeros(n,n);
|
2006-10-29 18:28:57 +01:00
|
|
|
A(1:M_.endo_nbr,1:M_.endo_nbr) = jacobia_(:,M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var));
|
2005-02-18 20:54:39 +01:00
|
|
|
% variables with the highest lead
|
2006-10-29 18:28:57 +01:00
|
|
|
k1 = find(kstate(:,2) == M_.maximum_endo_lag+M_.maximum_endo_lead+1);
|
|
|
|
if M_.maximum_endo_lead > 1
|
|
|
|
k2 = find(kstate(:,2) == M_.maximum_endo_lag+M_.maximum_endo_lead);
|
2005-09-11 16:15:35 +02:00
|
|
|
[junk,junk,k3] = intersect(kstate(k1,1),kstate(k2,1));
|
|
|
|
else
|
|
|
|
k2 = [1:M_.endo_nbr];
|
|
|
|
k3 = kstate(k1,1);
|
|
|
|
end
|
2005-02-18 20:54:39 +01:00
|
|
|
% Jacobian with respect to the variables with the highest lead
|
2005-09-11 16:15:35 +02:00
|
|
|
B(1:M_.endo_nbr,end-length(k2)+k3) = jacobia_(:,kstate(k1,3)+M_.endo_nbr);
|
2005-02-18 20:54:39 +01:00
|
|
|
offset = M_.endo_nbr;
|
2005-09-11 16:15:35 +02:00
|
|
|
k0 = [1:M_.endo_nbr];
|
2005-11-11 15:29:40 +01:00
|
|
|
gx1 = dr.ghx;
|
2006-10-29 18:28:57 +01:00
|
|
|
for i=1:M_.maximum_endo_lead-1
|
|
|
|
k1 = find(kstate(:,2) == M_.maximum_endo_lag+i+1);
|
2005-02-18 20:54:39 +01:00
|
|
|
[k2,junk,k3] = find(kstate(k1,3));
|
2005-09-11 16:15:35 +02:00
|
|
|
A(1:M_.endo_nbr,offset+k2) = jacobia_(:,k3+M_.endo_nbr);
|
2005-02-18 20:54:39 +01:00
|
|
|
n1 = length(k1);
|
2005-09-30 17:02:43 +02:00
|
|
|
A(offset+[1:n1],nstatic+[1:npred]) = -gx1(kstate(k1,1),1:npred);
|
|
|
|
gx1 = gx1*hx;
|
2005-09-11 16:15:35 +02:00
|
|
|
A(offset+[1:n1],offset+[1:n1]) = eye(n1);
|
2005-02-18 20:54:39 +01:00
|
|
|
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;
|
2005-09-11 16:15:35 +02:00
|
|
|
B(offset+[1:n1],offset-n0+[1:n0]) = -E(k4,:);
|
2005-02-18 20:54:39 +01:00
|
|
|
k0 = k1;
|
2005-09-11 16:15:35 +02:00
|
|
|
offset = offset + n1;
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
2006-10-29 18:28:57 +01:00
|
|
|
[junk,k1,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+M_.maximum_endo_lead+1,order_var));
|
2005-09-30 17:02:43 +02:00
|
|
|
A(1:M_.endo_nbr,nstatic+1:nstatic+npred)=...
|
|
|
|
A(1:M_.endo_nbr,nstatic+[1:npred])+jacobia_(:,k2)*gx1(k1,1:npred);
|
2005-09-11 16:15:35 +02:00
|
|
|
C = hx;
|
2005-02-18 20:54:39 +01:00
|
|
|
D = [rhs; zeros(n-M_.endo_nbr,size(rhs,2))];
|
2007-12-02 22:18:10 +01:00
|
|
|
|
2007-10-31 15:52:11 +01:00
|
|
|
if exist('gensylv') & (strcmp(version('-release'),'2007b') == 0)
|
2005-10-03 11:45:26 +02:00
|
|
|
dr.ghxx = gensylv(2,A,B,C,D);
|
2007-10-31 15:52:11 +01:00
|
|
|
elseif exist('gensylv75') & (strcmp(version('-release'),'2007b') == 1)
|
|
|
|
dr.ghxx = gensylv75(2,A,B,C,D);
|
2005-10-03 11:45:26 +02:00
|
|
|
else
|
|
|
|
C = kron(hx,hx);
|
|
|
|
x0 = sylvester3(A,B,C,D);
|
|
|
|
dr.ghxx = sylvester3a(x0,A,B,C,D);
|
|
|
|
end
|
2005-02-18 20:54:39 +01:00
|
|
|
|
|
|
|
%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,:));
|
2007-12-06 21:12:20 +01:00
|
|
|
if ~exist('sparse_hessian_times_B_kronecker_C') | ((strcmp(version('-release'),'2007b') ...
|
2007-12-07 14:23:57 +01:00
|
|
|
~= 1) & strcmpi(computer,'PCWIN'))
|
2007-12-02 22:18:10 +01:00
|
|
|
if nrzx*nrzx*nczx*M_.exo_nbr > 1e7
|
|
|
|
rhs = zeros(M_.endo_nbr,nczx*M_.exo_nbr);
|
|
|
|
k1 = 1;
|
|
|
|
for i1 = 1:nczx
|
|
|
|
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
|
2005-02-18 20:54:39 +01:00
|
|
|
else
|
2007-12-02 22:18:10 +01:00
|
|
|
rhs = sparse_hessian_times_B_kronecker_C(hessian,zx,zu);
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
2006-10-29 18:28:57 +01:00
|
|
|
nyf1 = sum(kstate(:,2) == M_.maximum_endo_lag+2);
|
2005-02-18 20:54:39 +01:00
|
|
|
hu1 = [hu;zeros(np-npred,M_.exo_nbr)];
|
2005-09-30 17:02:43 +02:00
|
|
|
%B1 = [B(1:M_.endo_nbr,:);zeros(size(A,1)-M_.endo_nbr,size(B,2))];
|
2007-01-08 11:14:30 +01:00
|
|
|
[nrhx,nchx] = size(hx);
|
|
|
|
[nrhu1,nchu1] = size(hu1);
|
2007-12-06 21:12:20 +01:00
|
|
|
if ~exist('A_times_B_kronecker_C') | ((strcmp(version('-release'),'2007b') ...
|
2007-12-07 14:23:57 +01:00
|
|
|
~= 1) & strcmpi(computer,'PCWIN'))
|
2007-12-02 22:18:10 +01:00
|
|
|
if nrhx*nrhu1*nchx*nchu1 > 1e7
|
|
|
|
B1 = zeros(size(dr.ghxx,1),nchx*nchu1);
|
|
|
|
k1 = 1;
|
|
|
|
for i1 = 1:nchx
|
|
|
|
for i2 = 1:nchu1
|
|
|
|
B1(:,k1) = dr.ghxx*kron(hx(:,i1),hu1(:,i2));
|
|
|
|
k1 = k1 + 1;
|
|
|
|
end
|
|
|
|
end
|
|
|
|
B1 = B*B1;
|
|
|
|
else
|
|
|
|
B1 = B*dr.ghxx*kron(hx,hu1);
|
|
|
|
end
|
2007-01-08 11:14:30 +01:00
|
|
|
else
|
2007-12-02 22:18:10 +01:00
|
|
|
B1 = B*A_times_B_kronecker_C(dr.ghxx,hx,hu1);
|
2007-01-08 11:14:30 +01:00
|
|
|
end
|
|
|
|
rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
|
2005-02-18 20:54:39 +01:00
|
|
|
|
2005-09-30 17:04:11 +02:00
|
|
|
|
2005-02-18 20:54:39 +01:00
|
|
|
%lhs
|
|
|
|
dr.ghxu = A\rhs;
|
|
|
|
|
|
|
|
%ghuu
|
|
|
|
%rhs
|
|
|
|
kk = reshape([1:np*np],np,np);
|
|
|
|
kk = kk(1:npred,1:npred);
|
2007-12-06 21:12:20 +01:00
|
|
|
if ~exist('sparse_hessian_times_B_kronecker_C') | ((strcmp(version('-release'),'2007b') ...
|
2007-12-07 14:23:57 +01:00
|
|
|
~= 1) & strcmpi(computer,'PCWIN'))
|
2007-12-02 22:18:10 +01:00
|
|
|
if nrzx*nrzx*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
|
2005-02-18 20:54:39 +01:00
|
|
|
else
|
2007-12-02 22:18:10 +01:00
|
|
|
rhs = sparse_hessian_times_B_kronecker_C(hessian,zu);
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
2007-12-06 21:12:20 +01:00
|
|
|
if ~exist('A_times_B_kronecker_C') | ((strcmp(version('-release'),'2007b') ...
|
2007-12-07 14:23:57 +01:00
|
|
|
~= 1) & strcmpi(computer,'PCWIN'))
|
2007-12-02 22:18:10 +01:00
|
|
|
if nrhu1*nrhu1*nchu1*nchu1 > 1e7
|
|
|
|
B1 = zeros(size(dr.ghxx,1),nchu1*nchu1);
|
|
|
|
k1 = 1;
|
|
|
|
for i1 = 1:nchu1
|
|
|
|
for i2 = 1:nchu1
|
|
|
|
B1(:,k1) = dr.ghxx*kron(hu1(:,i1),hu1(:,i2));
|
|
|
|
k1 = k1 + 1;
|
|
|
|
end
|
|
|
|
end
|
|
|
|
B1 = B*B1;
|
|
|
|
else
|
|
|
|
B1 = B*dr.ghxx*kron(hu1,hu1);
|
|
|
|
end
|
2007-01-08 11:14:30 +01:00
|
|
|
else
|
2007-12-02 22:18:10 +01:00
|
|
|
B1 = A_times_B_kronecker_C(B*dr.ghxx,hu1);
|
2007-01-08 11:14:30 +01:00
|
|
|
end
|
2007-01-08 12:00:02 +01:00
|
|
|
rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
|
2005-02-18 20:54:39 +01:00
|
|
|
|
|
|
|
%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);
|
2006-10-29 18:28:57 +01:00
|
|
|
LHS = jacobia_(:,M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var));
|
2005-02-18 20:54:39 +01:00
|
|
|
RHS = zeros(M_.endo_nbr,M_.exo_nbr^2);
|
2006-10-29 18:28:57 +01:00
|
|
|
kk = find(kstate(:,2) == M_.maximum_endo_lag+2);
|
2005-02-18 20:54:39 +01:00
|
|
|
gu = dr.ghu;
|
|
|
|
guu = dr.ghuu;
|
2005-09-11 16:15:35 +02:00
|
|
|
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)];
|
2005-02-18 20:54:39 +01:00
|
|
|
E = eye(M_.endo_nbr);
|
2006-10-29 18:28:57 +01:00
|
|
|
M_.lead_lag_incidenceordered = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
|
|
|
|
if M_.maximum_endo_lag > 0
|
|
|
|
M_.lead_lag_incidenceordered = [cumsum(M_.lead_lag_incidence(1:M_.maximum_endo_lag,order_var),1); M_.lead_lag_incidenceordered];
|
2005-09-11 16:15:35 +02:00
|
|
|
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)]';
|
2006-10-29 18:28:57 +01:00
|
|
|
M_.lead_lag_incidenceordered =reshape(M_.lead_lag_incidenceordered,M_.endo_nbr,M_.maximum_endo_lag+M_.maximum_endo_lead+1)';
|
2005-09-11 16:15:35 +02:00
|
|
|
kh = reshape([1:nk^2],nk,nk);
|
2006-10-29 18:28:57 +01:00
|
|
|
kp = sum(kstate(:,2) <= M_.maximum_endo_lag+1);
|
2005-09-11 16:15:35 +02:00
|
|
|
E1 = [eye(npred); zeros(kp-npred,npred)];
|
|
|
|
H = E1;
|
|
|
|
hxx = dr.ghxx(nstatic+[1:npred],:);
|
2006-10-29 18:28:57 +01:00
|
|
|
for i=1:M_.maximum_endo_lead
|
|
|
|
for j=i:M_.maximum_endo_lead
|
|
|
|
[junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+j+1,order_var));
|
2007-01-08 11:14:30 +01:00
|
|
|
[junk,k3a,k3] = ...
|
|
|
|
find(M_.lead_lag_incidenceordered(M_.maximum_endo_lag+j+1,:));
|
|
|
|
nk3a = length(k3a);
|
2007-12-06 21:12:20 +01:00
|
|
|
if ~exist('sparse_hessian_times_B_kronecker_C') | ((strcmp(version('-release'),'2007b') ...
|
2007-12-07 14:23:57 +01:00
|
|
|
~= 1) & strcmpi(computer,'PCWIN'))
|
2007-12-02 22:18:10 +01:00
|
|
|
if nk3a*nk3a*M_.exo_nbr*M_.exo_nbr > 1e7
|
|
|
|
B1 = zeros(M_.endo_nbr,M_.exo_nbr*M_.exo_nbr);
|
|
|
|
k1 = 1;
|
|
|
|
Hesse = hessian(:,kh(k3,k3));
|
|
|
|
guk3a = gu(k3a,:);
|
|
|
|
for i1 = 1:M_.exo_nbr
|
|
|
|
for i2 = 1:M_.exo_nbr
|
|
|
|
B1(:,k1) = Hesse*kron(guk3a(:,i1),guk3a(:,i2));
|
|
|
|
k1 = k1 + 1;
|
|
|
|
end
|
|
|
|
end
|
|
|
|
else
|
|
|
|
B1 = hessian(:,kh(k3,k3))*kron(gu(k3a,:),gu(k3a,:));
|
|
|
|
end
|
2007-01-08 11:14:30 +01:00
|
|
|
else
|
2007-12-02 22:18:10 +01:00
|
|
|
B1 = sparse_hessian_times_B_kronecker_C(hessian(:,kh(k3,k3)),gu(k3a,:));
|
2007-01-08 11:14:30 +01:00
|
|
|
end
|
|
|
|
RHS = RHS + jacobia_(:,k2)*guu(k2a,:)+B1;
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
|
|
|
|
|
|
|
% LHS
|
2006-10-29 18:28:57 +01:00
|
|
|
[junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+i+1,order_var));
|
2005-09-11 16:15:35 +02:00
|
|
|
LHS = LHS + jacobia_(:,k2)*(E(k2a,:)+[O1(k2a,:) dr.ghx(k2a,:)*H O2(k2a,:)]);
|
2005-02-18 20:54:39 +01:00
|
|
|
|
2006-10-29 18:28:57 +01:00
|
|
|
if i == M_.maximum_endo_lead
|
2005-02-18 20:54:39 +01:00
|
|
|
break
|
|
|
|
end
|
|
|
|
|
2006-10-29 18:28:57 +01:00
|
|
|
kk = find(kstate(:,2) == M_.maximum_endo_lag+i+1);
|
2005-09-11 16:15:35 +02:00
|
|
|
gu = dr.ghx*Gu;
|
2007-01-08 11:14:30 +01:00
|
|
|
[nrGu,ncGu] = size(Gu);
|
2007-12-06 21:12:20 +01:00
|
|
|
if ~exist('A_times_B_kronecker_C') | ((strcmp(version('-release'),'2007b') ...
|
2007-12-07 14:23:57 +01:00
|
|
|
~= 1) & strcmpi(computer,'PCWIN'))
|
2007-12-02 22:18:10 +01:00
|
|
|
if nrGu*nrGu*ncGu*ncGu > 1e7
|
|
|
|
G1 = zeros(M_.endo_nbr,ncGu*ncGu);
|
|
|
|
G2 = zeros(size(hxx,1),ncGu*ncGu);
|
|
|
|
k1 = 1;
|
|
|
|
for i1 = 1:nchx
|
|
|
|
for i2 = 1:nchu1
|
|
|
|
GuGu = kron(Gu(:,i1),Gu(:,i2));
|
|
|
|
G1(:,k1) = dr.ghxx*GuGu;
|
|
|
|
G2(:,k1) = hxx*GuGu;
|
|
|
|
k1 = k1 + 1;
|
|
|
|
end
|
|
|
|
end
|
|
|
|
else
|
|
|
|
GuGu = kron(Gu,Gu);
|
|
|
|
G1 = dr.ghxx*GuGu;
|
|
|
|
G2 = hxx*GuGu;
|
2007-01-08 11:14:30 +01:00
|
|
|
end
|
|
|
|
else
|
2007-12-02 22:18:10 +01:00
|
|
|
G1 = A_times_B_kronecker_C(dr.ghxx,Gu);
|
|
|
|
G2 = A_times_B_kronecker_C(hxx,Gu);
|
2007-01-08 11:14:30 +01:00
|
|
|
end
|
|
|
|
guu = dr.ghx*Guu+G1;
|
2005-09-11 16:15:35 +02:00
|
|
|
Gu = hx*Gu;
|
|
|
|
Guu = hx*Guu;
|
2007-01-08 11:14:30 +01:00
|
|
|
Guu(end-npred+1:end,:) = Guu(end-npred+1:end,:) + G2;
|
2005-09-11 16:15:35 +02:00
|
|
|
H = E1 + hx*H;
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
2005-09-22 16:28:25 +02:00
|
|
|
RHS = RHS*M_.Sigma_e(:);
|
2005-02-18 20:54:39 +01:00
|
|
|
dr.fuu = RHS;
|
2007-10-31 15:52:11 +01:00
|
|
|
%RHS = -RHS-dr.fbias;
|
|
|
|
RHS = -RHS;
|
2005-02-18 20:54:39 +01:00
|
|
|
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);
|
2006-06-02 09:42:00 +02:00
|
|
|
dr.ghxud = cell(M_.exo_det_length,1);
|
2005-02-18 20:54:39 +01:00
|
|
|
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);
|
2006-06-02 09:42:00 +02:00
|
|
|
for i = 2:M_.exo_det_length
|
2005-02-18 20:54:39 +01:00
|
|
|
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);
|
2006-06-02 09:42:00 +02:00
|
|
|
dr.ghudud = cell(M_.exo_det_length,1);
|
2005-02-18 20:54:39 +01:00
|
|
|
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);
|
2006-06-02 09:42:00 +02:00
|
|
|
for i = 2:M_.exo_det_length
|
2005-02-18 20:54:39 +01:00
|
|
|
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);
|
2006-06-02 09:42:00 +02:00
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|
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dr.ghudud = cell(M_.exo_det_length,M_.exo_det_length);
|
2005-02-18 20:54:39 +01:00
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|
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dr.ghudud{1,1} = -M1*R1-M2*dr.ghxx(kf,:)*kron(hud,hud);
|
2006-06-02 09:42:00 +02:00
|
|
|
for i = 2:M_.exo_det_length
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2005-02-18 20:54:39 +01:00
|
|
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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) ...
|
|
|
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+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
|
2005-09-11 16:15:35 +02:00
|
|
|
|
2005-02-18 20:54:39 +01:00
|
|
|
end
|
2007-12-02 22:18:10 +01:00
|
|
|
end
|