127 lines
3.8 KiB
Matlab
127 lines
3.8 KiB
Matlab
function dr=mult_elimination(varlist,M_, options_, oo_)
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% function mult_elimination()
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% replaces Lagrange multipliers in Ramsey policy by lagged value of state
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% and shock variables
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%
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% INPUT
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% none
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%
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% OUTPUT
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% dr: a structure with the new decision rule
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright © 2003-2018 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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dr = oo_.dr;
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nstatic = M_.nstatic;
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nspred = M_.nspred;
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order_var = dr.order_var;
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nstates = M_.endo_names(order_var(nstatic+(1:nspred)));
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il = strmatch('MULT_',nstates);
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nil = setdiff(1:nspred,il);
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m_nbr = length(il);
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nm_nbr = length(nil);
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AA1 = dr.ghx(:,nil);
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AA2 = dr.ghx(:,il);
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A1 = dr.ghx(nstatic+(1:nspred),nil);
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A2 = dr.ghx(nstatic+(1:nspred),il);
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B = dr.ghu(nstatic+(1:nspred),:);
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A11 = A1(nil,:);
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A21 = A1(il,:);
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A12 = A2(nil,:);
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A22 = A2(il,:);
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B1 = B(nil,:);
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B2 = B(il,:);
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[Q1,R1,E1] = qr([A12; A22]);
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n1 = sum(abs(diag(R1)) > 1e-8);
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Q1_12 = Q1(1:nm_nbr,n1+1:end);
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Q1_22 = Q1(nm_nbr+(1:m_nbr),n1+1:end);
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[Q2,R2,E2] = qr(Q1_22');
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n2 = sum(abs(diag(R2)) > 1e-8);
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R2_1 = inv(R2(1:n2,1:n2));
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M1 = AA1 - AA2*E2*[R2_1*Q2(:,1:n2)'*Q1_12'; zeros(m_nbr-n2,nm_nbr)];
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M2 = AA2*E2*[R2_1*Q2(:,1:n2)'*[Q1_12' Q1_22']*[A11;A21]; zeros(m_nbr-n2,length(nil))];
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M3 = dr.ghu;
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M4 = AA2*E2*[R2_1*Q2(:,1:n2)'*[Q1_12' Q1_22']*[B1;B2]; zeros(m_nbr-n2,size(B,2))];
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k1 = nstatic+(1:nspred);
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k1 = k1(nil);
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endo_nbr = M_.orig_endo_nbr;
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exo_nbr = M_.exo_nbr;
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lead_lag_incidence = M_.lead_lag_incidence(:,1:endo_nbr+exo_nbr);
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lead_lag_incidence1 = lead_lag_incidence(1,:) > 0;
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maximum_lag = M_.maximum_lag;
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for i=1:maximum_lag-1
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lead_lag_incidence1 = [lead_lag_incidence1; lead_lag_incidence(i,:)| ...
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lead_lag_incidence(i+1,:)];
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end
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lead_lag_incidence1 = [lead_lag_incidence1; ...
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lead_lag_incidence(M_.maximum_lag,:) > 0];
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k = find(lead_lag_incidence1');
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lead_lag_incidence1 = zeros(size(lead_lag_incidence1'));
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lead_lag_incidence1(k) = 1:length(k);
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lead_lag_incidence1 = lead_lag_incidence1';
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kstate = zeros(0,2);
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for i=maximum_lag:-1:1
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k = find(lead_lag_incidence(i,:));
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kstate = [kstate; [k' repmat(i+1,length(k),1)]];
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end
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dr.M1 = M1;
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dr.M2 = M2;
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dr.M3 = M3;
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dr.M4 = M4;
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nvar = length(varlist);
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if nvar > 0 && ~options_.noprint
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res_table = zeros(2*(nm_nbr+M_.exo_nbr),nvar);
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headers = {'Variables'};
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for i=1:length(varlist)
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k = strmatch(varlist{i}, M_.endo_names(dr.order_var), 'exact');
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headers = vertcat(headers, varlist{i});
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res_table(1:nm_nbr,i) = M1(k,:)';
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res_table(nm_nbr+(1:nm_nbr),i) = M2(k,:)';
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res_table(2*nm_nbr+(1:M_.exo_nbr),i) = M3(k,:)';
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res_table(2*nm_nbr+M_.exo_nbr+(1:M_.exo_nbr),i) = M4(k,:)';
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end
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my_title='ELIMINATION OF THE MULTIPLIERS';
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lab = nstates(nil);
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labels = cellfun(@(x) horzcat(x, '(-1)'), nstates(nil), 'UniformOutput', false);
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labels = vertcat(labels, cellfun(@(x) horzcat(x, '(-2)'), nstates(nil), 'UniformOutput', false));
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labels = vertcat(labels, M_.exo_names);
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labels = vertcat(labels, cellfun(@(x) horzcat(x, '(-1)'), M_.exo_names, 'UniformOutput', false));
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lh = size(labels,2)+2;
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dyntable(options_, my_title, headers, labels, res_table, lh, 10, 6);
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skipline()
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end
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