76 lines
2.2 KiB
Matlab
76 lines
2.2 KiB
Matlab
function dr=mult_elimination(void)
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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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% INPUT
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% none
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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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global M_ options_ oo_
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dr = oo_.dr;
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nstatic = dr.nstatic;
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npred = dr.npred;
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order_var = dr.order_var;
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nstates = M_.endo_names(order_var(nstatic+(1:npred)),:);
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il = strmatch('mult_',nstates);
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nil = setdiff(1:dr.npred,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:npred),nil);
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A2 = dr.ghx(nstatic+(1:npred),il);
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B = dr.ghu(nstatic+(1:npred),:);
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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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[Q1,R1,E1] = qr(A2);
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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:end,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(order_var,:) = AA1 - AA2*E2*[R2_1*Q2(:,1:n2)'*Q1_12'; zeros(m_nbr-n2,nm_nbr)];
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M2(order_var,:) = AA2*E2*[R2_1*Q2(:,1:n2)'*[Q1_12' Q1_22']*A1; zeros(m_nbr-n2,length(nil))];
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M3(order_var,:) = dr.ghu;
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M4(order_var,:) = AA2*E2*[R2_1*Q2(:,1:n2)'*[Q1_12' Q1_22']*B; zeros(m_nbr-n2,size(B,2))];
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endo_nbr = M_.orig_model.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; |