80 lines
2.5 KiB
Matlab
80 lines
2.5 KiB
Matlab
function [resids, rJ,mult] = ramsey_static(x)
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% computes the static first order conditions for optimal policy
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global M_ options_ it_
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% recovering usefull fields
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endo_nbr = M_.endo_nbr;
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exo_nbr = M_.exo_nbr;
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fname = M_.fname;
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% inst_nbr = M_.inst_nbr;
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% i_endo_no_inst = M_.endogenous_variables_without_instruments;
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max_lead = M_.maximum_lead;
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max_lag = M_.maximum_lag;
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beta = options_.planner_discount;
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% indices of all endogenous variables
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i_endo = [1:endo_nbr]';
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% indices of endogenous variable except instruments
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% i_inst = M_.instruments;
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% lead_lag incidence matrix for endogenous variables
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i_lag = M_.lead_lag_incidence;
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% value and Jacobian of objective function
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ex = zeros(1,M_.exo_nbr);
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[U,Uy,Uyy] = feval([fname '_objective_static'],x(i_endo),ex);
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Uy = Uy';
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Uyy = reshape(Uyy,endo_nbr,endo_nbr);
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% value and Jacobian of dynamic function
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y = repmat(x(i_endo),1,max_lag+max_lead+1);
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k = find(i_lag');
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it_ = 1;
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% [f,fJ,fH] = feval([fname '_dynamic'],y(k),ex);
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[f,fJ] = feval([fname '_dynamic'],y(k),ex);
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% indices of Lagrange multipliers
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inst_nbr = endo_nbr - size(f,1);
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i_mult = [endo_nbr+1:2*endo_nbr-inst_nbr]';
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% derivatives of Lagrangian with respect to endogenous variables
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% res1 = Uy;
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A = zeros(endo_nbr,endo_nbr-inst_nbr);
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for i=1:max_lag+max_lead+1
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% select variables present in the model at a given lag
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[junk,k1,k2] = find(i_lag(i,:));
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% res1(k1) = res1(k1) + beta^(max_lag-i+1)*fJ(:,k2)'*x(i_mult);
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A(k1,:) = A(k1,:) + beta^(max_lag-i+1)*fJ(:,k2)';
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end
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% i_inst = var_index(options_.olr_inst);
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% k = setdiff(1:size(A,1),i_inst);
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% mult = -A(k,:)\Uy(k);
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mult = -A\Uy;
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% resids = [f; Uy(i_inst)+A(i_inst,:)*mult];
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resids1 = Uy+A*mult;
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% resids = [f; sqrt(resids1'*resids1/endo_nbr)];
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[q,r,e] = qr([A Uy]');
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resids = [f; r(end,(endo_nbr-inst_nbr+1:end))'];
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rJ = [];
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return;
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% Jacobian of first order conditions
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n = nnz(i_lag)+exo_nbr;
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iH = reshape(1:n^2,n,n);
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rJ = zeros(2*endo_nbr-inst_nbr,2*endo_nbr-inst_nbr);
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rJ(i_endo,i_endo) = Uyy;
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for i=1:max_lag+max_lead+1
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% select variables present in the model at a given lag
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[junk,k1,k2] = find(i_lag(i,:));
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k3 = length(k2);
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rJ(k1,k1) = rJ(k1,k1) + beta^(max_lag-i+1)*reshape(fH(:,iH(k2,k2))'*x(i_mult),k3,k3);
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rJ(k1,i_mult) = rJ(k1,i_mult) + beta^(max_lag-1+1)*fJ(:,k2)';
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rJ(i_mult,k1) = rJ(i_mult,k1) + fJ(:,k2);
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end
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% rJ = 1e-3*rJ;
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% rJ(209,210) = rJ(209,210)+1-1e-3;
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