152 lines
4.5 KiB
Matlab
152 lines
4.5 KiB
Matlab
function [steady_state,params,check] = dyn_ramsey_static(x,M,options_,oo)
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% function [steady_state,params,check] = dyn_ramsey_static_(x)
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% Computes the static first order conditions for optimal policy
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%
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% INPUTS
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% x: vector of endogenous variables or instruments
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%
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% OUTPUTS
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% resids: residuals of non linear equations
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% rJ: Jacobian
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% mult: Lagrangian multipliers
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright (C) 2003-2010 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 <http://www.gnu.org/licenses/>.
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steady_state = [];
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params = M.params;
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check = 0;
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nl_func = @(x) dyn_ramsey_static_1(x,M,options_,oo);
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if options_.steadystate_flag
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k_inst = [];
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instruments = options_.instruments;
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inst_nbr = size(options_.instruments);
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for i = 1:inst_nbr
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k_inst = [k_inst; strmatch(options_.instruments(i,:), ...
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M.endo_names,'exact')];
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end
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ys = oo.steady_state;
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if inst_nbr == 1
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inst_val = csolve(nl_func,oo_.steady_state(k_inst),'',options_.solve_tolf,100);
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else
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[inst_val,info1] = dynare_solve(nl_func,ys(k_inst),0);
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end
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ys(k_inst) = inst_val;
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[x,params,check] = evaluate_steadystate_file(ys,exo_ss,params,M.fname,options_.steadystate_flag);
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if size(x,1) < M.endo_nbr
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if length(M.aux_vars) > 0
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x = feval([M.fname '_set_auxiliary_variables'],xx,...
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[oo.exo_steady_state,...
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oo.exo_det_steady_state],...
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M.params);
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else
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error([M.fname '_steadystate.m doesn''t match the model']);
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end
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end
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[junk,junk,multbar] = dyn_ramsey_static_1(x(k_inst),M,options_,oo_);
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steady_state = [x(1:M.orig_endo_nbr); multbar];
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else
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xx = oo.steady_state(1:M.orig_endo_nbr);
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[xx,info1] = dynare_solve(nl_func,xx,0);
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[junk,junk,multbar] = nl_func(xx);
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steady_state = [xx; multbar];
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end
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function [resids, rJ,mult] = dyn_ramsey_static_1(x,M,options_,oo)
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resids = [];
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rJ = [];
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mult = [];
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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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orig_endo_nbr = M.orig_endo_nbr;
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orig_eq_nbr = M.orig_eq_nbr;
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inst_nbr = orig_endo_nbr - orig_eq_nbr;
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% indices of Lagrange multipliers
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i_mult = [orig_endo_nbr+(1:orig_eq_nbr)]';
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fname = M.fname;
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max_lead = M.maximum_lead;
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max_lag = M.maximum_lag;
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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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if options_.steadystate_flag
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k_inst = [];
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instruments = options_.instruments;
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for i = 1:size(instruments,1)
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k_inst = [k_inst; strmatch(options_.instruments(i,:), ...
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M.endo_names,'exact')];
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end
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oo.steady_state(k_inst) = x;
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[x,check] = feval([M.fname '_steadystate'],...
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oo.steady_state,...
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[oo.exo_steady_state; ...
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oo.exo_det_steady_state]);
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end
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% setting steady state of auxiliary variables
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xx = zeros(endo_nbr,1);
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xx(1:orig_endo_nbr) = x(1:orig_endo_nbr);
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x = feval([M.fname '_set_auxiliary_variables'],xx,...
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[oo.exo_steady_state,...
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oo.exo_det_steady_state],...
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M.params);
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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,ex, M.params);
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Uy = Uy';
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Uyy = reshape(Uyy,endo_nbr,endo_nbr);
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% set multipliers to 0 to compute residuals
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[f,fJ] = feval([fname '_static'],x,[oo.exo_simul oo.exo_det_simul], ...
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M.params);
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aux_eq = [1:orig_endo_nbr orig_endo_nbr+orig_eq_nbr+1:size(fJ,1)];
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A = fJ(aux_eq,orig_endo_nbr+1:end);
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y = f(aux_eq);
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mult = -A\y;
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resids1 = y+A*mult;
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if inst_nbr == 1
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r1 = sqrt(resids1'*resids1);
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else
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[q,r,e] = qr([A y]');
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r1 = r(end,(orig_endo_nbr-inst_nbr+1:end))';
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end
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if options_.steadystate_flag
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resids = r1;
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else
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resids = [f(i_mult); r1];
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end
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rJ = [];
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