1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210
|
function [steady_state,params,check] = dyn_ramsey_static(ys_init,M,options_,oo)
% function [steady_state,params,check] = dyn_ramsey_static_(ys_init,M,options_,oo)
% Computes the steady state for optimal policy
%
% INPUTS
% ys_init: vector of endogenous variables or instruments
% M: Dynare model structure
% options: Dynare options structure
% oo: Dynare results structure
%
% OUTPUTS
% steady_state: steady state value
% params: parameters at steady state, potentially updated by
% steady_state file
% check: error indicator, 0 if everything is OK
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2003-2018 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
params = M.params;
check = 0;
options_.steadystate.nocheck = 1; %locally disable checking because Lagrange multipliers are not accounted for in evaluate_steady_state_file
% dyn_ramsey_static_1 is a subfunction
nl_func = @(x) dyn_ramsey_static_1(x,M,options_,oo);
% check_static_model is a subfunction
if check_static_model(ys_init,M,options_,oo) && ~options_.steadystate_flag
steady_state = ys_init;
return
elseif options_.steadystate_flag
k_inst = [];
inst_nbr = size(options_.instruments,1);
for i = 1:inst_nbr
k_inst = [k_inst; strmatch(options_.instruments{i}, M.endo_names, 'exact')];
end
if inst_nbr == 1
%solve for instrument, using univariate solver, starting at initial value for instrument
[inst_val, info1]= csolve(nl_func,ys_init(k_inst),'',options_.solve_tolf,options_.ramsey.maxit);
if info1==1 || info1==3
check=81;
end
if info1==4
check=87;
end
else
%solve for instrument, using multivariate solver, starting at
%initial value for instrument
opt = options_;
opt.jacobian_flag = false;
[inst_val,info1] = dynare_solve(nl_func,ys_init(k_inst), ...
opt);
if info1~=0
check=81;
end
end
ys_init(k_inst) = inst_val;
exo_ss = [oo.exo_steady_state oo.exo_det_steady_state];
[xx,params] = evaluate_steady_state_file(ys_init,exo_ss,M,options_,~options_.steadystate.nocheck); %run steady state file again to update parameters
[~,~,steady_state] = nl_func(inst_val); %compute and return steady state
else
n_var = M.orig_endo_nbr;
xx = oo.steady_state(1:n_var);
opt = options_;
opt.jacobian_flag = false;
[xx,info1] = dynare_solve(nl_func,xx,opt);
if info1~=0
check=81;
end
[~,~,steady_state] = nl_func(xx);
end
function [resids,rJ,steady_state] = dyn_ramsey_static_1(x,M,options_,oo)
resids = [];
rJ = [];
mult = [];
% recovering usefull fields
params = M.params;
endo_nbr = M.endo_nbr;
endo_names = M.endo_names;
orig_endo_nbr = M.orig_endo_nbr;
aux_vars_type = [M.aux_vars.type];
orig_endo_aux_nbr = orig_endo_nbr + min(find(aux_vars_type == 6)) - 1;
orig_eq_nbr = M.orig_eq_nbr;
inst_nbr = orig_endo_aux_nbr - orig_eq_nbr;
% indices of Lagrange multipliers
fname = M.fname;
if options_.steadystate_flag
k_inst = [];
instruments = options_.instruments;
for i = 1:size(instruments,1)
k_inst = [k_inst; strmatch(instruments{i}, endo_names, 'exact')];
end
ys_init=zeros(size(oo.steady_state)); %create starting vector for steady state computation as only instrument value is handed over
ys_init(k_inst) = x; %set instrument, the only value required for steady state computation, to current value
[x,params,check] = evaluate_steady_state_file(ys_init,... %returned x now has size endo_nbr as opposed to input size of n_instruments
[oo.exo_steady_state; ...
oo.exo_det_steady_state], ...
M,options_,~options_.steadystate.nocheck);
if any(imag(x(1:M.orig_endo_nbr))) %return with penalty
resids=ones(inst_nbr,1)+sum(abs(imag(x(1:M.orig_endo_nbr)))); %return with penalty
steady_state=NaN(endo_nbr,1);
return
end
if check %return
resids=ones(inst_nbr,1)+sum(abs(x(1:M.orig_endo_nbr))); %return with penalty
steady_state=NaN(endo_nbr,1);
return
end
end
xx = zeros(endo_nbr,1); %initialize steady state vector
xx(1:M.orig_endo_nbr) = x(1:M.orig_endo_nbr); %set values of original endogenous variables based on steady state file or initial value
% setting steady state of auxiliary variables that depends on original endogenous variables
if any([M.aux_vars.type] ~= 6) %auxiliary variables other than multipliers
needs_set_auxiliary_variables = 1;
if M.set_auxiliary_variables
fh = str2func([M.fname '.set_auxiliary_variables']);
s_a_v_func = @(z) fh(z,...
[oo.exo_steady_state,...
oo.exo_det_steady_state],...
params);
else
s_a_v_func = z;
end
xx = s_a_v_func(xx);
else
needs_set_auxiliary_variables = 0;
end
% value and Jacobian of objective function
ex = zeros(1,M.exo_nbr);
[U,Uy,Uyy] = feval([fname '.objective.static'],x,ex, params);
Uyy = reshape(Uyy,endo_nbr,endo_nbr);
% set multipliers and auxiliary variables that
% depends on multipliers to 0 to compute residuals
if (options_.bytecode)
[chck, res, junk] = bytecode('static',xx,[oo.exo_steady_state oo.exo_det_steady_state], ...
params, 'evaluate');
fJ = junk.g1;
else
[res,fJ] = feval([fname '.static'],xx,[oo.exo_steady_state oo.exo_det_steady_state], ...
params);
end
% index of multipliers and corresponding equations
% the auxiliary variables before the Lagrange multipliers are treated
% as ordinary endogenous variables
aux_eq = [1:orig_endo_aux_nbr, orig_endo_aux_nbr+orig_eq_nbr+1:size(fJ,1)];
A = fJ(1:orig_endo_aux_nbr,orig_endo_nbr+find(aux_vars_type==6));
y = res(1:orig_endo_aux_nbr);
mult = -A\y;
resids1 = y+A*mult;
if inst_nbr == 1
r1 = sqrt(resids1'*resids1);
else
[q,r,e] = qr([A y]');
k = size(A,1)+(1-inst_nbr:0);
r1 = r(end,k)';
end
if options_.steadystate_flag
resids = r1;
else
resids = [res(orig_endo_nbr+(1:orig_endo_nbr-inst_nbr)); r1];
end
rJ = [];
if needs_set_auxiliary_variables
steady_state = s_a_v_func([xx(1:orig_endo_aux_nbr); mult]);
else
steady_state = [xx(1:orig_endo_aux_nbr); mult];
end
function result = check_static_model(ys,M,options_,oo)
result = false;
if (options_.bytecode)
[chck, res, ~] = bytecode('static',ys,[oo.exo_steady_state oo.exo_det_steady_state], ...
M.params, 'evaluate');
else
res = feval([M.fname '.static'],ys,[oo.exo_steady_state oo.exo_det_steady_state], ...
M.params);
end
if norm(res) < options_.solve_tolf
result = true;
end
|