101 lines
3.2 KiB
Modula-2
101 lines
3.2 KiB
Modula-2
% this is the Smets and Wouters (2007) model for which Komunjer and Ng (2011)
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% derived the minimal state space system. In Dynare, however, we use more
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% powerful minreal function
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% created by Willi Mutschler (@wmutschl, willi@mutschler.eu)
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% =========================================================================
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% Copyright © 2020 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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% =========================================================================
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var y R g z c dy p YGR INFL INT;
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varobs y R p c YGR INFL INT;
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varexo e_r e_g e_z;
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parameters tau phi psi1 psi2 rhor rhog rhoz rrst pist gamst nu cyst;
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rrst = 1.0000;
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pist = 3.2000;
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gamst= 0.5500;
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tau = 2.0000;
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nu = 0.1000;
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kap = 0.3300;
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phi = tau*(1-nu)/nu/kap/exp(pist/400)^2;
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cyst = 0.8500;
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psi1 = 1.5000;
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psi2 = 0.1250;
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rhor = 0.7500;
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rhog = 0.9500;
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rhoz = 0.9000;
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model;
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#pist2 = exp(pist/400);
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#rrst2 = exp(rrst/400);
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#bet = 1/rrst2;
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#gst = 1/cyst;
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#cst = (1-nu)^(1/tau);
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#yst = cst*gst;
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1 = exp(-tau*c(+1)+tau*c+R-z(+1)-p(+1));
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(1-nu)/nu/phi/(pist2^2)*(exp(tau*c)-1) = (exp(p)-1)*((1-1/2/nu)*exp(p)+1/2/nu) - bet*(exp(p(+1))-1)*exp(-tau*c(+1)+tau*c+dy(+1)+p(+1));
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exp(c-y) = exp(-g) - phi*pist2^2*gst/2*(exp(p)-1)^2;
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R = rhor*R(-1) + (1-rhor)*psi1*p + (1-rhor)*psi2*(y-g) + e_r;
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g = rhog*g(-1) + e_g;
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z = rhoz*z(-1) + e_z;
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YGR = gamst+100*(dy+z);
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INFL = pist+400*p;
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INT = pist+rrst+4*gamst+400*R;
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dy = y - y(-1);
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end;
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shocks;
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var e_r; stderr 0.2/100;
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var e_g; stderr 0.6/100;
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var e_z; stderr 0.3/100;
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end;
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steady_state_model;
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z=0; g=0; c=0; y=0; p=0; R=0; dy=0;
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YGR=gamst; INFL=pist; INT=pist+rrst+4*gamst;
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end;
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stoch_simul(order=1,irf=0,periods=0);
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options_.qz_criterium = 1;
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indx = [M_.nstatic+(1:M_.nspred)]';
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indy = 1:M_.endo_nbr';
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SS.A = oo_.dr.ghx(indx,:);
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SS.B = oo_.dr.ghu(indx,:);
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SS.C = oo_.dr.ghx(indy,:);
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SS.D = oo_.dr.ghu(indy,:);
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[CheckCO,minnx,minSS] = identification.get_minimal_state_representation(SS,0);
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Sigmax_full = lyapunov_symm(SS.A, SS.B*M_.Sigma_e*SS.B', options_.lyapunov_fixed_point_tol, options_.qz_criterium, options_.lyapunov_complex_threshold, 1, options_.debug);
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Sigmay_full = SS.C*Sigmax_full*SS.C' + SS.D*M_.Sigma_e*SS.D';
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Sigmax_min = lyapunov_symm(minSS.A, minSS.B*M_.Sigma_e*minSS.B', options_.lyapunov_fixed_point_tol, options_.qz_criterium, options_.lyapunov_complex_threshold, 1, options_.debug);
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Sigmay_min = minSS.C*Sigmax_min*minSS.C' + minSS.D*M_.Sigma_e*minSS.D';
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([Sigmay_full(:) - Sigmay_min(:)]')
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sqrt(([diag(Sigmay_full), diag(Sigmay_min)]'))
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dx = norm( Sigmay_full - Sigmay_min, Inf);
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if dx > 1e-12
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error('something wrong with minimal state space computations')
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else
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fprintf('numerical error for moments computed from minimal state system is %d\n',dx)
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end
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