287 lines
14 KiB
Modula-2
287 lines
14 KiB
Modula-2
% DSGE model used in replication files of
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% An, Sungbae and Schorfheide, Frank, (2007), Bayesian Analysis of DSGE Models, Econometric Reviews, 26, issue 2-4, p. 113-172.
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% Adapted by Willi Mutschler (@wmutschl, willi@mutschler.eu)
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% =========================================================================
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% Copyright (C) 2020-2021 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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% Define testscenario
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@#define orderApp = 2
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@#define estimParams = 1
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% Note that we set the numerical optimization tolerance levels very large to speed up the testsuite
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@#define optimizer = 13
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var c p R g y z INFL INT YGR;
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varexo e_r e_g e_z;
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parameters tau nu kap cyst psi1 psi2 rhor rhog rhoz rrst pist gamst;
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varobs INT YGR INFL;
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tau = 2;
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nu = 0.1;
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kap = 0.33;
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cyst = 0.85;
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psi1 = 1.5;
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psi2 = 0.125;
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rhor = 0.75;
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rhog = 0.95;
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rhoz = 0.9;
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rrst = 1;
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pist = 3.2;
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gamst = 0.55;
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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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#phi = tau*(1-nu)/nu/kap/pist2^2;
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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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#dy = y-y(-1);
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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+y(+1)-y+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*(dy+z) + e_r/100;
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g = rhog*g(-1) + e_g/100;
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z = rhoz*z(-1) + e_z/100;
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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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end;
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steady_state_model;
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z = 0; p = 0; g = 0; r = 0; c = 0; y = 0;
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YGR = gamst; INFL = pist; INT = pist + rrst + 4*gamst;
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end;
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shocks;
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var e_r = 0.20^2;
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var e_g = 0.80^2;
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var e_z = 0.45^2;
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corr e_r,e_g = 0.2;
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end;
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@#if estimParams == 0
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% Define only initial values without bounds
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estimated_params;
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%tau, 1.50;
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%kap, 0.15;
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psi1, 1.20;
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psi2, 0.50;
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rhor, 0.50;
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%rhog, 0.50;
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%rhoz, 0.50;
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%rrst, 1.20;
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%pist, 3.00;
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gamst, 0.75;
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stderr e_r, 0.30;
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stderr e_g, 0.30;
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stderr e_z, 0.30;
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corr e_r,e_g, 0.10;
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end;
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@#endif
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@#if estimParams == 1
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% Define initial values and bounds
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estimated_params;
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%tau, 1.50, 1e-5, 10;
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%kap, 0.15, 1e-5, 10;
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psi1, 1.20, 1e-5, 10;
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psi2, 0.50, 1e-5, 10;
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rhor, 0.50, 1e-5, 0.99999;
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%rhog, 0.50, 1e-5, 0.99999;
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%rhoz, 0.50, 1e-5, 0.99999;
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%rrst, 1.20, 1e-5, 10;
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%pist, 3.00, 1e-5, 20;
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gamst, 0.75, -5, 5;
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stderr e_r, 0.30, 1e-8, 5;
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stderr e_g, 0.30, 1e-8, 5;
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stderr e_z, 0.30, 1e-8, 5;
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corr e_r,e_g, 0.10, -1, 1;
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end;
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@#endif
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@#if estimParams == 2
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% Define prior distribution
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estimated_params;
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%tau, 1.50, 1e-5, 10, gamma_pdf, 2.00, 0.50;
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%kap, 0.15, 1e-5, 10, gamma_pdf, 0.33, 0.10;
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psi1, 1.20, 1e-5, 10, gamma_pdf, 1.50, 0.25;
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psi2, 0.50, 1e-5, 10, gamma_pdf, 0.125, 0.25;
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rhor, 0.50, 1e-5, 0.99999, beta_pdf, 0.50, 0.20;
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%rhog, 0.50, 1e-5, 0.99999, beta_pdf, 0.80, 0.10;
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%rhoz, 0.50, 1e-5, 0.99999, beta_pdf, 0.66, 0.15;
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%rrst, 1.20, 1e-5, 10, gamma_pdf, 0.50, 0.50;
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%pist, 3.00, 1e-5, 20, gamma_pdf, 7.00, 2.00;
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gamst, 0.75, -5, 5, normal_pdf, 0.40, 0.20;
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stderr e_r, 0.30, 1e-8, 5, inv_gamma_pdf, 0.50, 0.26;
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stderr e_g, 0.30, 1e-8, 5, inv_gamma_pdf, 1.25, 0.65;
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stderr e_z, 0.30, 1e-8, 5, inv_gamma_pdf, 0.63, 0.33;
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corr e_r,e_g, 0.10, -1, 1, uniform_pdf, , , -1, 1;
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end;
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@#endif
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% Simulate data
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stoch_simul(order=@{orderApp},pruning,nodisplay,nomoments,periods=750,drop=500);
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save('AnScho_MoM_data_@{orderApp}.mat', options_.varobs{:} );
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pause(1);
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%--------------------------------------------------------------------------
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% Method of Moments Estimation
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%--------------------------------------------------------------------------
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matched_moments;
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YGR;
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INFL;
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INT;
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%second-order contemporenous product moments
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YGR*YGR;
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YGR*INFL;
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YGR*INT;
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INFL*INFL;
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INFL*INT;
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INT*INT;
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%second-order temporal product moments
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YGR*YGR(-1);
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INT*INT(-1);
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INFL*INFL(-1);
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end;
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% get indices in declaration order
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iYGR = strmatch('YGR', M_.endo_names,'exact');
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iINFL = strmatch('INFL', M_.endo_names,'exact');
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iINT = strmatch('INT', M_.endo_names,'exact');
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% first entry: number of variable in declaration order
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% second entry: lag
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% third entry: power
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matched_moments_ = {
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%first-order product moments
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[iYGR ] [0 ], [1 ];
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[iINFL ] [0 ], [1 ];
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[iINT ] [0 ], [1 ];
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%second-order contemporenous product moments
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[iYGR iYGR ] [0 0], [1 1];
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[iYGR iINFL] [0 0], [1 1];
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[iYGR iINT ] [0 0], [1 1];
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[iINFL iINFL] [0 0], [1 1];
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[iINFL iINT ] [0 0], [1 1];
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[iINT iINT ] [0 0], [1 1];
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%second-order temporal product moments
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[iYGR iYGR ] [0 -1], [1 1];
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%[iINT iYGR ] [0 -1], [1 1];
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%[iINFL iYGR ] [0 -1], [1 1];
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%[iYGR iINT ] [0 -1], [1 1];
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[iINT iINT ] [0 -1], [1 1];
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%[iINFL iINT ] [0 -1], [1 1];
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%[iYGR iINFL] [0 -1], [1 1];
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%[iINT iINFL] [0 -1], [1 1];
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[iINFL iINFL] [0 -1], [1 1];
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};
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if ~isequal(M_.matched_moments,matched_moments_)
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error('Translation to matched_moments-block failed')
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end
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@#for mommethod in ["GMM", "SMM"]
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method_of_moments(
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% Necessery options
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mom_method = @{mommethod} % method of moments method; possible values: GMM|SMM
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, datafile = 'AnScho_MoM_data_@{orderApp}.mat' % name of filename with data
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% Options for both GMM and SMM
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% , bartlett_kernel_lag = 20 % bandwith in optimal weighting matrix
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, order = @{orderApp} % order of Taylor approximation in perturbation
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% , penalized_estimator % include deviation from prior mean as additional moment restriction and use prior precision as weight
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, pruning % use pruned state space system at higher-order
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% , verbose % display and store intermediate estimation results
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, weighting_matrix = ['optimal'] % weighting matrix in moments distance objective function; possible values: OPTIMAL|IDENTITY_MATRIX|DIAGONAL|filename. Size of cell determines stages in iterated estimation, e.g. two state with ['DIAGONAL','OPTIMAL']
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%, weighting_matrix_scaling_factor=1 % scaling of weighting matrix in objective function
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, se_tolx=1e-6 % step size for numerical computation of standard errors
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% Options for SMM
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% , burnin=500 % number of periods dropped at beginning of simulation
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% , bounded_shock_support % trim shocks in simulation to +- 2 stdev
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% , seed = 24051986 % seed used in simulations
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% , simulation_multiple = 5 % multiple of the data length used for simulation
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% Options for GMM
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@#if mommethod == "GMM"
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, analytic_standard_errors % compute standard errors using analytical derivatives
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@#endif
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% General options
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% , dirname = 'MM' % directory in which to store estimation output
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% , graph_format = EPS % specify the file format(s) for graphs saved to disk
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% , nodisplay % do not display the graphs, but still save them to disk
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% , nograph % do not create graphs (which implies that they are not saved to the disk nor displayed)
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% , noprint % do not print stuff to console
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% , plot_priors = 1 % control plotting of priors
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% , prior_trunc = 1e-10 % probability of extreme values of the prior density that is ignored when computing bounds for the parameters
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% , TeX % print TeX tables and graphics
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% Data and model options
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% , first_obs = 501 % number of first observation
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% , logdata % if data is already in logs
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, nobs = 250 % number of observations
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% , prefilter=0 % demean each data series by its empirical mean and use centered moments
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% , xls_sheet = data % name/number of sheet with data in Excel
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% , xls_range = B2:D200 % range of data in Excel sheet
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% Optimization options that can be set by the user in the mod file, otherwise default values are provided
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% , huge_number=1e7 % value for replacing the infinite bounds on parameters by finite numbers. Used by some optimizers for numerical reasons
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, mode_compute = @{optimizer} % specifies the optimizer for minimization of moments distance
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, additional_optimizer_steps = [1] % vector of additional mode-finders run after mode_compute
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% optim: a list of NAME and VALUE pairs to set options for the optimization routines. Available options depend on mode_compute, some exemplary common options:
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, optim = ('TolFun' , 1e-6 % termination tolerance on the function value, a positive scalar
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,'TolX' , 1e-6 % termination tolerance on x, a positive scalar
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,'MaxIter' , 3000 % maximum number of iterations allowed, a positive integer
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,'MaxFunEvals' , 1D6 % maximum number of function evaluations allowed, a positive integer
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% ,'UseParallel' , 1 % when true (and supported by optimizer) solver estimates gradients in parallel (using Matlab/Octave's parallel toolbox)
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% ,'Jacobian' , 'off' % when 'off' gradient-based solvers approximate Jacobian using finite differences; for GMM we can also pass the analytical Jacobian to gradient-based solvers by setting this 'on'
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)
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, silent_optimizer % run minimization of moments distance silently without displaying results or saving files in between
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% Numerical algorithms options
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% , aim_solver % Use AIM algorithm to compute perturbation approximation
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% , k_order_solver % use k_order_solver in higher order perturbation approximations
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% , dr=default % method used to compute the decision rule; possible values are DEFAULT, CYCLE_REDUCTION, LOGARITHMIC_REDUCTION
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% , dr_cycle_reduction_tol = 1e-7 % convergence criterion used in the cycle reduction algorithm
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% , dr_logarithmic_reduction_tol = 1e-12 % convergence criterion used in the logarithmic reduction algorithm
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% , dr_logarithmic_reduction_maxiter = 100 % maximum number of iterations used in the logarithmic reduction algorithm
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% , lyapunov = DEFAULT % algorithm used to solve lyapunov equations; possible values are DEFAULT, FIXED_POINT, DOUBLING, SQUARE_ROOT_SOLVER
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% , lyapunov_complex_threshold = 1e-15 % complex block threshold for the upper triangular matrix in symmetric Lyapunov equation solver
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% , lyapunov_fixed_point_tol = 1e-10 % convergence criterion used in the fixed point Lyapunov solver
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% , lyapunov_doubling_tol = 1e-16 % convergence criterion used in the doubling algorithm
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% , sylvester = default % algorithm to solve Sylvester equation; possible values are DEFAULT, FIXED_POINT
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% , sylvester_fixed_point_tol = 1e-12 % convergence criterion used in the fixed point Sylvester solver
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% , qz_criterium = 0.999999 % value used to split stable from unstable eigenvalues in reordering the Generalized Schur decomposition used for solving first order problems
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% , qz_zero_threshold = 1e-6 % value used to test if a generalized eigenvalue is 0/0 in the generalized Schur decomposition
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% , schur_vec_tol=1e-11 % tolerance level used to find nonstationary variables in Schur decomposition of the transition matrix
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% , mode_check % plot the target function for values around the computed minimum for each estimated parameter in turn
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% , mode_check_neighbourhood_size = 5 % width of the window (expressed in percentage deviation) around the computed minimum to be displayed on the diagnostic plots
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% , mode_check_symmetric_plots=1 % ensure that the check plots are symmetric around the minimum
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% , mode_check_number_of_points = 20 % number of points around the minimum where the target function is evaluated (for each parameter)
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);
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@#endfor
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