207 lines
10 KiB
Modula-2
207 lines
10 KiB
Modula-2
% This mod file compares the functionality of Dynare's pruned_state_space.m with the
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% external Dynare pruning toolbox of Andreasen, Fernández-Villaverde and Rubio-Ramírez (2018):
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% "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications",
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% Review of Economic Studies, Volume 85, Issue 1, Pages 1–49.
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% The model under study is taken from An and Schorfheide (2007): "Bayesian Analysis of DSGE Models",
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% Econometric Reviews, Volume 26, Issue 2-4, Pages 113-172.
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% Note that we use version 2 of the toolbox, i.e. the one which is called
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% "Third-order GMM estimate package for DSGE models (version 2)" and can be
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% downloaded from https://sites.google.com/site/mandreasendk/home-1
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%
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% Created by @wmutschl (Willi Mutschler, willi@mutschler.eu)
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%
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% =========================================================================
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% Copyright (C) 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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% set this to 1 if you want to recompute using the Andreasen et al toolbox
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% otherwise the results are loaded from Andreasen_et_al_2018_Dynare44Pruning_v2.mat
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@#define Andreasen_et_al_toolbox = 0
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var YGR INFL INT
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c p R g y z; %if ordering of var is changed comparison code below needs to be adapted
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varexo e_r e_g e_z e_junk;
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parameters tau nu kap cyst psi1 psi2 rhor rhog rhoz rrst pist gamst;
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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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sig_r = .2;
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sig_g = .6;
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sig_z = .3;
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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*(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 + e_junk;
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INT = pist+rrst+4*gamst+400*R;
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end;
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shocks;
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var e_r = sig_r^2;
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var e_g = sig_g^2;
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var e_z = sig_z^2;
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var e_junk = 0;
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end;
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steady_state_model;
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y = 0;
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R = 0;
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g = 0;
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z = 0;
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c = 0;
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p = 0;
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YGR = gamst;
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INFL = pist;
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INT = pist + rrst + 4*gamst;
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end;
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steady; check; model_diagnostics;
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@#for orderApp in [1, 2, 3]
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stoch_simul(order=@{orderApp},pruning,irf=0,periods=0);
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pruned_state_space.order_@{orderApp} = pruned_state_space_system(M_, options_, oo_.dr, [], options_.ar, 1, 0);
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@#if Andreasen_et_al_toolbox
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addpath('Dynare44Pruning_v2/simAndMoments3order'); %provide path to toolbox
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optPruning.orderApp = @{orderApp};
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outAndreasenetal.order_@{orderApp} = RunDynarePruning(optPruning,oo_,M_,[oo_.dr.ghx oo_.dr.ghu]);
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rmpath('Dynare44Pruning_v2/simAndMoments3order');
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close all;
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@#endif
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@#endfor
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@#if Andreasen_et_al_toolbox
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delete Andreasen_et_al_2018_Dynare44Pruning_v2.mat;
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pause(3);
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save('Andreasen_et_al_2018_Dynare44Pruning_v2.mat', 'outAndreasenetal')
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pause(3);
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@#endif
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load('Andreasen_et_al_2018_Dynare44Pruning_v2.mat')
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% Make comparisons only at orders 1 and 2
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for iorder = 1:3
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fprintf('ORDER %d:\n',iorder);
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pruned = pruned_state_space.(sprintf('order_%d',iorder));
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outAndreasen = outAndreasenetal.(sprintf('order_%d',iorder));
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%make sure variable ordering is correct
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if ~isequal(M_.endo_names,[outAndreasen.label_y; outAndreasen.label_v(1:M_.nspred)])
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error('variable ordering is not the same, change declaration order');
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end
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norm_E_yx = norm(pruned.E_y(oo_.dr.inv_order_var) - [outAndreasen.Mean_y; outAndreasen.Mean_v(1:M_.nspred)] , Inf);
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fprintf('max(sum(abs(E[y;x]''))): %d\n',norm_E_yx);
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norm_Var_y = norm(pruned.Var_y(oo_.dr.inv_order_var(1:(M_.endo_nbr-M_.nspred)),oo_.dr.inv_order_var(1:(M_.endo_nbr-M_.nspred))) - outAndreasen.Var_y , Inf);
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fprintf('max(sum(abs(Var[y]''))):: %d\n',norm_Var_y);
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norm_Var_x = norm(pruned.Var_y(M_.nstatic+(1:M_.nspred),M_.nstatic+(1:M_.nspred)) - outAndreasen.Var_v(1:M_.nspred,1:M_.nspred) , Inf);
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fprintf('max(sum(abs(Var[x]''))): %d\n',norm_Var_x);
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norm_Corr_yi1 = norm(pruned.Corr_yi(oo_.dr.inv_order_var(1:(M_.endo_nbr-M_.nspred)),oo_.dr.inv_order_var(1:(M_.endo_nbr-M_.nspred)),1) - outAndreasen.Corr_y(:,:,1) , Inf);
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fprintf('max(sum(abs(Corr[y,y(-1)]''))): %d\n',norm_Corr_yi1);
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norm_Corr_yi2 = norm(pruned.Corr_yi(oo_.dr.inv_order_var(1:(M_.endo_nbr-M_.nspred)),oo_.dr.inv_order_var(1:(M_.endo_nbr-M_.nspred)),2) - outAndreasen.Corr_y(:,:,2) , Inf);
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fprintf('max(sum(abs(Corr[y,y(-2)]''))): %d\n',norm_Corr_yi2);
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norm_Corr_xi1 = norm(pruned.Corr_yi(M_.nstatic+(1:M_.nspred),M_.nstatic+(1:M_.nspred),1) - outAndreasen.Corr_v(1:M_.nspred,1:M_.nspred,1) , Inf);
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fprintf('max(sum(abs(Corr[x,x(-1)]''))): %d\n',norm_Corr_xi1);
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norm_Corr_xi2 = norm(pruned.Corr_yi(M_.nstatic+(1:M_.nspred),M_.nstatic+(1:M_.nspred),2) - outAndreasen.Corr_v(1:M_.nspred,1:M_.nspred,2) , Inf);
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fprintf('max(sum(abs(Corr[x,x(-2)]''))): %d\n',norm_Corr_xi2);
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if iorder < 3 && any([norm_E_yx norm_Var_y norm_Var_x norm_Corr_yi1 norm_Corr_yi2 norm_Corr_xi1 norm_Corr_xi2] > 1e-5)
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error('Something wrong with pruned_state_space.m compared to Andreasen et al 2018 Toolbox v2 at order %d.',iorder);
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end
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if iorder==3
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pruned_without_shock = load(['AnSchorfheide_pruned_state_space' filesep 'Output' filesep 'AnSchorfheide_pruned_state_space_results.mat']);
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pruned_without_shock = pruned_without_shock.oo_.pruned;
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norm_E_yx = norm(pruned.E_y - pruned_without_shock.E_y , Inf);
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fprintf('max(sum(abs(E[y;x]''))): %d\n',norm_E_yx);
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norm_Var_y = norm(pruned.Var_y - pruned_without_shock.Var_y, Inf);
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fprintf('max(sum(abs(Var[x]''))): %d\n',norm_Var_x);
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norm_Corr_yi1 = norm(pruned.Corr_yi(:,:,1) - pruned_without_shock.Corr_yi(:,:,1), Inf);
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fprintf('max(sum(abs(Corr[y,y(-1)]''))): %d\n',norm_Corr_yi1);
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norm_Corr_yi2 = norm(pruned.Corr_yi(:,:,2) - pruned_without_shock.Corr_yi(:,:,2), Inf);
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fprintf('max(sum(abs(Corr[y,y(-2)]''))): %d\n',norm_Corr_yi2);
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end
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end
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% skipline();
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% fprintf('Note that at third order, there is an error in the computation of Var_z in Andreasen et al (2018)''s toolbox, @wmutschl is in contact to clarify this.\n');
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% fprintf('EXAMPLE:\n')
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% fprintf(' Consider Var[kron(kron(xf,xf),xf)] = E[kron(kron(kron(kron(kron(xf,xf),xf),xf),xf),xf)] - E[kron(kron(xf,xf),xf)]*E[kron(kron(xf,xf),xf)].''\n');
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% fprintf(' Now note that xf=hx*xf(-1)+hu*u is Gaussian, that is E[kron(kron(xf,xf),xf)]=0, and Var[kron(kron(xf,xf),xf)] are the sixth-order product moments\n');
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% fprintf(' which can be computed using the prodmom.m function by providing E[xf*xf''] as covariance matrix.\n');
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% fprintf(' In order to replicate this you have to change UnconditionalMoments_3rd_Lyap.m to also output Var_z.\n')
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%
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% dynare_nx = M_.nspred;
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% dynare_E_xf2 = pruned_state_space.order_3.Var_z(1:dynare_nx,1:dynare_nx);
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% dynare_E_xf6 = pruned_state_space.order_3.Var_z((end-dynare_nx^3+1):end,(end-dynare_nx^3+1):end);
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% dynare_E_xf6 = dynare_E_xf6(:);
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%
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% Andreasen_nx = M_.nspred+M_.exo_nbr;
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% Andreasen_E_xf2 = outAndreasenetal.order_3.Var_z(1:Andreasen_nx,1:Andreasen_nx);
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% Andreasen_E_xf6 = outAndreasenetal.order_3.Var_z((end-Andreasen_nx^3+1):end,(end-Andreasen_nx^3+1):end);
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% Andreasen_E_xf6 = Andreasen_E_xf6(:);
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%
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% fprintf('Second-order product moments of xf and u are the same:\n')
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% norm_E_xf2 = norm(dynare_E_xf2-Andreasen_E_xf2(1:M_.nspred,1:M_.nspred),Inf)
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% norm_E_uu = norm(M_.Sigma_e-Andreasen_E_xf2(M_.nspred+(1:M_.exo_nbr),M_.nspred+(1:M_.exo_nbr)),Inf)
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%
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% % Compute unique sixth-order product moments of xf, i.e. unique(E[kron(kron(kron(kron(kron(xf,xf),xf),xf),xf),xf)],'stable')
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% dynare_nx6 = dynare_nx*(dynare_nx+1)/2*(dynare_nx+2)/3*(dynare_nx+3)/4*(dynare_nx+4)/5*(dynare_nx+5)/6;
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% dynare_Q6Px = Q6_plication(dynare_nx);
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% dynare_COMBOS6 = flipud(allVL1(dynare_nx, 6)); %all possible (unique) combinations of powers that sum up to six
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% dynare_true_E_xf6 = zeros(dynare_nx6,1); %only unique entries
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% for j6 = 1:size(dynare_COMBOS6,1)
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% dynare_true_E_xf6(j6) = prodmom(dynare_E_xf2, 1:dynare_nx, dynare_COMBOS6(j6,:));
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% end
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% dynare_true_E_xf6 = dynare_Q6Px*dynare_true_E_xf6; %add duplicate entries
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% norm_dynare_E_xf6 = norm(dynare_true_E_xf6 - dynare_E_xf6, Inf);
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%
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% Andreasen_nx6 = Andreasen_nx*(Andreasen_nx+1)/2*(Andreasen_nx+2)/3*(Andreasen_nx+3)/4*(Andreasen_nx+4)/5*(Andreasen_nx+5)/6;
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% Andreasen_Q6Px = Q6_plication(Andreasen_nx);
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% Andreasen_COMBOS6 = flipud(allVL1(Andreasen_nx, 6)); %all possible (unique) combinations of powers that sum up to six
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% Andreasen_true_E_xf6 = zeros(Andreasen_nx6,1); %only unique entries
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% for j6 = 1:size(Andreasen_COMBOS6,1)
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% Andreasen_true_E_xf6(j6) = prodmom(Andreasen_E_xf2, 1:Andreasen_nx, Andreasen_COMBOS6(j6,:));
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% end
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% Andreasen_true_E_xf6 = Andreasen_Q6Px*Andreasen_true_E_xf6; %add duplicate entries
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% norm_Andreasen_E_xf6 = norm(Andreasen_true_E_xf6 - Andreasen_E_xf6, Inf);
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%
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% fprintf('Sixth-order product moments of xf and u are not the same!\n');
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% fprintf(' Dynare maximum absolute deviations of sixth-order product moments of xf: %d\n',norm_dynare_E_xf6)
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% fprintf(' Andreasen et al maximum absolute deviations of sixth-order product moments of xf: %d\n',norm_Andreasen_E_xf6)
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% skipline();
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% fprintf('Note that the standard deviations are set quite high to make the numerical differences more apparent.\n');
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