diff --git a/matlab/prodmom.m b/matlab/prodmom.m
index 1728f9d694ab3195147ad557411ffba363cd452a..30ab675e09f066a2fa2d0acead65a330d43ef702 100644
--- a/matlab/prodmom.m
+++ b/matlab/prodmom.m
@@ -68,6 +68,10 @@ end
% Use bivariate normal results when there are only two distinct indices
%
if m==2
+ if V(1,1)==0 || V(2,2)==0
+ y=0;
+ return
+ end
rho = V(1,2)/sqrt(V(1,1)*V(2,2));
y = V(1,1)^(nu(1)/2)*V(2,2)^(nu(2)/2)*bivmom(nu,rho);
return
diff --git a/matlab/prodmom_deriv.m b/matlab/prodmom_deriv.m
index 511cc0103bd27203a3b62dbb9648c79b63a23396..1c13422e6e27bf554d09c96fb5642fabee907dc2 100644
--- a/matlab/prodmom_deriv.m
+++ b/matlab/prodmom_deriv.m
@@ -93,6 +93,13 @@ end
% Use bivariate normal results when there are only two distinct indices
%
if m==2
+ if V(1,1)==0 || V(2,2)==0
+ y=0;
+ if nargout>1
+ dy=zeros(1,size(dV,3));
+ end
+ return
+ end
rho = V(1,2)/sqrt(V(1,1)*V(2,2));
if nargout > 1
drho = dC(ii(1),ii(2),:);
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 7f66c697b53afa41c576faf4fd4513b4a67d669f..ae05fc9292d72fe934b84b5f06c0e1d1ff016958 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -25,6 +25,7 @@ MODFILES = \
analytic_derivatives/BrockMirman_PertParamsDerivs.mod \
analytic_derivatives/burnside_3_order_PertParamsDerivs.mod \
pruning/AnSchorfheide_pruned_state_space.mod \
+ pruning/AS_pruned_state_space_red_shock.mod \
measurement_errors/fs2000_corr_me_ml_mcmc/fs2000_corr_ME.mod \
TeX/fs2000_corr_ME.mod \
estimation/MH_recover/fs2000_recover_tarb.mod \
@@ -845,6 +846,8 @@ discretionary_policy/Gali_2015_chapter_3_nonlinear.o.trs: discretionary_policy/G
particle/local_state_space_iteration_k_test.m.trs: particle/first_spec.m.trs
particle/local_state_space_iteration_k_test.o.trs: particle/first_spec.o.trs
+pruning/AS_pruned_state_space_red_shock.m.trs: pruning/AnSchorfheide_pruned_state_space.m.trs
+pruning/AS_pruned_state_space_red_shock.o.trs: pruning/AnSchorfheide_pruned_state_space.o.trs
observation_trends_and_prefiltering/MCMC: m/observation_trends_and_prefiltering/MCMC o/observation_trends_and_prefiltering/MCMC
m/observation_trends_and_prefiltering/MCMC: $(patsubst %.mod, %.m.trs, $(filter observation_trends_and_prefiltering/MCMC/%.mod, $(MODFILES)))
diff --git a/tests/pruning/AS_pruned_state_space_red_shock.mod b/tests/pruning/AS_pruned_state_space_red_shock.mod
new file mode 100644
index 0000000000000000000000000000000000000000..dfbc3571c851d68071716b8b5a7705c84cbeb9c1
--- /dev/null
+++ b/tests/pruning/AS_pruned_state_space_red_shock.mod
@@ -0,0 +1,206 @@
+% This mod file compares the functionality of Dynare's pruned_state_space.m with the
+% external Dynare pruning toolbox of Andreasen, Fernández-Villaverde and Rubio-Ramírez (2018):
+% "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications",
+% Review of Economic Studies, Volume 85, Issue 1, Pages 1–49.
+% The model under study is taken from An and Schorfheide (2007): "Bayesian Analysis of DSGE Models",
+% Econometric Reviews, Volume 26, Issue 2-4, Pages 113-172.
+% Note that we use version 2 of the toolbox, i.e. the one which is called
+% "Third-order GMM estimate package for DSGE models (version 2)" and can be
+% downloaded from https://sites.google.com/site/mandreasendk/home-1
+%
+% Created by @wmutschl (Willi Mutschler, willi@mutschler.eu)
+%
+% =========================================================================
+% Copyright (C) 2020 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 <https://www.gnu.org/licenses/>.
+% =========================================================================
+
+% set this to 1 if you want to recompute using the Andreasen et al toolbox
+% otherwise the results are loaded from Andreasen_et_al_2018_Dynare44Pruning_v2.mat
+@#define Andreasen_et_al_toolbox = 0
+
+var YGR INFL INT
+ c p R g y z; %if ordering of var is changed comparison code below needs to be adapted
+varexo e_r e_g e_z e_junk;
+parameters tau nu kap cyst psi1 psi2 rhor rhog rhoz rrst pist gamst;
+
+tau = 2;
+nu = 0.1;
+kap = 0.33;
+cyst = 0.85;
+psi1 = 1.5;
+psi2 = 0.125;
+rhor = 0.75;
+rhog = 0.95;
+rhoz = 0.9;
+rrst = 1;
+pist = 3.2;
+gamst = 0.55;
+sig_r = .2;
+sig_g = .6;
+sig_z = .3;
+
+model;
+#pist2 = exp(pist/400);
+#rrst2 = exp(rrst/400);
+#bet = 1/rrst2;
+#phi = tau*(1-nu)/nu/kap/pist2^2;
+#gst = 1/cyst;
+#cst = (1-nu)^(1/tau);
+#yst = cst*gst;
+#dy = y-y(-1);
+1 = exp(-tau*c(+1)+tau*c+R-z(+1)-p(+1));
+(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));
+exp(c-y) = exp(-g) - phi*pist2^2*gst/2*(exp(p)-1)^2;
+R = rhor*R(-1) + (1-rhor)*psi1*p + (1-rhor)*psi2*(y-g) + e_r;
+g = rhog*g(-1) + e_g;
+z = rhoz*z(-1) + e_z;
+YGR = gamst+100*(dy+z);
+INFL = pist+400*p + e_junk;
+INT = pist+rrst+4*gamst+400*R;
+end;
+
+shocks;
+var e_r = sig_r^2;
+var e_g = sig_g^2;
+var e_z = sig_z^2;
+var e_junk = 0;
+end;
+
+steady_state_model;
+y = 0;
+R = 0;
+g = 0;
+z = 0;
+c = 0;
+p = 0;
+YGR = gamst;
+INFL = pist;
+INT = pist + rrst + 4*gamst;
+end;
+
+steady; check; model_diagnostics;
+
+@#for orderApp in [1, 2, 3]
+ stoch_simul(order=@{orderApp},pruning,irf=0,periods=0);
+ pruned_state_space.order_@{orderApp} = pruned_state_space_system(M_, options_, oo_.dr, [], options_.ar, 1, 0);
+ @#if Andreasen_et_al_toolbox
+ addpath('Dynare44Pruning_v2/simAndMoments3order'); %provide path to toolbox
+ optPruning.orderApp = @{orderApp};
+ outAndreasenetal.order_@{orderApp} = RunDynarePruning(optPruning,oo_,M_,[oo_.dr.ghx oo_.dr.ghu]);
+ rmpath('Dynare44Pruning_v2/simAndMoments3order');
+ close all;
+ @#endif
+@#endfor
+
+@#if Andreasen_et_al_toolbox
+ delete Andreasen_et_al_2018_Dynare44Pruning_v2.mat;
+ pause(3);
+ save('Andreasen_et_al_2018_Dynare44Pruning_v2.mat', 'outAndreasenetal')
+ pause(3);
+@#endif
+
+load('Andreasen_et_al_2018_Dynare44Pruning_v2.mat')
+
+% Make comparisons only at orders 1 and 2
+for iorder = 1:3
+ fprintf('ORDER %d:\n',iorder);
+ pruned = pruned_state_space.(sprintf('order_%d',iorder));
+ outAndreasen = outAndreasenetal.(sprintf('order_%d',iorder));
+ %make sure variable ordering is correct
+ if ~isequal(M_.endo_names,[outAndreasen.label_y; outAndreasen.label_v(1:M_.nspred)])
+ error('variable ordering is not the same, change declaration order');
+ end
+ norm_E_yx = norm(pruned.E_y(oo_.dr.inv_order_var) - [outAndreasen.Mean_y; outAndreasen.Mean_v(1:M_.nspred)] , Inf);
+ fprintf('max(sum(abs(E[y;x]''))): %d\n',norm_E_yx);
+ 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);
+ fprintf('max(sum(abs(Var[y]''))):: %d\n',norm_Var_y);
+ 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);
+ fprintf('max(sum(abs(Var[x]''))): %d\n',norm_Var_x);
+ 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);
+ fprintf('max(sum(abs(Corr[y,y(-1)]''))): %d\n',norm_Corr_yi1);
+ 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);
+ fprintf('max(sum(abs(Corr[y,y(-2)]''))): %d\n',norm_Corr_yi2);
+ 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);
+ fprintf('max(sum(abs(Corr[x,x(-1)]''))): %d\n',norm_Corr_xi1);
+ 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);
+ fprintf('max(sum(abs(Corr[x,x(-2)]''))): %d\n',norm_Corr_xi2);
+
+ 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)
+ error('Something wrong with pruned_state_space.m compared to Andreasen et al 2018 Toolbox v2 at order %d.',iorder);
+ end
+ if iorder==3
+ pruned_without_shock = load('AnSchorfheide_pruned_state_space_results.mat');
+ pruned_without_shock = pruned_without_shock.oo_.pruned;
+ norm_E_yx = norm(pruned.E_y - pruned_without_shock.E_y , Inf);
+ fprintf('max(sum(abs(E[y;x]''))): %d\n',norm_E_yx);
+ norm_Var_y = norm(pruned.Var_y - pruned_without_shock.Var_y, Inf);
+ fprintf('max(sum(abs(Var[x]''))): %d\n',norm_Var_x);
+ norm_Corr_yi1 = norm(pruned.Corr_yi(:,:,1) - pruned_without_shock.Corr_yi(:,:,1), Inf);
+ fprintf('max(sum(abs(Corr[y,y(-1)]''))): %d\n',norm_Corr_yi1);
+ norm_Corr_yi2 = norm(pruned.Corr_yi(:,:,2) - pruned_without_shock.Corr_yi(:,:,2), Inf);
+ fprintf('max(sum(abs(Corr[y,y(-2)]''))): %d\n',norm_Corr_yi2);
+ end
+end
+% skipline();
+% 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');
+% fprintf('EXAMPLE:\n')
+% 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');
+% 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');
+% fprintf(' which can be computed using the prodmom.m function by providing E[xf*xf''] as covariance matrix.\n');
+% fprintf(' In order to replicate this you have to change UnconditionalMoments_3rd_Lyap.m to also output Var_z.\n')
+%
+% dynare_nx = M_.nspred;
+% dynare_E_xf2 = pruned_state_space.order_3.Var_z(1:dynare_nx,1:dynare_nx);
+% dynare_E_xf6 = pruned_state_space.order_3.Var_z((end-dynare_nx^3+1):end,(end-dynare_nx^3+1):end);
+% dynare_E_xf6 = dynare_E_xf6(:);
+%
+% Andreasen_nx = M_.nspred+M_.exo_nbr;
+% Andreasen_E_xf2 = outAndreasenetal.order_3.Var_z(1:Andreasen_nx,1:Andreasen_nx);
+% Andreasen_E_xf6 = outAndreasenetal.order_3.Var_z((end-Andreasen_nx^3+1):end,(end-Andreasen_nx^3+1):end);
+% Andreasen_E_xf6 = Andreasen_E_xf6(:);
+%
+% fprintf('Second-order product moments of xf and u are the same:\n')
+% norm_E_xf2 = norm(dynare_E_xf2-Andreasen_E_xf2(1:M_.nspred,1:M_.nspred),Inf)
+% norm_E_uu = norm(M_.Sigma_e-Andreasen_E_xf2(M_.nspred+(1:M_.exo_nbr),M_.nspred+(1:M_.exo_nbr)),Inf)
+%
+% % Compute unique sixth-order product moments of xf, i.e. unique(E[kron(kron(kron(kron(kron(xf,xf),xf),xf),xf),xf)],'stable')
+% dynare_nx6 = dynare_nx*(dynare_nx+1)/2*(dynare_nx+2)/3*(dynare_nx+3)/4*(dynare_nx+4)/5*(dynare_nx+5)/6;
+% dynare_Q6Px = Q6_plication(dynare_nx);
+% dynare_COMBOS6 = flipud(allVL1(dynare_nx, 6)); %all possible (unique) combinations of powers that sum up to six
+% dynare_true_E_xf6 = zeros(dynare_nx6,1); %only unique entries
+% for j6 = 1:size(dynare_COMBOS6,1)
+% dynare_true_E_xf6(j6) = prodmom(dynare_E_xf2, 1:dynare_nx, dynare_COMBOS6(j6,:));
+% end
+% dynare_true_E_xf6 = dynare_Q6Px*dynare_true_E_xf6; %add duplicate entries
+% norm_dynare_E_xf6 = norm(dynare_true_E_xf6 - dynare_E_xf6, Inf);
+%
+% Andreasen_nx6 = Andreasen_nx*(Andreasen_nx+1)/2*(Andreasen_nx+2)/3*(Andreasen_nx+3)/4*(Andreasen_nx+4)/5*(Andreasen_nx+5)/6;
+% Andreasen_Q6Px = Q6_plication(Andreasen_nx);
+% Andreasen_COMBOS6 = flipud(allVL1(Andreasen_nx, 6)); %all possible (unique) combinations of powers that sum up to six
+% Andreasen_true_E_xf6 = zeros(Andreasen_nx6,1); %only unique entries
+% for j6 = 1:size(Andreasen_COMBOS6,1)
+% Andreasen_true_E_xf6(j6) = prodmom(Andreasen_E_xf2, 1:Andreasen_nx, Andreasen_COMBOS6(j6,:));
+% end
+% Andreasen_true_E_xf6 = Andreasen_Q6Px*Andreasen_true_E_xf6; %add duplicate entries
+% norm_Andreasen_E_xf6 = norm(Andreasen_true_E_xf6 - Andreasen_E_xf6, Inf);
+%
+% fprintf('Sixth-order product moments of xf and u are not the same!\n');
+% fprintf(' Dynare maximum absolute deviations of sixth-order product moments of xf: %d\n',norm_dynare_E_xf6)
+% fprintf(' Andreasen et al maximum absolute deviations of sixth-order product moments of xf: %d\n',norm_Andreasen_E_xf6)
+% skipline();
+% fprintf('Note that the standard deviations are set quite high to make the numerical differences more apparent.\n');
diff --git a/tests/pruning/AnSchorfheide_pruned_state_space.mod b/tests/pruning/AnSchorfheide_pruned_state_space.mod
index a4afa3aed0194bd1b0bc53b590f6dda1ee61894d..7a720c1e3799f384e56296b981bd20c1c8035349 100644
--- a/tests/pruning/AnSchorfheide_pruned_state_space.mod
+++ b/tests/pruning/AnSchorfheide_pruned_state_space.mod
@@ -142,6 +142,9 @@ for iorder = 1:3
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)
error('Something wrong with pruned_state_space.m compared to Andreasen et al 2018 Toolbox v2 at order %d.',iorder);
end
+ if iorder == 3
+ oo_.pruned=pruned; %required by later tests
+ end
end
% skipline();
% 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');