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Commit fa3c1381 authored by Johannes Pfeifer's avatar Johannes Pfeifer
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evaluate_planner_objective.m: fix output for linear-quadratic problems solved at second order 

Welfare does not correspond to the steady state in this case. Cherry-picked from b5c74199
parent 4497c7ee
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1 merge request!2059evaluate_planner_objective.m: fix output for linear-quadratic problems solved at second order
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matlab/evaluate_planner_objective.m
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......@@ -43,7 +43,7 @@ function planner_objective_value = evaluate_planner_objective(M_,options_,oo_)
% Similarly, taking the unconditional expectation of a second-order approximation of utility around the non-stochastic steady state yields a second-order approximation of unconditional welfare
% E(W) = (1 - beta)^{-1} ( Ubar + U_x h_y E(yhat) + 0.5 ( (U_xx h_y^2 + U_x h_yy) E(yhat^2) + (U_xx h_u^2 + U_x h_uu) E(u^2) + U_x h_ss )
% where E(yhat), E(yhat^2) and E(u^2) can be derived from oo_.mean and oo_.var.
% where E(yhat), E(yhat^2) and E(u^2) can be derived from oo_.mean and oo_.var.
% Importantly, E(yhat) and E(yhat^2) are second-order approximations, which is not the same as approximations computed with all the information provided by decision rules approximated up to the second order. The latter might include terms that are order 3 or 4 for the approximation of E(yhat^2), which we exclude here.
% As for conditional welfare, the second-order approximation of welfare around the non-stochastic steady state leads to
......@@ -90,245 +90,243 @@ if beta>=1
fprintf('evaluate_planner_objective: the planner discount factor is not strictly smaller than 1. Unconditional welfare will not be finite.\n')
end
if options_.ramsey_policy
if oo_.gui.ran_perfect_foresight
T = size(oo_.endo_simul,2);
[U_term] = feval([M_.fname '.objective.static'],oo_.endo_simul(:,T-M_.maximum_lead),oo_.exo_simul(T-M_.maximum_lead,:), M_.params);
EW = U_term/(1-beta);
W = EW;
for t=T-M_.maximum_lead:-1:1+M_.maximum_lag
[U] = feval([M_.fname '.objective.static'],oo_.endo_simul(:,t),oo_.exo_simul(t,:), M_.params);
W = U + beta*W;
end
planner_objective_value = struct('conditional', W, 'unconditional', EW);
if options_.ramsey_policy && oo_.gui.ran_perfect_foresight
T = size(oo_.endo_simul,2);
[U_term] = feval([M_.fname '.objective.static'],oo_.endo_simul(:,T-M_.maximum_lead),oo_.exo_simul(T-M_.maximum_lead,:), M_.params);
EW = U_term/(1-beta);
W = EW;
for t=T-M_.maximum_lead:-1:1+M_.maximum_lag
[U] = feval([M_.fname '.objective.static'],oo_.endo_simul(:,t),oo_.exo_simul(t,:), M_.params);
W = U + beta*W;
end
planner_objective_value = struct('conditional', W, 'unconditional', EW);
else
planner_objective_value = struct('conditional', struct('zero_initial_multiplier', 0., 'steady_initial_multiplier', 0.), 'unconditional', 0.);
if isempty(oo_.dr) || ~isfield(oo_.dr,'ys')
error('evaluate_planner_objective requires decision rules to have previously been computed (e.g. by stoch_simul or discretionary_policy)')
else
planner_objective_value = struct('conditional', struct('zero_initial_multiplier', 0., 'steady_initial_multiplier', 0.), 'unconditional', 0.);
if isempty(oo_.dr) || ~isfield(oo_.dr,'ys')
error('evaluate_planner_objective requires decision rules to have previously been computed (e.g. by stoch_simul)')
else
ys = oo_.dr.ys;
ys = oo_.dr.ys;
end
if options_.order == 1 && ~options_.discretionary_policy
[U,Uy] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
Gy = dr.ghx(nstatic+(1:nspred),:);
Gu = dr.ghu(nstatic+(1:nspred),:);
gy(dr.order_var,:) = dr.ghx;
gu(dr.order_var,:) = dr.ghu;
%% Unconditional welfare
EW = U/(1-beta);
planner_objective_value.unconditional = EW;
%% Conditional welfare starting from the non-stochastic steady-state (i) with Lagrange multipliers set to their steady-state value (ii) with Lagrange multipliers set to 0
Wbar = U/(1-beta);
Wy = Uy*gy/(eye(nspred)-beta*Gy);
Wu = Uy*gu + beta*Wy*Gu;
[yhat_L_SS,yhat_L_0, u]=get_initial_state(ys,M_,dr,oo_);
W_L_SS = Wbar+Wy*yhat_L_SS+Wu*u;
W_L_0 = Wbar+Wy*yhat_L_0+Wu*u;
planner_objective_value.conditional.steady_initial_multiplier = W_L_SS;
planner_objective_value.conditional.zero_initial_multiplier = W_L_0;
elseif options_.order == 2 && ~M_.hessian_eq_zero %full second order approximation
[U,Uy,Uyy] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
Gy = dr.ghx(nstatic+(1:nspred),:);
Gu = dr.ghu(nstatic+(1:nspred),:);
Gyy = dr.ghxx(nstatic+(1:nspred),:);
Gyu = dr.ghxu(nstatic+(1:nspred),:);
Guu = dr.ghuu(nstatic+(1:nspred),:);
Gss = dr.ghs2(nstatic+(1:nspred),:);
gy(dr.order_var,:) = dr.ghx;
gu(dr.order_var,:) = dr.ghu;
gyy(dr.order_var,:) = dr.ghxx;
gyu(dr.order_var,:) = dr.ghxu;
guu(dr.order_var,:) = dr.ghuu;
gss(dr.order_var,:) = dr.ghs2;
Uyy = full(Uyy);
Uyygygy = A_times_B_kronecker_C(Uyy,gy,gy);
Uyygugu = A_times_B_kronecker_C(Uyy,gu,gu);
Uyygugy = A_times_B_kronecker_C(Uyy,gu,gy);
%% Unconditional welfare
old_noprint = options_.noprint;
if ~old_noprint
options_.noprint = 1;
end
if options_.order == 1 || M_.hessian_eq_zero
[U,Uy] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
Gy = dr.ghx(nstatic+(1:nspred),:);
Gu = dr.ghu(nstatic+(1:nspred),:);
gy(dr.order_var,:) = dr.ghx;
gu(dr.order_var,:) = dr.ghu;
%% Unconditional welfare
EW = U/(1-beta);
planner_objective_value.unconditional = EW;
%% Conditional welfare starting from the non-stochastic steady-state (i) with Lagrange multipliers set to their steady-state value (ii) with Lagrange multipliers set to 0
Wbar = U/(1-beta);
Wy = Uy*gy/(eye(nspred)-beta*Gy);
Wu = Uy*gu + beta*Wy*Gu;
[yhat_L_SS,yhat_L_0, u]=get_initial_state(ys,M_,dr,oo_);
W_L_SS = Wbar+Wy*yhat_L_SS+Wu*u;
W_L_0 = Wbar+Wy*yhat_L_0+Wu*u;
planner_objective_value.conditional.steady_initial_multiplier = W_L_SS;
planner_objective_value.conditional.zero_initial_multiplier = W_L_0;
elseif options_.order == 2 && ~M_.hessian_eq_zero
[U,Uy,Uyy] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
Gy = dr.ghx(nstatic+(1:nspred),:);
Gu = dr.ghu(nstatic+(1:nspred),:);
Gyy = dr.ghxx(nstatic+(1:nspred),:);
Gyu = dr.ghxu(nstatic+(1:nspred),:);
Guu = dr.ghuu(nstatic+(1:nspred),:);
Gss = dr.ghs2(nstatic+(1:nspred),:);
gy(dr.order_var,:) = dr.ghx;
gu(dr.order_var,:) = dr.ghu;
gyy(dr.order_var,:) = dr.ghxx;
gyu(dr.order_var,:) = dr.ghxu;
guu(dr.order_var,:) = dr.ghuu;
gss(dr.order_var,:) = dr.ghs2;
Uyy = full(Uyy);
Uyygygy = A_times_B_kronecker_C(Uyy,gy,gy);
Uyygugu = A_times_B_kronecker_C(Uyy,gu,gu);
Uyygugy = A_times_B_kronecker_C(Uyy,gu,gy);
%% Unconditional welfare
old_noprint = options_.noprint;
if ~old_noprint
options_.noprint = 1;
end
var_list = M_.endo_names(dr.order_var(nstatic+(1:nspred)));
if options_.pruning
fprintf('evaluate_planner_objective: pruning option is not supported and will be ignored\n')
end
oo_=disp_th_moments(dr,var_list,M_,options_,oo_);
if ~old_noprint
options_.noprint = 0;
end
if any(isnan(oo_.mean)) || any(any(isnan(oo_.var)))
fprintf('evaluate_planner_objective: encountered NaN moments in the endogenous variables often associated\n')
fprintf('evaluate_planner_objective: with either non-stationary variables or singularity due e.g. including\n')
fprintf('evaluate_planner_objective: the planner objective function (or additive parts of it) in the model.\n')
fprintf('evaluate_planner_objective: I will replace the NaN with a large number, but tread carefully,\n')
fprintf('evaluate_planner_objective: check your model, and watch out for strange results.\n')
end
oo_.mean(isnan(oo_.mean)) = options_.huge_number;
oo_.var(isnan(oo_.var)) = options_.huge_number;
Ey = oo_.mean;
Eyhat = Ey - ys(dr.order_var(nstatic+(1:nspred)));
Eyhatyhat = oo_.var(:);
Euu = M_.Sigma_e(:);
EU = U + Uy*gy*Eyhat + 0.5*((Uyygygy + Uy*gyy)*Eyhatyhat + (Uyygugu + Uy*guu)*Euu + Uy*gss);
EW = EU/(1-beta);
planner_objective_value.unconditional = EW;
%% Conditional welfare starting from the non-stochastic steady-state (i) with Lagrange multipliers set to their steady-state value (ii) with Lagrange multipliers set to 0
Wbar = U/(1-beta);
Wy = Uy*gy/(eye(nspred)-beta*Gy);
Wu = Uy*gu + beta*Wy*Gu;
if isempty(options_.qz_criterium)
options_.qz_criterium = 1+1e-6;
end
%solve Lyapunuv equation Wyy=gy'*Uyy*gy+Uy*gyy+beta*Wy*Gyy+beta*Gy'Wyy*Gy
Wyy = reshape(lyapunov_symm(sqrt(beta)*Gy',reshape(Uyygygy + Uy*gyy + beta*Wy*Gyy,nspred,nspred),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 3, options_.debug),1,nspred*nspred);
Wyygugu = A_times_B_kronecker_C(Wyy,Gu,Gu);
Wyygugy = A_times_B_kronecker_C(Wyy,Gu,Gy);
Wuu = Uyygugu + Uy*guu + beta*(Wyygugu + Wy*Guu);
Wss = (Uy*gss + beta*(Wy*Gss + Wuu*M_.Sigma_e(:)))/(1-beta);
Wyu = Uyygugy + Uy*gyu + beta*(Wyygugy + Wy*Gyu);
[yhat_L_SS,yhat_L_0, u]=get_initial_state(ys,M_,dr,oo_);
Wyu_yu_L_SS = A_times_B_kronecker_C(Wyu,yhat_L_SS,u);
Wyy_yy_L_SS = A_times_B_kronecker_C(Wyy,yhat_L_SS,yhat_L_SS);
Wuu_uu_L_SS = A_times_B_kronecker_C(Wuu,u,u);
W_L_SS = Wbar+Wy*yhat_L_SS+Wu*u+Wyu_yu_L_SS+0.5*(Wss+Wyy_yy_L_SS+Wuu_uu_L_SS);
Wyu_yu_L_0 = A_times_B_kronecker_C(Wyu,yhat_L_0,u);
Wyy_yy_L_0 = A_times_B_kronecker_C(Wyy,yhat_L_0,yhat_L_0);
Wuu_uu_L_0 = A_times_B_kronecker_C(Wuu,u,u);
W_L_0 = Wbar+Wy*yhat_L_0+Wu*u+Wyu_yu_L_0+0.5*(Wss+Wyy_yy_L_0+Wuu_uu_L_0);
planner_objective_value.conditional.steady_initial_multiplier = W_L_SS;
planner_objective_value.conditional.zero_initial_multiplier = W_L_0;
else
%Order k code will go here!
if ~isempty(M_.endo_histval)
fprintf('\nevaluate_planner_objective: order>2 conditional and unconditional welfare calculations not yet supported when an histval block is provided\n')
else
fprintf('\nevaluate_planner_objective: order>2 conditional welfare with initial Lagrange multipliers set to zero and unconditional welfare calculations not yet supported\n')
planner_objective_value.conditional.steady_initial_multiplier = k_order_welfare(dr, M_, options_);
planner_objective_value.conditional.zero_initial_multiplier = NaN;
planner_objective_value.unconditional = NaN;
end
return
var_list = M_.endo_names(dr.order_var(nstatic+(1:nspred)));
if options_.pruning
fprintf('evaluate_planner_objective: pruning option is not supported and will be ignored\n')
end
oo_=disp_th_moments(dr,var_list,M_,options_,oo_);
if ~old_noprint
options_.noprint = 0;
end
end
elseif options_.discretionary_policy
ys = oo_.dr.ys;
planner_objective_value = struct('conditional', struct('zero_initial_multiplier', 0., 'steady_initial_multiplier', 0.), 'unconditional', 0.);
[U,Uy,Uyy] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
Gy = dr.ghx(nstatic+(1:nspred),:);
Gu = dr.ghu(nstatic+(1:nspred),:);
gy(dr.order_var,:) = dr.ghx;
gu(dr.order_var,:) = dr.ghu;
Uyy = full(Uyy);
Uyygygy = A_times_B_kronecker_C(Uyy,gy,gy);
Uyygugu = A_times_B_kronecker_C(Uyy,gu,gu);
Uyygugy = A_times_B_kronecker_C(Uyy,gu,gy);
%% Unconditional welfare
old_noprint = options_.noprint;
if ~old_noprint
options_.noprint = 1;
end
var_list = M_.endo_names(dr.order_var(nstatic+(1:nspred)));
oo_=disp_th_moments(dr,var_list,M_,options_,oo_);
if ~old_noprint
options_.noprint = 0;
if any(isnan(oo_.mean)) || any(any(isnan(oo_.var)))
fprintf('evaluate_planner_objective: encountered NaN moments in the endogenous variables often associated\n')
fprintf('evaluate_planner_objective: with either non-stationary variables or singularity due e.g. including\n')
fprintf('evaluate_planner_objective: the planner objective function (or additive parts of it) in the model.\n')
fprintf('evaluate_planner_objective: I will replace the NaN with a large number, but tread carefully,\n')
fprintf('evaluate_planner_objective: check your model, and watch out for strange results.\n')
end
oo_.mean(isnan(oo_.mean)) = options_.huge_number;
oo_.var(isnan(oo_.var)) = options_.huge_number;
Ey = oo_.mean;
Eyhat = Ey - ys(dr.order_var(nstatic+(1:nspred)));
Eyhatyhat = oo_.var(:);
Euu = M_.Sigma_e(:);
EU = U + Uy*gy*Eyhat + 0.5*((Uyygygy + Uy*gyy)*Eyhatyhat + (Uyygugu + Uy*guu)*Euu + Uy*gss);
EW = EU/(1-beta);
planner_objective_value.unconditional = EW;
%% Conditional welfare starting from the non-stochastic steady-state (i) with Lagrange multipliers set to their steady-state value (ii) with Lagrange multipliers set to 0
Wbar = U/(1-beta);
Wy = Uy*gy/(eye(nspred)-beta*Gy);
Wu = Uy*gu + beta*Wy*Gu;
if isempty(options_.qz_criterium)
options_.qz_criterium = 1+1e-6;
end
%solve Lyapunuv equation Wyy=gy'*Uyy*gy+Uy*gyy+beta*Wy*Gyy+beta*Gy'Wyy*Gy
Wyy = reshape(lyapunov_symm(sqrt(beta)*Gy',reshape(Uyygygy + Uy*gyy + beta*Wy*Gyy,nspred,nspred),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 3, options_.debug),1,nspred*nspred);
Wyygugu = A_times_B_kronecker_C(Wyy,Gu,Gu);
Wyygugy = A_times_B_kronecker_C(Wyy,Gu,Gy);
Wuu = Uyygugu + Uy*guu + beta*(Wyygugu + Wy*Guu);
Wss = (Uy*gss + beta*(Wy*Gss + Wuu*M_.Sigma_e(:)))/(1-beta);
Wyu = Uyygugy + Uy*gyu + beta*(Wyygugy + Wy*Gyu);
[yhat_L_SS,yhat_L_0, u]=get_initial_state(ys,M_,dr,oo_);
Wyu_yu_L_SS = A_times_B_kronecker_C(Wyu,yhat_L_SS,u);
Wyy_yy_L_SS = A_times_B_kronecker_C(Wyy,yhat_L_SS,yhat_L_SS);
Wuu_uu_L_SS = A_times_B_kronecker_C(Wuu,u,u);
W_L_SS = Wbar+Wy*yhat_L_SS+Wu*u+Wyu_yu_L_SS+0.5*(Wss+Wyy_yy_L_SS+Wuu_uu_L_SS);
Wyu_yu_L_0 = A_times_B_kronecker_C(Wyu,yhat_L_0,u);
Wyy_yy_L_0 = A_times_B_kronecker_C(Wyy,yhat_L_0,yhat_L_0);
Wuu_uu_L_0 = A_times_B_kronecker_C(Wuu,u,u);
W_L_0 = Wbar+Wy*yhat_L_0+Wu*u+Wyu_yu_L_0+0.5*(Wss+Wyy_yy_L_0+Wuu_uu_L_0);
planner_objective_value.conditional.steady_initial_multiplier = W_L_SS;
planner_objective_value.conditional.zero_initial_multiplier = W_L_0;
elseif (options_.order == 2 && M_.hessian_eq_zero) || options_.discretionary_policy %linear quadratic problem
[U,Uy,Uyy] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
Gy = dr.ghx(nstatic+(1:nspred),:);
Gu = dr.ghu(nstatic+(1:nspred),:);
gy(dr.order_var,:) = dr.ghx;
gu(dr.order_var,:) = dr.ghu;
Uyy = full(Uyy);
Uyygygy = A_times_B_kronecker_C(Uyy,gy,gy);
Uyygugu = A_times_B_kronecker_C(Uyy,gu,gu);
Uyygugy = A_times_B_kronecker_C(Uyy,gu,gy);
%% Unconditional welfare
old_noprint = options_.noprint;
if ~old_noprint
options_.noprint = 1;
end
var_list = M_.endo_names(dr.order_var(nstatic+(1:nspred)));
oo_=disp_th_moments(dr,var_list,M_,options_,oo_);
if ~old_noprint
options_.noprint = 0;
end
oo_.mean(isnan(oo_.mean)) = options_.huge_number;
oo_.var(isnan(oo_.var)) = options_.huge_number;
Ey = oo_.mean;
Eyhat = Ey - ys(dr.order_var(nstatic+(1:nspred)));
Eyhatyhat = oo_.var(:);
Euu = M_.Sigma_e(:);
EU = U + Uy*gy*Eyhat + 0.5*(Uyygygy*Eyhatyhat + Uyygugu*Euu);
EW = EU/(1-beta);
planner_objective_value.unconditional = EW;
%% Conditional welfare starting from the non-stochastic steady-state
Wbar = U/(1-beta);
Wy = Uy*gy/(eye(nspred)-beta*Gy);
Wu = Uy*gu + beta*Wy*Gu;
%solve Lyapunuv equation Wyy=gy'*Uyy*gy+beta*Gy'Wyy*Gy
Wyy = reshape(lyapunov_symm(sqrt(beta)*Gy',reshape(Uyygygy,nspred,nspred),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 3, options_.debug),1,nspred*nspred);
Wyygugu = A_times_B_kronecker_C(Wyy,Gu,Gu);
Wyygugy = A_times_B_kronecker_C(Wyy,Gu,Gy);
Wuu = Uyygugu + beta*Wyygugu;
Wss = beta*Wuu*M_.Sigma_e(:)/(1-beta);
Wyu = Uyygugy + beta*Wyygugy;
[yhat_L_SS,yhat_L_0, u]=get_initial_state(ys,M_,dr,oo_);
Wyu_yu_L_SS = A_times_B_kronecker_C(Wyu,yhat_L_SS,u);
Wyy_yy_L_SS = A_times_B_kronecker_C(Wyy,yhat_L_SS,yhat_L_SS);
Wuu_uu_L_SS = A_times_B_kronecker_C(Wuu,u,u);
W_L_SS = Wbar+Wy*yhat_L_SS+Wu*u+Wyu_yu_L_SS+0.5*(Wss+Wyy_yy_L_SS+Wuu_uu_L_SS);
Wyu_yu_L_0 = A_times_B_kronecker_C(Wyu,yhat_L_0,u);
Wyy_yy_L_0 = A_times_B_kronecker_C(Wyy,yhat_L_0,yhat_L_0);
Wuu_uu_L_0 = A_times_B_kronecker_C(Wuu,u,u);
W_L_0 = Wbar+Wy*yhat_L_0+Wu*u+Wyu_yu_L_0+0.5*(Wss+Wyy_yy_L_0+Wuu_uu_L_0);
planner_objective_value.conditional.steady_initial_multiplier = W_L_SS;
planner_objective_value.conditional.zero_initial_multiplier = W_L_0;
else
%Order k code will go here!
if ~isempty(M_.endo_histval)
fprintf('\nevaluate_planner_objective: order>2 conditional and unconditional welfare calculations not yet supported when an histval block is provided\n')
else
fprintf('\nevaluate_planner_objective: order>2 conditional welfare with initial Lagrange multipliers set to zero and unconditional welfare calculations not yet supported\n')
planner_objective_value.conditional.steady_initial_multiplier = k_order_welfare(dr, M_, options_);
planner_objective_value.conditional.zero_initial_multiplier = NaN;
planner_objective_value.unconditional = NaN;
end
return
end
oo_.mean(isnan(oo_.mean)) = options_.huge_number;
oo_.var(isnan(oo_.var)) = options_.huge_number;
Ey = oo_.mean;
Eyhat = Ey - ys(dr.order_var(nstatic+(1:nspred)));
Eyhatyhat = oo_.var(:);
Euu = M_.Sigma_e(:);
EU = U + Uy*gy*Eyhat + 0.5*(Uyygygy*Eyhatyhat + Uyygugu*Euu);
EW = EU/(1-beta);
planner_objective_value.unconditional = EW;
%% Conditional welfare starting from the non-stochastic steady-state
Wbar = U/(1-beta);
Wy = Uy*gy/(eye(nspred)-beta*Gy);
Wu = Uy*gu + beta*Wy*Gu;
%solve Lyapunuv equation Wyy=gy'*Uyy*gy+beta*Gy'Wyy*Gy
Wyy = reshape(lyapunov_symm(sqrt(beta)*Gy',reshape(Uyygygy,nspred,nspred),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 3, options_.debug),1,nspred*nspred);
Wyygugu = A_times_B_kronecker_C(Wyy,Gu,Gu);
Wyygugy = A_times_B_kronecker_C(Wyy,Gu,Gy);
Wuu = Uyygugu + beta*Wyygugu;
Wss = beta*Wuu*M_.Sigma_e(:)/(1-beta);
Wyu = Uyygugy + beta*Wyygugy;
[yhat_L_SS,yhat_L_0, u]=get_initial_state(ys,M_,dr,oo_);
Wyu_yu_L_SS = A_times_B_kronecker_C(Wyu,yhat_L_SS,u);
Wyy_yy_L_SS = A_times_B_kronecker_C(Wyy,yhat_L_SS,yhat_L_SS);
Wuu_uu_L_SS = A_times_B_kronecker_C(Wuu,u,u);
W_L_SS = Wbar+Wy*yhat_L_SS+Wu*u+Wyu_yu_L_SS+0.5*(Wss+Wyy_yy_L_SS+Wuu_uu_L_SS);
Wyu_yu_L_0 = A_times_B_kronecker_C(Wyu,yhat_L_0,u);
Wyy_yy_L_0 = A_times_B_kronecker_C(Wyy,yhat_L_0,yhat_L_0);
Wuu_uu_L_0 = A_times_B_kronecker_C(Wuu,u,u);
W_L_0 = Wbar+Wy*yhat_L_0+Wu*u+Wyu_yu_L_0+0.5*(Wss+Wyy_yy_L_0+Wuu_uu_L_0);
planner_objective_value.conditional.steady_initial_multiplier = W_L_SS;
planner_objective_value.conditional.zero_initial_multiplier = W_L_0;
end
if ~options_.noprint
if options_.ramsey_policy
if oo_.gui.ran_perfect_foresight
fprintf('\nSimulated value of unconditional welfare: %10.8f\n', planner_objective_value.unconditional)
fprintf('\nSimulated value of conditional welfare: %10.8f\n', planner_objective_value.conditional)
fprintf('\nSimulated value of unconditional welfare: %10.8f\n', planner_objective_value.unconditional)
fprintf('\nSimulated value of conditional welfare: %10.8f\n', planner_objective_value.conditional)
else
fprintf('\nApproximated value of unconditional welfare: %10.8f\n', planner_objective_value.unconditional)
fprintf('\nApproximated value of conditional welfare:\n')
fprintf(' - with initial Lagrange multipliers set to 0: %10.8f\n', planner_objective_value.conditional.zero_initial_multiplier)
fprintf(' - with initial Lagrange multipliers set to steady state: %10.8f\n\n', planner_objective_value.conditional.steady_initial_multiplier)
fprintf('\nApproximated value of unconditional welfare: %10.8f\n', planner_objective_value.unconditional)
fprintf('\nApproximated value of conditional welfare:\n')
fprintf(' - with initial Lagrange multipliers set to 0: %10.8f\n', planner_objective_value.conditional.zero_initial_multiplier)
fprintf(' - with initial Lagrange multipliers set to steady state: %10.8f\n\n', planner_objective_value.conditional.steady_initial_multiplier)
end
elseif options_.discretionary_policy
fprintf('\nApproximated value of unconditional welfare with discretionary policy: %10.8f\n', planner_objective_value.unconditional)
fprintf('\nApproximated value of conditional welfare with discretionary policy:\n')
fprintf(' - with initial Lagrange multipliers set to 0: %10.8f\n', planner_objective_value.conditional.zero_initial_multiplier)
fprintf(' - with initial Lagrange multipliers set to steady state: %10.8f\n\n', planner_objective_value.conditional.steady_initial_multiplier)
fprintf('\nApproximated value of unconditional welfare with discretionary policy: %10.8f\n', planner_objective_value.unconditional)
fprintf('\nApproximated value of conditional welfare with discretionary policy:\n')
fprintf(' - with initial Lagrange multipliers set to 0: %10.8f\n', planner_objective_value.conditional.zero_initial_multiplier)
fprintf(' - with initial Lagrange multipliers set to steady state: %10.8f\n\n', planner_objective_value.conditional.steady_initial_multiplier)
end
end
......@@ -339,8 +337,8 @@ yhat_L_SS = ys;
% initialize Lagrange multipliers to 0 in yhat_L_0
yhat_L_0 = zeros(M_.endo_nbr,1);
if ~isempty(M_.aux_vars)
mult_indicator=([M_.aux_vars(:).type]==6);
mult_indices=[M_.aux_vars(mult_indicator).endo_index];
mult_indicator=([M_.aux_vars(:).type]==6);
mult_indices=[M_.aux_vars(mult_indicator).endo_index];
else
mult_indices=[];
end
......@@ -357,7 +355,7 @@ yhat_L_SS = yhat_L_SS(dr.order_var(M_.nstatic+(1:M_.nspred)),1)-ys(dr.order_var(
if ~isempty(M_.det_shocks)
if ~all(oo_.exo_simul(1,:)==0)
fprintf(['\nevaluate_planner_objective: oo_.exo_simul contains simulated values for the initial period.\n'...
'evaluate_planner_objective: Dynare will ignore them and use the provided initial condition.\n'])
'evaluate_planner_objective: Dynare will ignore them and use the provided initial condition.\n'])
end
u =oo_.exo_steady_state;
periods=[M_.det_shocks(:).periods];
......@@ -367,14 +365,14 @@ if ~isempty(M_.det_shocks)
end
if any(periods>1)
fprintf(['\nevaluate_planner_objective: Shock values for periods not contained in the initial information set (t=1) have been provided.\n' ...
'evaluate_planner_objective: Note that they will be ignored.\n'])
'evaluate_planner_objective: Note that they will be ignored.\n'])
end
shock_indices=find(periods==1);
shock_indices=find(periods==1);
if any([M_.det_shocks(shock_indices).multiplicative])
fprintf(['\nevaluate_planner_objective: Shock values need to be specified as additive.\n'])
fprintf(['\nevaluate_planner_objective: Shock values need to be specified as additive.\n'])
end
u([M_.det_shocks(shock_indices).exo_id])=[M_.det_shocks(shock_indices).value];
else
u = oo_.exo_simul(1,:)'; %first value of simulation series (set by simult.m if periods>0), 1 otherwise
u = oo_.exo_simul(1,:)'; %first value of simulation series (set by simult.m if periods>0), 1 otherwise
end
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