diff --git a/matlab/evaluate_planner_objective.m b/matlab/evaluate_planner_objective.m
index 7b816a07d250f655c75d25250d760c1c34943415..e096c6c6353e13c64f57f7372a0424e8395c7e08 100644
--- a/matlab/evaluate_planner_objective.m
+++ b/matlab/evaluate_planner_objective.m
@@ -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
-
+