evaluate_planner_objective.m: correctly rely on lag/lead structure for perfect foresight
Also cosmetic changes to indentationtrust-region-mex
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@ -6,8 +6,8 @@ function planner_objective_value = evaluate_planner_objective(M_,options_,oo_)
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% oo_: (structure) output results
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% OUTPUT
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% planner_objective_value (double)
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%
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%Returns a vector containing first order or second-order approximations of
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%
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%Returns a vector containing first order or second-order approximations of
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% - the unconditional expectation of the planner's objective function
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% - the conditional expectation of the planner's objective function starting from the non-stochastic steady state and allowing for future shocks
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% depending on the value of options_.order.
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@ -52,7 +52,7 @@ function planner_objective_value = evaluate_planner_objective(M_,options_,oo_)
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% W(y,0,1) = Wbar + 0.5*Wss
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% In the discretionary case, the model is assumed to be linear and the utility is assumed to be linear-quadratic. This changes 2 aspects of the results delinated above:
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% 1) the second-order derivatives of the policy and transition functions h and g are zero.
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% 1) the second-order derivatives of the policy and transition functions h and g are zero.
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% 2) the unconditional expectation of states coincides with its steady-state, which entails E(yhat) = 0
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% Therefore, the unconditional welfare can now be approximated as
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% E(W) = (1 - beta)^{-1} ( Ubar + 0.5 ( U_xx h_y^2 E(yhat^2) + U_xx h_u^2 E(u^2) )
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@ -91,47 +91,47 @@ planner_objective_value = zeros(2,1);
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if options_.ramsey_policy
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if oo_.gui.ran_perfect_foresight
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T = size(oo_.endo_simul,2);
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[U_term] = feval([M_.fname '.objective.static'],oo_.endo_simul(:,T),oo_.exo_simul(T,:), M_.params);
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[U_term] = feval([M_.fname '.objective.static'],oo_.endo_simul(:,T-M_.maximum_lead),oo_.exo_simul(T-M_.maximum_lead,:), M_.params);
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EW = U_term/(1-beta);
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W = EW;
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for t=T:-1:2
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for t=T-M_.maximum_lead:-1:1+M_.maximum_lag
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[U] = feval([M_.fname '.objective.static'],oo_.endo_simul(:,t),oo_.exo_simul(t,:), M_.params);
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W = U + beta*W;
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end
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planner_objective_value(1) = EW;
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planner_objective_value(2) = W;
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else
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ys = oo_.dr.ys;
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ys = oo_.dr.ys;
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if options_.order == 1 || M_.hessian_eq_zero
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[U] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
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planner_objective_value(1) = U/(1-beta);
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planner_objective_value(2) = U/(1-beta);
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planner_objective_value(2) = U/(1-beta);
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elseif options_.order == 2 && ~M_.hessian_eq_zero
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[U,Uy,Uyy] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
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Gy = dr.ghx(nstatic+(1:nspred),:);
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Gu = dr.ghu(nstatic+(1:nspred),:);
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Gyy = dr.ghxx(nstatic+(1:nspred),:);
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Gyu = dr.ghxu(nstatic+(1:nspred),:);
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Guu = dr.ghuu(nstatic+(1:nspred),:);
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Gss = dr.ghs2(nstatic+(1:nspred),:);
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gy(dr.order_var,:) = dr.ghx;
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gu(dr.order_var,:) = dr.ghu;
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gyy(dr.order_var,:) = dr.ghxx;
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gyu(dr.order_var,:) = dr.ghxu;
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guu(dr.order_var,:) = dr.ghuu;
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gss(dr.order_var,:) = dr.ghs2;
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Uyy = full(Uyy);
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Uyygygy = A_times_B_kronecker_C(Uyy,gy,gy);
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Uyygugu = A_times_B_kronecker_C(Uyy,gu,gu);
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%% Unconditional welfare
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old_noprint = options_.noprint;
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if ~old_noprint
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options_.noprint = 1;
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end
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@ -143,25 +143,25 @@ if options_.ramsey_policy
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if ~old_noprint
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options_.noprint = 0;
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end
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oo_.mean(isnan(oo_.mean)) = options_.huge_number;
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oo_.var(isnan(oo_.var)) = options_.huge_number;
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Ey = oo_.mean;
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Eyhat = Ey - ys(dr.order_var(nstatic+(1:nspred)));
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var_corr = Eyhat*Eyhat';
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Eyhatyhat = oo_.var(:) + var_corr(:);
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Euu = M_.Sigma_e(:);
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EU = U + Uy*gy*Eyhat + 0.5*((Uyygygy + Uy*gyy)*Eyhatyhat + (Uyygugu + Uy*guu)*Euu + Uy*gss);
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EW = EU/(1-beta);
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%% Conditional welfare starting from the non-stochastic steady-state
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Wbar = U/(1-beta);
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Wy = Uy*gy/(eye(nspred)-beta*Gy);
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if isempty(options_.qz_criterium)
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options_.qz_criterium = 1+1e-6;
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end
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@ -171,7 +171,7 @@ if options_.ramsey_policy
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Wuu = Uyygugu + Uy*guu + beta*(Wyygugu + Wy*Guu);
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Wss = (Uy*gss + beta*(Wy*Gss + Wuu*M_.Sigma_e(:)))/(1-beta);
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W = Wbar + 0.5*Wss;
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planner_objective_value(1) = EW;
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planner_objective_value(2) = W;
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else
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@ -184,23 +184,23 @@ if options_.ramsey_policy
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end
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elseif options_.discretionary_policy
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ys = oo_.dr.ys;
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[U,Uy,Uyy] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
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Gy = dr.ghx(nstatic+(1:nspred),:);
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Gu = dr.ghu(nstatic+(1:nspred),:);
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gy(dr.order_var,:) = dr.ghx;
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gu(dr.order_var,:) = dr.ghu;
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Uyy = full(Uyy);
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Uyygygy = A_times_B_kronecker_C(Uyy,gy,gy);
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Uyygugu = A_times_B_kronecker_C(Uyy,gu,gu);
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%% Unconditional welfare
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old_noprint = options_.noprint;
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if ~old_noprint
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options_.noprint = 1;
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end
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@ -209,36 +209,33 @@ elseif options_.discretionary_policy
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if ~old_noprint
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options_.noprint = 0;
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end
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oo_.mean(isnan(oo_.mean)) = options_.huge_number;
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oo_.var(isnan(oo_.var)) = options_.huge_number;
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Ey = oo_.mean;
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Eyhat = Ey - ys(dr.order_var(nstatic+(1:nspred)));
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var_corr = Eyhat*Eyhat';
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Eyhatyhat = oo_.var(:) + var_corr(:);
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Euu = M_.Sigma_e(:);
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EU = U + Uy*gy*Eyhat + 0.5*(Uyygygy*Eyhatyhat + Uyygugu*Euu);
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EW = EU/(1-beta);
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%% Conditional welfare starting from the non-stochastic steady-state
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Wbar = U/(1-beta);
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Wy = Uy*gy/(eye(nspred)-beta*Gy);
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if isempty(options_.qz_criterium)
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options_.qz_criterium = 1+1e-6;
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end
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%solve Lyapunuv equation Wyy=gy'*Uyy*gy+beta*Gy'Wyy*Gy
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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);
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Wyygugu = A_times_B_kronecker_C(Wyy,Gu,Gu);
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Wuu = Uyygugu + beta*Wyygugu;
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Wss = beta*Wuu*M_.Sigma_e(:)/(1-beta);
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W = Wbar + 0.5*Wss;
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planner_objective_value(1) = EW;
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planner_objective_value(2) = W;
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end
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@ -250,7 +247,7 @@ if ~options_.noprint
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else
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fprintf('\nApproximated value of unconditional welfare: %10.8f\n', planner_objective_value(1))
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fprintf('\nApproximated value of conditional welfare: %10.8f\n', planner_objective_value(2))
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end
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end
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elseif options_.discretionary_policy
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fprintf('\nApproximated value of unconditional welfare with discretionary policy: %10.8f\n', planner_objective_value(1))
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fprintf('\nApproximated value of conditional welfare with discretionary policy: %10.8f\n', planner_objective_value(2))
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@ -23,7 +23,7 @@ r=1;
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end;
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histval;
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r(0)=1;
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a(0)=-1;
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end;
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steady_state_model;
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@ -42,4 +42,5 @@ end;
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options_.dr_display_tol=0;
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planner_objective(ln(c)-phi*((n^(1+gamma))/(1+gamma)));
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ramsey_model(planner_discount=0.99,instruments=(r));
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stoch_simul(order=1,periods=500);
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stoch_simul(order=1);
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evaluate_planner_objective;
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