Merge branch 'perfect_foresight_planner' into 'master'
Ref. #1680: perfect foresight See merge request Dynare/dynare!1833time-shift
Sébastien Villemot
commit
ea41f19008
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@ -49,6 +49,8 @@ function planner_objective_value = evaluate_planner_objective(M_,options_,oo_)
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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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% As for the conditional welfare, the second-order formula above is still valid, but the derivatives of W no longer contain any second-order derivatives of the policy and transition functions h and g.
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% In the deterministic case, resorting to approximations for welfare is no longer required as it is possible to simulate the model given initial conditions for pre-determined variables and terminal conditions for forward-looking variables, whether these initial and terminal conditions are explicitly or implicitly specified. Assuming that the number of simulated periods is high enough for the new steady-state to be reached, the new unconditional welfare is thus the last period's welfare. As for the conditional welfare, it can be derived using backward recursions on the equation W = U + beta*W(+1) starting from the final unconditional steady-state welfare.
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% INPUTS
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% M_: (structure) model description
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% options_: (structure) options
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@ -81,87 +83,101 @@ nstatic = M_.nstatic;
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nspred = M_.nspred;
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beta = get_optimal_policy_discount_factor(M_.params, M_.param_names);
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ys = oo_.dr.ys;
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planner_objective_value = zeros(2,1);
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if options_.ramsey_policy
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if options_.order == 1
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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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elseif options_.order == 2
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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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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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EW = U_term/(1-beta);
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W = EW;
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for t=T:-1:2
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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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var_list = M_.endo_names(dr.order_var(nstatic+(1:nspred)));
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[info, oo_, options_] = stoch_simul(M_, options_, oo_, var_list); %get decision rules and moments
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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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%solve Lyapunuv equation Wyy=gy'*Uyy*gy+Uy*gyy+beta*Wy*Gyy+beta*Gy'Wyy*Gy
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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);
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Wyygugu = A_times_B_kronecker_C(Wyy,Gu,Gu);
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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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%Order k code will go here!
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fprintf('\nevaluate_planner_objective: order>2 not yet supported\n')
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planner_objective_value(1) = NaN;
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planner_objective_value(2) = NaN;
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return
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ys = oo_.dr.ys;
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if options_.order == 1
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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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elseif options_.order == 2
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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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var_list = M_.endo_names(dr.order_var(nstatic+(1:nspred)));
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[info, oo_, options_] = stoch_simul(M_, options_, oo_, var_list); %get decision rules and moments
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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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%solve Lyapunuv equation Wyy=gy'*Uyy*gy+Uy*gyy+beta*Wy*Gyy+beta*Gy'Wyy*Gy
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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);
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Wyygugu = A_times_B_kronecker_C(Wyy,Gu,Gu);
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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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%Order k code will go here!
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fprintf('\nevaluate_planner_objective: order>2 not yet supported\n')
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planner_objective_value(1) = NaN;
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planner_objective_value(2) = NaN;
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return
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end
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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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@ -221,11 +237,15 @@ elseif options_.discretionary_policy
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end
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if ~options_.noprint
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if options_.ramsey_policy
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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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if oo_.gui.ran_perfect_foresight
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fprintf('\nSimulated value of unconditional welfare: %10.8f\n', planner_objective_value(1))
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fprintf('\nSimulated value of conditional welfare: %10.8f\n', planner_objective_value(2))
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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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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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end
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end
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@ -580,6 +580,9 @@ MFILES = histval_initval_file/ramst_initval_file_data.m
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optimal_policy/neo_growth_ramsey.m.trs: optimal_policy/neo_growth.m.trs
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optimal_policy/neo_growth_ramsey.o.trs: optimal_policy/neo_growth.o.trs
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optimal_policy/neo_growth_ramsey_foresight.m.trs: optimal_policy/neo_growth_foresight.m.trs
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optimal_policy/neo_growth_ramsey_foresight.o.trs: optimal_policy/neo_growth_foresight.o.trs
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example1_use_dll.m.trs: example1.m.trs
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example1_use_dll.o.trs: example1.o.trs
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@ -1185,6 +1188,8 @@ EXTRA_DIST = \
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observation_trends_and_prefiltering/Trend_model_calib_no_prefilter_common.inc \
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observation_trends_and_prefiltering/Trend_load_data_common.inc \
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observation_trends_and_prefiltering/Trend_no_prefilter_conditional_forecast.inc \
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optimal_policy/neo_growth_common.inc \
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optimal_policy/neo_growth_ramsey_common.inc \
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optimal_policy/Ramsey/oo_ramsey_policy_initval.mat \
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optimizers/optimizer_function_wrapper.m \
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optimizers/fs2000.common.inc \
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@ -21,34 +21,7 @@
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* It is called by neo_growth_ramsey.mod to compare by-hand calculations of unconditional
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* and conditional welfares and the output of the evaluate_planner_objective function.
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*/
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var U k z c W;
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varexo e;
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parameters beta gamma alpha delta rho s;
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beta = 0.987;
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gamma = 1;
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delta = 0.012;
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alpha = 0.4;
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rho = 0.95;
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s = 0.007;
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model;
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c^(-gamma)=beta*c(+1)^(-gamma)*(alpha*exp(z(+1))*k^(alpha-1)+1-delta);
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W = U + beta*W(+1);
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k=exp(z)*k(-1)^(alpha)-c+(1-delta)*k(-1);
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z=rho*z(-1)+s*e;
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U=ln(c);
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end;
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steady_state_model;
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k = ((1/beta-(1-delta))/alpha)^(1/(alpha-1));
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c = k^alpha-delta*k;
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z = 0;
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U = ln(c);
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W = U/(1-beta);
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end;
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@#include "neo_growth_common.inc"
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shocks;
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var e;
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@ -57,4 +30,5 @@ end;
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steady;
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resid;
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stoch_simul(order=2, irf=0);
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@ -0,0 +1,28 @@
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var U k z c W;
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varexo e;
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parameters beta gamma alpha delta rho s;
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beta = 0.987;
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gamma = 1;
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delta = 0.012;
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alpha = 0.4;
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rho = 0.95;
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s = 0.007;
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model;
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c^(-gamma)=beta*c(+1)^(-gamma)*(alpha*exp(z(+1))*k^(alpha-1)+1-delta);
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W = U + beta*W(+1);
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k=exp(z)*k(-1)^(alpha)-c+(1-delta)*k(-1);
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z=rho*z(-1)+s*e;
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U=ln(c);
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end;
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steady_state_model;
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k = ((1/beta-(1-delta))/alpha)^(1/(alpha-1));
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c = k^alpha-delta*k;
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z = 0;
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U = ln(c);
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W = U/(1-beta);
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end;
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@ -0,0 +1,41 @@
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/*
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* Copyright (C) 2021 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 <http://www.gnu.org/licenses/>.
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*/
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/*
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* This file simulates the neo-classical growth model in a perfect foresight framework.
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* It is called by neo_growth_ramsey_foresight.mod to compare by-hand calculations of unconditional
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* and conditional welfares and the output of the evaluate_planner_objective function.
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*/
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@#include "neo_growth_common.inc"
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initval;
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z = 0;
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end;
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steady;
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shocks;
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var e;
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periods 1;
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values 1;
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end;
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resid;
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perfect_foresight_setup(periods=200);
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perfect_foresight_solver;
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@ -22,43 +22,13 @@
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* and compares them to a by-hand assessment stemming from the results the model neo_growth.mod incur.
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*/
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var k z c;
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varexo e;
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parameters beta gamma alpha delta rho s;
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beta = 0.987;
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gamma = 1;
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delta = 0.012;
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alpha = 0.4;
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rho = 0.95;
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s = 0.007;
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model;
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k=exp(z)*k(-1)^(alpha)-c+(1-delta)*k(-1);
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z=rho*z(-1)+s*e;
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end;
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steady_state_model;
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z = 0;
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end;
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@#include "neo_growth_ramsey_common.inc"
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shocks;
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var e;
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stderr 1;
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end;
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planner_objective ln(c);
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ramsey_model(instruments=(k,c), planner_discount=beta);
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initval;
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k = ((1/beta-(1-delta))/alpha)^(1/(alpha-1));
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c = k^alpha-delta*k;
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end;
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steady;
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resid;
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stoch_simul(order=2, irf=0);
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planner_objective_value = evaluate_planner_objective(M_, options_, oo_);
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@ -0,0 +1,32 @@
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var k z c;
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varexo e;
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parameters beta gamma alpha delta rho s;
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beta = 0.987;
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gamma = 1;
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delta = 0.012;
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alpha = 0.4;
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rho = 0.95;
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s = 0.007;
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model;
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k=exp(z)*k(-1)^(alpha)-c+(1-delta)*k(-1);
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z=rho*z(-1)+s*e;
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end;
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steady_state_model;
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z = 0;
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||||
end;
|
||||
|
||||
planner_objective ln(c);
|
||||
ramsey_model(instruments=(k,c), planner_discount=beta);
|
||||
|
||||
initval;
|
||||
k = ((1/beta-(1-delta))/alpha)^(1/(alpha-1));
|
||||
c = k^alpha-delta*k;
|
||||
end;
|
||||
|
||||
steady;
|
||||
resid;
|
||||
|
|
@ -0,0 +1,53 @@
|
|||
/*
|
||||
* Copyright (C) 2021 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 <http://www.gnu.org/licenses/>.
|
||||
*/
|
||||
/*
|
||||
* This file simulates a perfect-foresight version of the neo-classical growth model.
|
||||
* It assesses the conditional and unconditional welfares computed by the evaluate_planner_objective function
|
||||
* and compares them to a by-hand assessment stemming from the results of the model neo_growth_foresight.mod
|
||||
*/
|
||||
|
||||
@#include "neo_growth_ramsey_common.inc"
|
||||
|
||||
shocks;
|
||||
var e;
|
||||
periods 1;
|
||||
values 1;
|
||||
end;
|
||||
|
||||
perfect_foresight_setup(periods=200);
|
||||
perfect_foresight_solver;
|
||||
|
||||
planner_objective_value = evaluate_planner_objective(M_, options_, oo_);
|
||||
|
||||
if ~exist('neo_growth_foresight_results.mat','file');
|
||||
error('neo_growth_foresight must be run first');
|
||||
end;
|
||||
|
||||
oo1 = load('neo_growth_foresight_results','oo_');
|
||||
M1 = load('neo_growth_foresight_results','M_');
|
||||
options1 = load('neo_growth_foresight_results','options_');
|
||||
cond_W_hand = oo1.oo_.endo_simul(strmatch('W',M1.M_.endo_names,'exact'),2);
|
||||
unc_W_hand = oo1.oo_.endo_simul(strmatch('W',M1.M_.endo_names,'exact'),end);
|
||||
|
||||
if abs((unc_W_hand - planner_objective_value(1))/unc_W_hand) > 1e-6;
|
||||
error('Inaccurate unconditional welfare assessment');
|
||||
end;
|
||||
if abs((cond_W_hand - planner_objective_value(2))/cond_W_hand) > 1e-6;
|
||||
error('Inaccurate conditional welfare assessment');
|
||||
end;
|
||||
Loading…
Reference in New Issue