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Merge branch 'evaluate_planner' into 'master' 

evaluate_planner_objective.m: correctly rely on lag/lead structure for perfect foresight

See merge request Dynare/dynare!1890
trust-region-mex
Sébastien Villemot 2021-07-23 14:01:22 +00:00
parent 5d5fefca25 e09d215964
commit b34be496c5
2 changed files with 42 additions and 44 deletions
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81
matlab/evaluate_planner_objective.m
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@ -6,8 +6,8 @@ function planner_objective_value = evaluate_planner_objective(M_,options_,oo_)
% oo_: (structure) output results
% OUTPUT
% planner_objective_value (double)
%
%Returns a vector containing first order or second-order approximations of
%
%Returns a vector containing first order or second-order approximations of
% - the unconditional expectation of the planner's objective function
% - the conditional expectation of the planner's objective function starting from the non-stochastic steady state and allowing for future shocks
% depending on the value of options_.order.
@ -52,7 +52,7 @@ function planner_objective_value = evaluate_planner_objective(M_,options_,oo_)
% W(y,0,1) = Wbar + 0.5*Wss
% 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:
% 1) the second-order derivatives of the policy and transition functions h and g are zero.
% 1) the second-order derivatives of the policy and transition functions h and g are zero.
% 2) the unconditional expectation of states coincides with its steady-state, which entails E(yhat) = 0
% Therefore, the unconditional welfare can now be approximated as
% E(W) = (1 - beta)^{-1} ( Ubar + 0.5 ( U_xx h_y^2 E(yhat^2) + U_xx h_u^2 E(u^2) )
@ -91,47 +91,47 @@ planner_objective_value = zeros(2,1);
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),oo_.exo_simul(T,:), M_.params);
[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:-1:2
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(1) = EW;
planner_objective_value(2) = W;
else
ys = oo_.dr.ys;
ys = oo_.dr.ys;
if options_.order == 1 || M_.hessian_eq_zero
[U] = feval([M_.fname '.objective.static'],ys,zeros(1,exo_nbr), M_.params);
planner_objective_value(1) = U/(1-beta);
planner_objective_value(2) = U/(1-beta);
planner_objective_value(2) = U/(1-beta);
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);
%% Unconditional welfare
old_noprint = options_.noprint;
if ~old_noprint
options_.noprint = 1;
end
@ -143,25 +143,25 @@ if options_.ramsey_policy
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)));
var_corr = Eyhat*Eyhat';
Eyhatyhat = oo_.var(:) + var_corr(:);
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);
%% Conditional welfare starting from the non-stochastic steady-state
Wbar = U/(1-beta);
Wy = Uy*gy/(eye(nspred)-beta*Gy);
if isempty(options_.qz_criterium)
options_.qz_criterium = 1+1e-6;
end
@ -171,7 +171,7 @@ if options_.ramsey_policy
Wuu = Uyygugu + Uy*guu + beta*(Wyygugu + Wy*Guu);
Wss = (Uy*gss + beta*(Wy*Gss + Wuu*M_.Sigma_e(:)))/(1-beta);
W = Wbar + 0.5*Wss;
planner_objective_value(1) = EW;
planner_objective_value(2) = W;
else
@ -184,23 +184,23 @@ if options_.ramsey_policy
end
elseif options_.discretionary_policy
ys = oo_.dr.ys;
[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);
%% Unconditional welfare
old_noprint = options_.noprint;
if ~old_noprint
options_.noprint = 1;
end
@ -209,36 +209,33 @@ elseif options_.discretionary_policy
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)));
var_corr = Eyhat*Eyhat';
Eyhatyhat = oo_.var(:) + var_corr(:);
Euu = M_.Sigma_e(:);
EU = U + Uy*gy*Eyhat + 0.5*(Uyygygy*Eyhatyhat + Uyygugu*Euu);
EW = EU/(1-beta);
%% Conditional welfare starting from the non-stochastic steady-state
Wbar = U/(1-beta);
Wy = Uy*gy/(eye(nspred)-beta*Gy);
if isempty(options_.qz_criterium)
options_.qz_criterium = 1+1e-6;
end
%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);
Wuu = Uyygugu + beta*Wyygugu;
Wss = beta*Wuu*M_.Sigma_e(:)/(1-beta);
W = Wbar + 0.5*Wss;
planner_objective_value(1) = EW;
planner_objective_value(2) = W;
end
@ -250,7 +247,7 @@ if ~options_.noprint
else
fprintf('\nApproximated value of unconditional welfare: %10.8f\n', planner_objective_value(1))
fprintf('\nApproximated value of conditional welfare: %10.8f\n', planner_objective_value(2))
end
end
elseif options_.discretionary_policy
fprintf('\nApproximated value of unconditional welfare with discretionary policy: %10.8f\n', planner_objective_value(1))
fprintf('\nApproximated value of conditional welfare with discretionary policy: %10.8f\n', planner_objective_value(2))

5
tests/optimal_policy/Ramsey/ramsey_histval.mod
View File

@ -23,7 +23,7 @@ r=1;
end;
histval;
r(0)=1;
a(0)=-1;
end;
steady_state_model;
@ -42,4 +42,5 @@ end;
options_.dr_display_tol=0;
planner_objective(ln(c)-phi*((n^(1+gamma))/(1+gamma)));
ramsey_model(planner_discount=0.99,instruments=(r));
stoch_simul(order=1,periods=500);
stoch_simul(order=1);
evaluate_planner_objective;