Commit 34bcc9a2 authored by Stéphane Adjemian's avatar Stéphane Adjemian
Browse files

Added burnside asset pricing model in tests/ep.

parent 59247ddc
addpath ..
var y x;
varexo e;
parameters beta theta rho xbar;
xbar = 0.0179;
rho = -0.139;
theta = -1.5;
beta = 0.95;
model(use_dll);
1 = beta*exp(theta*x(+1))*(1+y(+1))/y;
x = (1-rho)*xbar + rho*x(-1)+e;
end;
shocks;
var e; stderr 0.0348;
end;
initval;
x = xbar;
y = beta*exp(theta*xbar)/(1-beta*exp(theta*xbar));
end;
resid(1);
steady;
if beta*exp(theta*xbar+.5*theta^2*M_.Sigma_e/(1-rho)^2)>1-eps
disp('The model doesn''t have a solution!')
return
end
set_dynare_seed('default');
stoch_simul(order=1,irf=0,periods=5000);
y_perturbation_1 = oo_.endo_simul(1,:)';
set_dynare_seed('default');
stoch_simul(order=2,irf=0,periods=5000);
y_perturbation_2 = oo_.endo_simul(1,:)';
set_dynare_seed('default');
stoch_simul(order=2,pruning,irf=0,periods=5000);
y_perturbation_2_pruning = oo_.endo_simul(1,:)';
options_.maxit_ = 100;
options_.ep.verbosity = 0;
options_.ep.stochastic.order = 0;
options_.ep.stochastic.nodes = 2;
options_.console_mode = 0;
set_dynare_seed('default');
ts = extended_path([],5000);
options_.ep.stochastic.order = 2;
set_dynare_seed('default');
ts1_4 = extended_path([],5000);
set_dynare_seed('default');
ytrue=exact_solution(M_,oo_,800);
disp('True mean and standard deviation')
disp(mean(ytrue(101:end)))
disp(sqrt(var(ytrue(101:end))))
disp('Order 1 perturbation mean and standard deviation')
disp(mean(y_perturbation_1(101:end)))
disp(sqrt(var(y_perturbation_1(101:end))))
disp('Order 2 perturbation mean and standard deviation')
disp(mean(y_perturbation_2(101:end)))
disp(sqrt(var(y_perturbation_2(101:end))))
disp('Order 2 perturbation (with pruning) mean and standard deviation')
disp(mean(y_perturbation_2_pruning(101:end)))
disp(sqrt(var(y_perturbation_2_pruning(101:end))))
disp('Extended path mean and standard deviation')
disp(mean(ts(1,101:end)))
disp(sqrt(var(ts(1,101:end))))
disp('Stochastic extended path mean and standard deviation')
disp(mean(ts1_4(1,101:end)))
disp(sqrt(var(ts1_4(1,101:end))))
disp('Accuracy error (order 1 perturbation)')
disp(mean(100*abs(y_perturbation_1-ytrue')./ytrue'));
disp(max(100*abs(y_perturbation_1-ytrue')./ytrue'));
disp('Accuracy error (order 2 perturbation)')
disp(mean(100*abs(y_perturbation_2-ytrue')./ytrue'));
disp(max(100*abs(y_perturbation_2-ytrue')./ytrue'));
disp('Accuracy error (order 2 perturbation with pruning)')
disp(100*mean(abs(y_perturbation_2_pruning-ytrue')./ytrue'));
disp(100*max(abs(y_perturbation_2_pruning-ytrue')./ytrue'));
disp('Accuracy error (extended path)')
disp(mean(100*abs(ts(1,:)'-ytrue')./ytrue'));
disp(max(100*abs(ts(1,:)'-ytrue')./ytrue'));
disp('Accuracy error (stochastic extended path)')
disp(mean(100*abs(ts1_4(1,:)'-ytrue')./ytrue'));
disp(max(100*abs(ts1_4(1,:)'-ytrue')./ytrue'));
function y=exact_solution(M,oo,n)
beta = M.params(1);
theta = M.params(2);
rho = M.params(3);
xbar = M.params(4);
sigma2 = M.Sigma_e;
if beta*exp(theta*xbar+.5*theta^2*sigma2/(1-rho)^2)>1-eps
disp('The model doesn''t have a solution!')
return
end
i = 1:n;
a = theta*xbar*i+(theta^2*sigma2)/(2*(1-rho)^2)*(i-2*rho*(1-rho.^i)/(1-rho)+rho^2*(1-rho.^(2*i))/(1-rho^2));
b = theta*rho*(1-rho.^i)/(1-rho);
x = oo.endo_simul(2,:);
xhat = x-xbar;
n2 = size(x,2);
y = zeros(1,n2);
for j=1:n2
y(j) = sum(beta.^i.*exp(a+b*xhat(j)));
end
disp(sum(beta.^i.*exp(theta*xbar*i)))
disp(sum(beta.^i.*exp(a)))
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