I am trying to simulate the Bansal/Yaron (2004) long-run risk model, and have it set up with their equations and parameter values. Although the model is simulated at monthly frequency, according to them the simulations should imply an annualized first-order autocorrelation of consumption of around .49. Yet when I simulate it using the code below, consumption has a first-order autocorrelation of only .03. I’d be really grateful if anyone could perhaps suggest where I am going wrong. Thanks.

var x y vol rf ;

varexo e_x e_u e_v ;

parameters rho sigma_x mu_y mu_v v sigma_v ;

mu_y = 0.0015;

rho = 0.979;

sigma_x = .044;

mu_v = 0.00788;

v = 0.987;

sigma_v = 0.0000023;

phi=3;

model;

x=rho*x(-1) + sigma_x*vol(-1)*e_x;
y=mu_y + x(-1) + vol(-1) e_u;
vol^2=mu_v^2+v(vol(-1)^2-mu_v^2)+sigma_v*e_v;

(1+y(+1))^(-1/2)*(1+rf)*.99=1;

end;

initval;

x=0;

y=mu_y;

vol=mu_v;

end;

steady;

shocks;

var e_x;

stderr 1;

var e_u;

stderr 1;

var e_v;

stderr 1;

var e_d;

stderr 1;

end;

stoch_simul(periods=15000, drop=100, irf=30, order=3, pruning, nograph);