I am trying to estimate the equity premium predicted by the simple Lucas Tree Model. I have risk aversion of 5, standard deviation of consumption growth of 6%, and trend consumption growth of 3%. v is the price-dividend ratio; re is the gross return on equity (paying consumption as dividend) and rf the net risk free rate (from basic Euler equation.)
To get the gross equity return, I solve for the price-dividend ratio and use a formula that converts this to gross return (as in pg 57-58 of the NYU Practicing Dynare Guide).
My problem is that the equity premium comes out as -7% for pretty reasonable values; in addition the premium falls as risk aversion rises. I’m fairly new to Dynare and would be extremely grateful for any guidance of what I’m doing wrong. My code is below:
var gc v rf re ep ;
varexo eps ;
parameters beta theta sigma ;
beta = .99;
theta = 5 ;
sigma=.06;
model;
v = beta*(exp(gc(+1)))^(1-theta)(1+v(+1));
gc=.03+sigmaeps;
re=(1+gc(+1))(1+v(+1))/v;
rf=-1+ 1/(beta(1+gc(+1))^(-theta));
ep=re-1-rf;
end;
initval;
gc=.03;
re=1.2;
v=9;
ep=.015;
end;
shocks;
var eps; stderr 1;
end;
steady;
check;
stoch_simul(periods=5500, irf=30, order=3, nograph);