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+sigma*eps;

re=(1+gc(+1))

*(1+v(+1))/v;*

rf=-1+ 1/(beta(1+gc(+1))^(-theta));

rf=-1+ 1/(beta

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);