// simplest model: power utility + representative + no labor

var S c C R_f;

varexo shock;

parameters beta gamma mu sigma rho;

beta = 0.93;
gamma = 3;
mu = 0.02;
sigma = 0.11;
rho = 1;
model;

// Exogenous dividend process

c = rho*c(-1) + mu + sigma*shock;

C = exp(c);

// Euler equation for equity premium
1 = beta*(C(+1)/C)^(-gamma)*(S(+1)+C(+1))/S;

// Define gross risk-free rate
1 = (beta*(C(+1)/C)^(-gamma))*R_f;

end;

initval;
c = 0;
end;

steady_state_model;
c = 0;
C = exp(c);
S = C/(1/beta-1);
R_f = 1/beta;
end;

steady(nocheck);
check;


shocks;
var shock; stderr 1;
end;

set_dynare_seed('default')
stoch_simul(order=2,periods=10000,drop=0,irf=0) S c C R_f;