Hi,

I have a simple NK model with asset returns. Here is the code. I am not sure how to read the IRF output from Dynare.

For example, in the IRF graph, one standard deviation monetary policy shock(-15 bps quarterly) corresponding to 0.002 increase in log returns. Is this 20 bps changes in return? How to convert to annually? So, 15 bps quarterly ==> 60bps annually for monetary policy shock and 0.002*4 = 0.008 or 80 bps increase in asset return?

Thanks.

Max

var x y y_n div m re_div p_d pi i a;

varexo

//structural shocks

eps_a

eps_i

;

parameters

beta sigma phi

theta delta epsilon mu kappa

i_pi i_x sigma_i rho_i i_bar

rho_a mu_a a_bar sigma_a;

beta =0.98;

sigma =1; // risk aversion

phi =0.35; // Utility parameter on Labor N(t) – Inverse of Frisch labor elasticity

a_bar = 0.0047; // long run growth rate of productivity 0.0047

mu_a =a_bar*(1-rho_a);

rho_a = 0.8; // persistency of log TFP

delta = 1; // leverage ratio

epsilon = 6; // goods aggregation parameter

mu = log(epsilon/(epsilon-1));

theta =0.65; //price dispersion

kappa =(1 - theta )*(1 - theta * beta )*( sigma + phi )/ theta;

i_pi = 1.5; //1.5

i_x = 0.125;

rho_i = 0.63; //interest rates smoothing

i_bar = - log(beta); // constant in the policy rule - make DIS equation stationary & x_ss = 0

sigma_a = 0.1; //0.202 Gourio(2012)

sigma_i = 0.183/(i_x*(1-rho_i)); //0.151

model;

x = x(+1) - 1/ sigma *(i - pi(+1) + log(beta) + sigma*(1-rho_a)*(1+phi)*(a - a_bar)/(sigma+phi) ); //DIS

pi = kappa * x + beta * pi(+1); //NKPC

i = rho_i*i(-1) + (1-rho_i)*(i_bar + i_pi*(pi) + i_x* x - i_x*(sigma_i/100)*eps_i ); //Taylor

a = (1-rho_a)*a_bar + rho_a*a(-1) + (sigma_a/100)*eps_a; //State Equation - Permanent log(TFP)

//////update here

// Asset Pricing

y_n = a*(1+phi)/(sigma+phi) - mu/(sigma+phi); // log nature output level

y = x + y_n; // log output level

div = (1+phi)*a - (sigma+phi) y; // firm real profit, or dividend*(y-y(-1))); // log pricing kernal

exp(m) = betaexp(-sigma

exp(re_div) = (1 + exp(p_d))*exp(delta*div)/(exp(p_d(-1) + delta*div(-1)));

1 = exp(m(+1)+re_div(+1));

end ;

initval;

x = 0;

pi = 0;

y_n = a_bar*(1+phi)/(sigma+phi)- mu/(sigma+phi);

y = a_bar*(1+phi)/(sigma+phi)- mu/(sigma+phi);

div = mu;

m = log(beta); //log(beta)-sigma*a_bar

re_div = - log(beta);

p_d = log(beta/(1-beta)); //

i = i_bar;

a = a_bar;

end;

resid(1);

steady;

check;

shocks;

var eps_a = 1;

var eps_i = 1;

end;