I am replicating the model of Gali(2005) ,i simplified your code Gali_Monacelli_2005.mod,but the same linear equations generate different rusults .
Gali2005_1.mod
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var
pih x y ynat rnat r s pi p
ph e ystar pistar n nx real_wage a c deprec_rate ;
varexo
eps_star eps_a ;
parameters
sigma eta gamma phi epsilon theta beta alpha
phi_pi rhoa rhoy rho omega sigma_a Theta lambda kappa_a Gamma Psi;
sigma = 1;
eta = 1 ;
gamma = 1;
phi =3;
epsilon = 6;
theta = 0.75;
beta = 0.99;
alpha = 0.4;
phi_pi = 1.5;
rhoa = 0.9;
rhoy = 0.86;
rho = beta^(-1)-1;
omega = sigma*gamma+(1-alpha)*(sigma*eta-1);
sigma_a =sigma/((1-alpha)+alpha*omega);
Theta=(sigma*gamma-1)+(1-alpha)*(sigma*eta-1);
lambda = (1-(beta*theta))*(1-theta)/theta;
kappa_a =lambda*(sigma_a+phi);
Gamma = (1+phi)/(sigma_a+phi);
Psi = -Theta*sigma_a/(sigma_a+phi);
model(linear);
//1. Equation (37), IS Curve
x = x(+1) - sigma_a^(-1)*(r - pih(+1) - rnat) ;
//2. Equation (36), Philips Curve
pih = beta * pih(+1)+ kappa_a*x;
//3. Equation below (37)
rnat = -sigma_a*Gamma*(1-rhoa)*a + alpha*sigma_a*(Theta+Psi)*(ystar(+1)-ystar);
//4. Equation (35), definition natural level of output
ynat = Gamma*a + alpha*Psi*ystar;
//5. Equation above (35), definition output gap
x = y - ynat;
//6. Equation (29)
y = ystar + sigma_a^(-1)*s;
//7. Equation (14)
pi = pih + alpha*(s-s(-1));
//8. Equation 15 (first difference)
s = s(-1) + e - e(-1) + pistar - pih;
//9. Constant world inflation, see p.724 (Given constant world prices)
pistar = 0;
//10. Equation (22), employment
y = a + n;
//11. Equation (31), net exports
nx = alpha*(omega/sigma-1)*s;
//12. Equation (27), defines consumption
y = c+alpha*omega/sigma*s;
//13. Above equation (11), defines real wage
real_wage = sigma*c+phi*n;
//10-12. Equations on p. 723, stochastic processes
a = rhoa*a(-1) + eps_a;
ystar= rhoy*ystar(-1) + eps_star;
//definition consumer price level
pi = p - p(-1);
//definition domestic price level
pih = ph - ph(-1);
//definition nominal depreciation rate of exchange rate
deprec_rate=e-e(-1);
pih=0;
end;
shocks;
var eps_a = 1;
end;
stoch_simul(order=1,irf=20,irf_plot_threshold=0)pih ;
the result is correct
but when i change the order of equation 3 Gali2005_2.mod
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//1. Equation (37), IS Curve
x = x(+1) - sigma_a^(-1)*(r - pih(+1) - rnat) ;
//3. Equation below (37)
rnat = -sigma_a*Gamma*(1-rhoa)*a + alpha*sigma_a*(Theta+Psi)*(ystar(+1)-ystar);
//2. Equation (36), Philips Curve
pih = beta * pih(+1)+ kappa_a*x;
//4. Equation (35), definition natural level of output
ynat = Gamma*a + alpha*Psi*ystar;
//5. Equation above (35), definition output gap
x = y - ynat;
the irf of pih is strange
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oo_.irfs.pih_eps_a'
ans =
1.0e-32 *
0.5208
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
the irf value of pih should be zero and the policy function is :
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pih
s(-1) 0
p(-1) 0
ph(-1) 0
e(-1) 0
a(-1) 0
ystar(-1) 0
eps_star 0
eps_a 0
