%--------------------------------------------------------------------------
% 1. Declaration of variables and parameters
%--------------------------------------------------------------------------
var  y c i g     pi R k q n     s r_n v a;
varexo      e_r e_v e_s e_g e_a;
parameters  beta sigma kappa eta delta
            gamma_c gamma_i gamma_g 
            phi_y phi_pi rho 
            rho_r rho_v rho_s rho_g alpha
            rho_a;
beta  = 0.99;
sigma  = 0.5;
kappa  = 0.2;
eta       = 0.5;
gamma_c = 0.65;
gamma_i  = 0.15;
gamma_g = 0.20;
delta   = 0.1; % in the exercise delta = 0.1 (but that is very high)
rho       = 0.8;
alpha  = 0.33;
phi_pi  = 1.5;
phi_y  = 0.5;
rho_s   = 0.5;
rho_r  = 0.5;
rho_v  = 0.5;
rho_g    = 0.5;
rho_a = 0.5;
%--------------------------------------------------------------------------
% 2. Model
%--------------------------------------------------------------------------
model (linear); 
pi = beta * pi(+1) + kappa * y;
c = c(+1) - 1/sigma *(R - pi(+1) - r_n);
i = eta * q;
q = (1 - beta *(1 - delta)) * y(+1)- (R - pi(+1)) + beta * q(+1) + s;
R = (1 - rho) * (phi_pi + phi_y) + rho * R(-1) + v;
y = a + alpha * k + (1 - alpha) * n;
k = (1 - delta) * k(-1) + delta * i;
y = gamma_c * c + gamma_i * i + gamma_g * g;
a = rho_a * a(-1) + e_a;
s = rho_s * s(-1) + e_s;
g = rho_g * g(-1) + e_g;
v = rho_v * v(-1) + e_v;
r_n = rho_r * r_n(-1) + e_r;
end ;
%--------------------------------------------------------------------------
% 3. Shocks
%--------------------------------------------------------------------------
shocks ;
var e_s = 0.25^2;
var e_r = 0.25^2;
var e_v = 0.25^2;
var e_g = 0.25^2;
var e_a = 0.25^2;
end ;
%--------------------------------------------------------------------------
% 4. Simulations
%--------------------------------------------------------------------------
stoch_simul(irf =15);