// Simple New Keynesian DSGE model with nominal rigidities and Taylor rule



var   y  pi  mc  i  a;


varexo eps_a;


parameters beta  lambda  xi_p  phi  sigma  phi_pi  rho_a;



beta = 0.99; 

lambda = (1 - (beta*xi_p))*(1 - xi_p)/xi_p; 

xi_p = 0.75; 

sigma = 0.33; 

phi = 3; 

phi_pi = 1.5; 

rho_a = 0.9; 





// Complete model


model(linear);


y = y(+1) - (i - pi(+1))/sigma; // Euler equation


mc = (sigma + phi)*y - (1 - phi)*a; // Marginal cost


pi = beta*pi(+1) + lambda*mc; // NKPK


i = phi_pi*pi; // Simple Taylor rule


a = rho_a*a(-1) + eps_a; // AR(1) process for productivity

end;


check;

shocks;
var eps_a; stderr 1;

end;

stoch_simul;