// Estimation of the Clarida, Gali, Gertler Model

var pie x r rstar da tau dy; 	   // DECLARATION OF THE ENDOGENOUS VARIABLES. 
varexo eps_a eps_tau;    // DECLARATION OF THE STRUCTURAL INNOVATIONS.

parameters phi beta kappa phi_x phi_pie alpha rho lambda; 

beta    = 0.99;
phi_x   = 0;    
phi_pie = 1.5;
alpha   = 0;
rho     = 0.2;
lambda  = 0.5;
phi     = 1;
theta   = 0.75;
kappa   = ((1-theta)*(1-beta*theta)*(1+phi))/(theta);

// DECLARATION OF THE (LINEAR) DSGE MODEL: 
model(linear);

    beta*pie(+1) + kappa*x = pie;                                      // Calvo Pricing Equation
    r - pie(+1)-rstar   = x(+1) - x;                                   // Intertemporal Equation
    alpha*r(-1) + (1-alpha)*phi_pie*pie + (1-alpha)*phi_x*x = r;   // Monetary Policy Rule
    rstar = rho*da + (1-lambda)/(1+phi)*tau;                           // Definition of the Natural Rate  
    da = rho*da(-1) + eps_a;                                           // Exogenous Stochastic Processes
    tau       = lambda*tau(-1) + eps_tau;
    dy  = x - x(-1) + da - (tau - tau(-1))/(1+phi);                    // construction of output growth

end;



// maximum likelihood estimation:
estimated_params;
beta    , 0.99;
phi_x   , 0;    
phi_pie , 1.5;
alpha   , 0;
rho     , 0.2;
lambda  , 0.5;
phi     , 1;
//stderr eps_a, 0.001;
//stderr eps_tau, 0.001;
end;

varobs pie x ;

estimation(datafile=simdata);