close all;

var a b;
varexo e_a e_b;

parameters rho_a rho_b psi_b;
rho_a = 0.75;
rho_b = 0.439830978471861;
psi_b = 0.5;

model;
a = rho_a*a(-1) + psi_b*b + e_a;
b = rho_b*b(-1) + e_b;
end;

initval;
a=0;
b=0;
end;


shocks;
var e_a = 0.01^2;
var e_b = 0.000240311927771282^2;
end;

stoch_simul(order = 1, irf=20);

estimated_params;

stderr e_a, INV_GAMMA_PDF,0.001,2;
rho_a, beta_pdf, 0.75, 0.15;
psi_b, Normal_pdf, 0, 1;

stderr e_b, 0.000240311927771282, INV_GAMMA_PDF,0.001,2;
rho_b, 0.439830978471861, beta_pdf, 0.75, 0.15;

end;

varobs a b;


estimation(datafile=data_AR_1, mode_compute=4, order = 1, mode_check, mh_replic=0) a b;