Dynare exercise

// Basic New Keynesian Model with Standard Taylor Rule //NKM.dyn var x, // 1.Output Gap pi, // 2.Inflation i, // 3.Nominal interest rate r, // 4.Real interest rate v, // 5.Policy shock u; // 6.Cost Push Shock varexo e_v,e_u; // policy, and inflation shocks parameters beta, // Subjective discount factor eta, // Labor supply coef. in utility function sigma, // Consumption index coef. in utility function omega, // Calvo parameter (Fraction of firms not adjusting prices) kappa, // Inflation elasticity w.r.t output gap phi_pi, // Taylor Rule Coef. on inflation phi_x, // Taylor Rule Coef. on output-gap rho_v // Monetary Policy Shock persistance rho_u, // Cost push shock persistance sde_v, // Standard deviation for policy shock sde_u, // Stadard deviation for cost push shock alpha1; // // parameter values beta = 0.99; eta = 1.0; sigma = 1.0; omega = 0.8; phi_pi = 1.5; phi_x = 0; //.5/4; rho_v = 0.5; rho_u = 0.9; sde_v = 0.01; sde_u = 0.002; alpha1 = 0; // measure of the degree of backward looking behavior in price setting (see pp306 of Walsh) // Implied Parameters kappa = (sigma + eta)*(1-omega)*(1-omega*beta)/omega; model(linear); x = x(+1) - (1/sigma)*( i - pi(+1) ); // IS curve; (8.31) in Walsh without u pi = (1-alpha1)*beta*pi(+1) +alpha1*pi(-1)+ kappa*x + u; // New Keynesian Phillips curve (8.23) of Walsh //for the value of alpha1 less than 0, the above equation becomes a modified NKPH given by (7.42) on pp306 of Walsh i = phi_pi*pi + phi_x*x + v ; // Taylor Rule see bottom of pp333 of Walsh r = i - pi(+1); // Real interest rate v = rho_v*v(-1) + e_v; u = rho_u*u(-1) + e_u; end; steady; check; shocks; var e_v = 1; //(sde_v)^2; var e_u = 1; //(sde_u)^2; end; ///////////////////////////////////////// // Computing Theoretical Moments and IRF's //////////////////////////////////////// stoch_simul(order=1,ar=4,irf=10);