//Endogenous Variables var c i pi c_m tau v_m c_d pi_star pi_m x tau_star y_star v_x s y pi_d mc_d mc_m i_star b_star v_s v_px wp a n ys_obs pis_obs is_obs i_obs ds_obs pi_obs y_obs_real y_obs_nonf y_obs_mark xs_obs im_obs tot_obs a_obs; // Declare exogenous Variables (shock variables) varexo e_d e_pi e_i e_ystar e_pistar e_istar e_m e_s e_a e_x e_px em_r em_f em_m em_xs em_im em_tot em_a; // Declare Model Parameters parameters gamma eta delta delta_x beta theta_d theta_m omega alpha psi phi phi_y phi_pi phi_i p_ystar p_pistar p_istar p_m p_s p_a p_x p_px; // Initialise Parameters gamma = 3; eta = 2; delta = 0.9; delta_x = 0.05; beta = 0.99; theta_d = 0.75; theta_m = 0.75; omega = 0.3; alpha = 0.18; psi = 0.01; phi = 2; phi_y = 0.5; phi_pi = 1.5; phi_i = 0.5; //p_ystar = 0.9; //p_pistar = 0.8; //p_istar = 0.7; p_m = 0.5; p_s = 0.5; p_a = 0.5; p_x = 0.5; p_px = 0.5; // Describe Model Equations model(linear); //Parameter Definitions #mu_f_d = (beta*theta_d)/(theta_d + omega*(1-theta_d*(1-beta))); #mu_f_f = (beta*theta_m)/(theta_m + omega*(1-theta_m*(1-beta))); #mu_b_d = omega/(theta_d + omega*(1-theta_d*(1-beta))); #mu_b_f = omega/(theta_m + omega*(1-theta_m*(1-beta))); #lambda_d = ((1-omega)*(1-theta_d)*(1-theta_d*beta))/(theta_d + omega*(1-theta_d*(1-beta))); #lambda_f = ((1-omega)*(1-theta_m)*(1-theta_m*beta))/(theta_m + omega*(1-theta_m*(1-beta))); #rho = gamma - eta + eta*gamma; // A1: Consumption Euler Equation c = (gamma/rho)*c(+1) - ((eta*(1-gamma))/rho)*c(-1) - (1/rho)*(i-pi(+1)) + e_d; // A2: Consumer Demand for Imported Goods c_m = c - delta*tau + v_m; // A3: Consumer Demand for Domestic Goods c_d = c + delta*tau; // A4: Relative price of imported goods tau = tau(-1) + pi_m - pi; // A5: Export Demand x = -delta_x*tau_star + y_star + v_x; // A6: Relative Price of goods produced domestically sold to the world tau_star = pi - pi_star - (s - s(-1)) + tau_star(-1); // A7: Domestic Resource Constraint y = (1-alpha)*c_d + alpha*x; // A8: Inflation of domestically produced goods //MAYBE COST PUSH SHOCK IS AN AR PROCESS? pi_d = mu_f_d*pi(+1) + mu_b_d*pi(-1) +lambda_d*mc_d + e_pi; // A9: Inflation of imported goods pi_m = mu_f_f*pi_m(+1) + mu_b_f*pi_m(-1) + lambda_f*mc_m + e_pi; // A10: CPI Inflation pi = (1-alpha)*pi_d + alpha*pi_m; // A11: Uncovered Interest Parity Condition i = i_star + (s(+1) - s) - psi*b_star(-1) + v_s; // A12: Flow budget constraint b_star = b_star(-1) + x - c_m + v_px + (s-s(-1)); // A13: Labour Supply Decision wp = phi*n + gamma*(c - eta*c(-1)); // A14: Labour Supply decision //w - p = phi*(y-a) + gamma*(c - eta*c(-1)); // A15: Real Domestic Marginal Cost mc_d = gamma*(c - eta*c(-1)) + phi*n - a; // A16: Real Domestic Marginal Cost mc_d = gamma*(c - eta*c(-1)) + phi*y - (phi + 1)*a; // A17: Real Marginal Cost of Imported goods //mc_m = s + p_star - p; // A18: Real Marginal Cost of Imported goods mc_m = (s-s(-1)) + pi_star - pi + mc_m(-1); // A19: Taylor Rule i = phi_y*y(-1) + phi_pi*pi(-1) + phi_pi*i(-1) + e_i; // Unrestricted VAR for exogenous World Variables // y_star = p_ystar*y_star(-1) + e_ystar; // pi_star = p_pistar*pi_star(-1) + e_pistar; // i_star = p_istar*i_star(-1) +e_istar; y_star = 0.9798*y_star(-1) - 0.1015*pi_star(-1) - 0.1400*i_star(-1) + e_ystar; pi_star = -0.0545*y_star(-1) - 0.0843*pi_star(-1) + 0.128*i_star(-1) + e_pistar; i_star = 0.1922*y_star(-1) + 0.3197*pi_star(-1) + 0.726*i_star(-1) + e_istar; // Exogenous Shock processes v_m = p_m*v_m(-1) + e_m; v_s = p_s*v_s(-1) + e_s; a = p_a*a(-1) + e_a; v_x = p_x*v_x(-1) + e_x; v_px = p_px*v_px(-1) + e_px; // Measurement Equations ys_obs = y_star ; pis_obs = pi_star; is_obs = i_star; i_obs = i; ds_obs = s - s(-1); pi_obs = pi; y_obs_real = y + em_r; y_obs_nonf = y + em_f; y_obs_mark = y + em_m; xs_obs = x - y + em_xs; im_obs = c_m - y + em_im; tot_obs = v_px - mc_m + em_tot; a_obs = a + em_a; end; // Initialisation values initval; c = 0; i = 0; pi = 0; c_m = 0; tau = 0; v_m = 0; c_d = 0; pi_star = 0; pi_m = 0; x = 0; tau_star = 0; y_star = 0; v_x = 0; s = 0; y = 0; pi_d = 0; mc_d = 0; mc_m = 0; i_star = 0; b_star = 0; v_s = 0; v_px = 0; wp = 0; //p = 0; //p_star = 0; a = 0; n= 0; end; steady; check; //Priors Distributions estimated_params; // Households and Firms gamma, normal_pdf, 3, 0.44; eta, normal_pdf, 2, 0.66; phi, normal_pdf, 2, 0.44; omega, beta_pdf, 0.3, 0.10; delta, normal_pdf, 1, 0.1; delta_x, normal_pdf, 1, 0.1; theta_d, beta_pdf, 0.75, 0.04; theta_m, beta_pdf, 0.75, 0.04; psi, normal_pdf, 0.01, 0.02; phi_y, normal_pdf, 0.5, 0.25; phi_pi, normal_pdf, 1.5, 0.29; phi_i, beta_pdf, 0.5, 0.25; p_a, beta_pdf, 0.5, 0.28; p_s, beta_pdf, 0.5, 0.28; p_px, beta_pdf, 0.5, 0.28; p_x, beta_pdf, 0.5, 0.28; p_m, beta_pdf, 0.5, 0.28; p_ystar, beta_pdf, 0.9, 0.05; p_pistar, beta_pdf, 0.8, 0.1; p_istar, beta_pdf, 0.8, 0.1; // Exogenous Shock Processes stderr e_a, uniform_pdf, , , 0, realmax; stderr e_s, uniform_pdf, , , 0, realmax; stderr e_d, uniform_pdf, , , 0, realmax; stderr e_pi,uniform_pdf, , , 0, realmax; stderr e_px,uniform_pdf, , , 0, realmax; stderr e_x, uniform_pdf, , , 0, realmax; stderr e_m, uniform_pdf, , , 0, realmax; stderr e_i, uniform_pdf, , , 0, realmax; // Exogenous International Shock Processes stderr e_ystar, uniform_pdf, , , 0, realmax; stderr e_pistar, uniform_pdf, , , 0, realmax; stderr e_istar, uniform_pdf, , , 0, realmax; // Measurement Errors stderr em_r, uniform_pdf, , , 0, realmax; stderr em_f, uniform_pdf, , , 0, realmax; stderr em_m, uniform_pdf, , , 0, realmax; stderr em_xs, uniform_pdf, , , 0, realmax; stderr em_im, uniform_pdf, , , 0, realmax; stderr em_tot, uniform_pdf, , , 0, realmax; stderr em_a, uniform_pdf, , , 0, realmax; end; varobs ys_obs pis_obs is_obs i_obs ds_obs pi_obs y_obs_real xs_obs im_obs tot_obs a_obs; estimation( datafile = SmallOEDSGE_RBA, first_obs = 6, mode_compute = 6, mh_replic=40000, mh_nblocks = 2, mh_jscale=.47, nograph, mh_init_scale = 0.92 );