%% Declaration of model variables parameters alpha p_beta_u zeta_p lambda_f delta p_gamma adp p_zeta Csi_ratio C_ratio h sigma_u sigma_r zeta_w nu chi_wu Sdp kappa lambda_w rho_zeta Y_ss rho_B phi_T rho_r phi_pi phi_y p_zetaprime omega_u omega_r p_lnPi B_ratio rho_z rho_mu rho_vp rho_b sigma_B sigma_mu sigma_m sigma_b sigma_vp sigma_T sigma_zeta; var mc rhk wh Kh Lh Yh X_pnu X_pnr X_pdu X_pdr Csi_u Csi_r pi uh Kbh Ih C_u C_r zetah rL r X_wnu X_wnr X_wdu X_wdr Bh BhL GS qh z mu b_u b_r vp_u vp_r lmbd eps_zeta; varexo eps_B eps_m eps_mu eps_b_u eps_b_r eps_vp_u eps_vp_r eps_z eps_lmbd eps_T nu_zeta; %% Calibration (median of prior distribution of parameters) alpha = 0.33; delta = 0.025; lambda_f = 1.45; lambda_w = 1.05; p_gamma = 20.4667; p_lnPi = 1.9585; p_beta_u = 0.9792; p_zeta = 0.001806*400; B_ratio = 0.9867; Sdp = 3.9170; adp = 0.1836; h = 0.6029; sigma_u = 1.8360; sigma_r = 1.8360; p_zetaprime = 1.2846; omega_u = 0.7334; omega_r = 1 - omega_u; Csi_ratio = 0.9180; C_ratio = 0.9180; chi_wu = 0.6143; nu = 1.9585; zeta_w = 0.5; zeta_p = 0.5; kappa = 0.00483; phi_T = 1.4448; rho_r = 0.7068; phi_pi = 1.7026; phi_y = 0.3672; rho_z = 0.3857; rho_zeta = 0.8135; rho_B = 0.8135; rho_mu = 0.7595; rho_b = 0.7595; rho_vp = 0.7595; sigma_B = 0.3686; sigma_mu = 0.3433; sigma_b = 0.3433; sigma_z = 0.3433; sigma_vp = 0.3433; sigma_m = 0.1700; sigma_lmbd = 0.3433; sigma_T = 0.3433; sigma_zeta = 0.1700; %% Steady-state values Y_ss = 1; % Model equations model(linear); # gamma = p_gamma/400; #lnPi = p_lnPi/400; #beta_u = 1/(1+p_beta_u/400); #zeta = p_zeta/400; #beta_r = beta_u/(1+zeta); #zetaprime = p_zetaprime/100; # RL = (1+exp(gamma)*lnPi)/beta_r; // #RL = (exp(gamma)*exp(lnPi))/beta_r; # R = RL/(1+zeta); #betabar = (omega_u*beta_u*Csi_ratio + omega_r*beta_r)/(omega_u*Csi_ratio + omega_r); #rk = exp(gamma)/betabar - (1-delta); #KBAR = exp(gamma)*(alpha/(1+lambda_f))*(1/rk); #I_ss = (exp(gamma)-(1-delta))*(alpha/(1+lambda_f))*(1/rk); #C_r_ss = (1-I_ss)/(omega_u*C_ratio + omega_r); #C_u_ss = C_ratio * C_r_ss; #chi_pu = (omega_u)/(omega_u + omega_r * ((1-beta_u*zeta_p)/(1-beta_r*zeta_p)) * Csi_ratio^(-1)); #qu = (betabar/beta_r - 1) * (1/zeta); #coef1 = (B_ratio)/(RL-kappa); #coef2 = ((1-exp(-gamma)*(exp(lnPi))^(-1)*kappa)*RL)/(RL-kappa); #coef3 = 1/(1+ (1+lambda_w)/lambda_w * (nu)); #BL = (zeta)^(1/rho_zeta)*(RL-kappa); #B = BL/B_ratio; #GS_ss = -(1-beta_u^(-1))*B-( (1/(RL-kappa))-(RL/(RL-kappa))*(1/(exp(gamma)*exp(lnPi))) ) * BL; #L_ss = (alpha/(1+lambda_f))^(-alpha/(1-alpha)) * rk^(alpha/(1-alpha)); z = rho_z * z(-1) + eps_z; mu = rho_mu * mu(-1) + eps_mu; b_u = rho_b * b_u(-1) + sigma_b * eps_b_u; b_r = rho_b * b_r(-1) + sigma_b * eps_b_r; vp_u = rho_vp * vp_u(-1) + sigma_vp * eps_vp_u; vp_r = rho_vp * vp_r(-1) + sigma_vp * eps_vp_r; lmbd = eps_lmbd; eps_zeta = rho_zeta * eps_zeta(-1) + nu_zeta; mc = alpha * rhk + (1-alpha) * wh; Kh = wh - rhk + Lh; Yh = alpha * Kh + (1-alpha) * Lh; X_pnu = (1-beta_u*zeta_p) * (Csi_u + Yh + mc + lmbd) + beta_u * zeta_p * ((1+lambda_f)/lambda_f * pi(+1) + X_pnu(+1)); X_pnr = (1-beta_r*zeta_p) * (Csi_r + Yh + mc + lmbd) + beta_r * zeta_p * ((1+lambda_f)/lambda_f * pi(+1) + X_pnr(+1)); X_pdu = (1-beta_u*zeta_p) * (Csi_u + Yh) + beta_u * zeta_p * ( pi(+1)/lambda_f + X_pdu(+1) ); X_pdr = (1-beta_r*zeta_p) * (Csi_r + Yh) + beta_r * zeta_p * ( pi(+1)/lambda_f + X_pdr(+1) ); pi = ((1-zeta_p)/zeta_p) * (chi_pu*(X_pnu-X_pdu) + (1-chi_pu)*(X_pnr-X_pdr)); Kh = -z + uh + Kbh(-1); Kbh = (1-delta) * exp(-gamma) * (Kbh(-1)-z) + (1-(1-delta)*exp(-gamma)) * (Ih + mu); rhk*rk = adp*uh; qh = betabar * exp(-gamma) * (rk*rhk(+1) + (1-delta)*qh(+1)) - z(+1) + qu * ( ((1+zeta)/(1+qu*zeta)) * Csi_u(+1) - Csi_u) + (1-qu) * ( (1/(1+qu*zeta)) * Csi_r(+1) - Csi_r); 0 = qh + mu - exp(2*gamma)*Sdp*(z+Ih-Ih(-1)) + betabar * exp(2*gamma) * Sdp * (z(+1) + Ih(+1) - Ih); Csi_u = (1/(1-beta_u*h)) * (b_u - beta_u*h*b_u(+1)) + (1/(1-beta_u*h)) * (-sigma_u/(1-h)) * ((1+beta_u*h^2)*C_u - beta_u*h*C_u(+1) - h*C_u(-1)); Csi_r = (1/(1-beta_r*h)) * (b_r - beta_r*h*b_r(+1)) + (1/(1-beta_r*h)) * (-sigma_r/(1-h)) * ((1+beta_r*h^2)*C_r - beta_r*h*C_r(+1) - h*C_r(-1)); Csi_u = r + Csi_u(+1) - z(+1) - pi(+1); zetah + Csi_u = (RL/(RL-kappa)) * rL + Csi_u(+1) - z(+1) - pi(+1) - (kappa/(RL-kappa)) * rL(+1); Csi_r = (RL/(RL-kappa)) * rL + Csi_r(+1) - z(+1) - pi(+1) - (kappa/(RL-kappa)) * rL(+1); X_wnu = (1-zeta_w*beta_u)*( b_u + vp_u + (1+nu)*Lh + (1+lambda_w)/lambda_w*(1+nu)*wh ) + zeta_w * beta_u * ( (1+lambda_w)/lambda_w*(1+nu)*(pi(+1)+z(+1)) + X_wnu(+1)); X_wnr = (1-zeta_w*beta_r)*( b_r + vp_r + (1+nu)*Lh + (1+lambda_w)/lambda_w*(1+nu)*wh ) + zeta_w * beta_r * ( (1+lambda_w)/lambda_w*(1+nu)*(pi(+1)+z(+1)) + X_wnr(+1)); X_wdu = (1-zeta_w*beta_u)*(Csi_u + Lh + ((1+lambda_w)/lambda_w)*wh) + zeta_w*beta_u * ((1/lambda_w)*(pi(+1) + z(+1)) + X_wdu(+1)); X_wdr = (1-zeta_w*beta_r)*(Csi_r + Lh + ((1+lambda_w)/lambda_w)*wh) + zeta_w*beta_r * ((1/lambda_w)*(pi(+1) + z(+1)) + X_wdr(+1)); wh = (1-zeta_w) * coef3 * (chi_wu * (X_wnu - X_wdu) + (1-chi_wu) * (X_wnr - X_wdr)) + zeta_w * (wh(-1) - pi - z); Bh + coef1 * BhL = (1/beta_u)*(Bh(-1)+r(-1)) + coef1 * (1/beta_r) * BhL(-1) + coef2 * coef1 * rL - GS/B - ( (1/beta_u) + coef1 * (1/beta_r) ) * (z+pi); BhL - (RL/(RL-kappa)) * rL = rho_B * (BhL(-1) - (RL/(RL-kappa)) * rL(-1)) - eps_B; %%Choque negativo -> mesmo shape do paper GS/GS_ss = phi_T * (Bh(-1) + coef1 * BhL(-1) - (RL/(RL-kappa))* coef1 * rL(-1))/(1+coef1) + eps_T; // zetah = zetaprime * BhL -zetaprime* (RL/(RL-kappa)) * rL+ eps_zeta; zetah = zetaprime * BhL + eps_zeta; Yh = (omega_u*C_u_ss/Y_ss) * C_u + (omega_r*C_r_ss/Y_ss) * C_r + I_ss/Y_ss * Ih + (exp(-gamma)*rk*KBAR/Y_ss)*uh; r = rho_r * r(-1) + (1-rho_r) * (phi_pi * pi + phi_y * (Yh-Yh(-4)+z(-3)+z(-2)+z(-1)+z)) + eps_m; end; resid(1); steady; check; shocks; var eps_B = sigma_B; var eps_m = sigma_m; var eps_vp_u = 1; var eps_vp_r = 1; var eps_lmbd = sigma_lmbd; var eps_b_u = 1; var eps_b_r = 1; var eps_T = sigma_T; var nu_zeta = sigma_zeta; end; stoch_simul(irf=31, relative_irf, periods=500, nograph);