%% Based on: %% %% This version: Gerret Halberstadt (2017) var % domestic variables C_t, % Cosumption dS_t, % Change if nominal exchange rate E_t, % Employment I_t, % Investment K_t, % Stock of capital Keff_t, % Effective capital L_t, % Hours worked Mc_t, % Domestic marginal costs McMC_t, % Marginal costs of consumption goods importing firms McMI_t, % Marginal costs of investment goods importing firms McX_t, % Marginal costs of exporting firms Pi_t, % Domestic inflation rate PiCpi_t, % CPI inflation rate PiMC_t, % Inflation rate for imported consumption goods PiMI_t, % Inflation rate for imported investment goods PiX_t, % Inflation rate for exported goods Qk_t, % R_t, % Rf_t, % Rk_t, % U_t, % W_t, % X_t, % Y_t, % a, % gamma_cdhat, % gamma_fhat, % gamma_idhat, % gamma_mcdhat, % gamma_midhat, % gamma_xstar, % m_barhat, % mu_hat, % psi_zhat, % q_hat, % % Observables Obs_R, Obs_Pi, Obs_Y, Obs_RStar, Obs_PiStar, Obs_YStar, Obs_W, % Foreign variables YStar_t, PiStar_t, RStar_t, % Fiscal variables TauK_t, TauY_t, TauC_t, TauW_t, G_t, % shock processes Sh_E_t, Sh_MuZ_t, Sh_LaF_t, Sh_LaMC_t, Sh_LaMI_t, Sh_LaX_t, Sh_Upsilon_t, Sh_PiCpiTarget_t, Sh_ZetaC_t, Sh_ZetaH_t, Sh_ZetaQ_t, Sh_PhiTilde_t, Sh_ZTilde_t, Sh_R_t; varexo % Foreign shocks eps_Sh_YStar, eps_Sh_PiStar, eps_Sh_RStar, % Fiscal shocks eps_Sh_TauK, eps_Sh_TauY, eps_Sh_TauC, eps_Sh_TauW, eps_Sh_G, % domestic shocks eps_Sh_E, eps_Sh_MuZ, eps_Sh_LaF, eps_Sh_LaMC, eps_Sh_LaMI, eps_Sh_LaX, eps_Sh_Upsilon, eps_Sh_PiCpiTarget, eps_Sh_ZetaC, eps_Sh_ZetaH, eps_Sh_ZetaQ, eps_Sh_PhiTilde, eps_Sh_ZTilde, eps_Sh_R; varobs Obs_R, Obs_Pi, Obs_Y, Obs_RStar, Obs_PiStar, Obs_YStar, Obs_W; parameters rho_R, psi_pi, psi_y, psi_x, psi_dpi, psi_dy, zeta_w, zeta_d, zeta_mc, zeta_mi, zeta_x, zeta_e, iota_w, iota_d, iota_mc, iota_mi, iota_x, beta, alpha, eta_c, sigma_a, mu, sigma_L, delta, lambda_w, omega_i, omega_c, nu, rho_pibar, A_q, A_L, sigma_q, lambda_d, lambda_mi, lambda_mc, S_tilde, b, eta_i, eta_f, mu_z, phi_a, tau_k, tau_y, tau_w, gr, tau_c, b_w, eta_0, eta_1, eta_2, eta_3, eta_4, eta_5, eta_6, eta_7, eta_8, eta_9, eta_10, eta_11, pi, R, R_f, eta_mc, eta_mi, gamma_id, gamma_cd, gamma_dc, gamma_cmc, gamma_mcc, gamma_imi, gamma_mii, r_k, w_bar, k_H, D1, D2, D3, D4, H, c, psi_z, y_bar, g, q, m_bar, k, k_bar, i, c_m, i_m, y_star, % Foreign parameters ForLag111, ForLag112, ForLag113, ForLag211, ForLag212, ForLag213, ForLag311, ForLag312, ForLag313, ForLag411, ForLag412, ForLag413, ForShock11, ForShock12, ForShock13, ForLag121, ForLag122, ForLag123, ForLag221, ForLag222, ForLag223, ForLag321, ForLag322, ForLag323, ForLag421, ForLag422, ForLag423, ForShock21, ForShock22, ForShock23, ForLag131, ForLag132, ForLag133, ForLag231, ForLag232, ForLag233, ForLag331, ForLag332, ForLag333, ForLag431, ForLag432, ForLag433, ForShock31, ForShock32, ForShock33, % Fiscal parameters FisLag111, FisLag112, FisLag113, FisLag114, FisLag115, FisLag211, FisLag212, FisLag213, FisLag214, FisLag215, FisShock11, FisShock12, FisShock13, FisShock14, FisShock15, FisLag121, FisLag122, FisLag123, FisLag124, FisLag125, FisLag221, FisLag222, FisLag223, FisLag224, FisLag225, FisShock21, FisShock22, FisShock23, FisShock24, FisShock25, FisLag131, FisLag132, FisLag133, FisLag134, FisLag135, FisLag231, FisLag232, FisLag233, FisLag234, FisLag235, FisShock31, FisShock32, FisShock33, FisShock34, FisShock35, FisLag141, FisLag142, FisLag143, FisLag144, FisLag145, FisLag241, FisLag242, FisLag243, FisLag244, FisLag245, FisShock41, FisShock42, FisShock43, FisShock44, FisShock45, FisLag151, FisLag152, FisLag153, FisLag154, FisLag155, FisLag251, FisLag252, FisLag253, FisLag254, FisLag255, FisShock51, FisShock52, FisShock53, FisShock54, FisShock55, % shock parameters rho_Sh_E, rho_Sh_MuZ, rho_Sh_LaF, rho_Sh_LaMC, rho_Sh_LaMI, rho_Sh_LaX, rho_Sh_Upsilon, rho_Sh_PiCpiTarget, rho_Sh_ZetaC, rho_Sh_ZetaH, rho_Sh_ZetaQ, rho_Sh_PhiTilde, rho_Sh_ZTilde, rho_Sh_R, sig_Sh_E, sig_Sh_MuZ, sig_Sh_LaF, sig_Sh_LaMC, sig_Sh_LaMI, sig_Sh_LaX, sig_Sh_Upsilon, sig_Sh_PiCpiTarget, sig_Sh_ZetaC, sig_Sh_ZetaH, sig_Sh_ZetaQ, sig_Sh_PhiTilde, sig_Sh_ZTilde, sig_Sh_R; %% parameterization rho_R = 0.87400000; psi_pi = 1.71000000; psi_y = 0.07800000; psi_x = -0.00900000; psi_dpi = 0.31700000; psi_dy = 0.11600000; zeta_w = 0.69700000; zeta_d = 0.88300000; zeta_mc = 0.46300000; zeta_mi = 0.74000000; zeta_x = 0.63900000; zeta_e = 0.79200000; iota_w = 0.51600000; iota_d = 0.21200000; iota_mc = 0.16100000; iota_mi = 0.18700000; iota_x = 0.13900000; beta = 0.99900000; alpha = 0.29000000; eta_c = 5.00000000; sigma_a = 1000000.00000000; mu = 1.01000000; sigma_L = 1.00000000; delta = 0.01300000; lambda_w = 1.05000000; omega_i = 0.55000000; omega_c = 0.31000000; nu = 1.00000000; rho_pibar = 0.97500000; A_q = 0.37760000; A_L = 7.50000000; sigma_q = 10.62000000; lambda_d = 1.16800000; lambda_mi = 1.22600000; lambda_mc = 1.61900000; S_tilde = 8.73200000; b = 0.69000000; eta_i = 1.66900000; eta_f = 1.46000000; mu_z = 1.00500000; phi_a = 0.14500000; tau_k = 0.13700000; tau_y = 0.17710000; tau_w = 0.18600000; gr = 0.20370000; tau_c = 0.12490000; % Foreign parameters ForLag111 = 0.17780000; ForLag112 = -0.03620000; ForLag113 = -0.12380000; ForLag121 = -0.35510000; ForLag122 = 0.28170000; ForLag123 = 0.22230000; ForLag131 = 0.48780000; ForLag132 = -0.07080000; ForLag133 = 0.75050000; ForLag211 = 0.21230000; ForLag212 = -0.01330000; ForLag213 = -0.01970000; ForLag221 = 0.17260000; ForLag222 = 0.48650000; ForLag223 = 0.03530000; ForLag231 = 0.04220000; ForLag232 = 0.16230000; ForLag233 = 0.09100000; ForLag311 = 0.37930000; ForLag312 = 0.00430000; ForLag313 = 0.08950000; ForLag321 = 0.38310000; ForLag322 = 0.08750000; ForLag323 = -0.07920000; ForLag331 = 0.01760000; ForLag332 = 0.11010000; ForLag333 = 0.32010000; ForLag411 = 0.05150000; ForLag412 = 0.06010000; ForLag413 = 0.05270000; ForLag421 = 0.37170000; ForLag422 = 0.08250000; ForLag423 = -0.20130000; ForLag431 = 0.10630000; ForLag432 = -0.15810000; ForLag433 = -0.26080000; ForShock11 = 0.25850000; ForShock12 = 0.00000000; ForShock13 = 0.00000000; ForShock21 = 0.00000000; ForShock22 = 0.33750000; ForShock23 = 0.00000000; ForShock31 = -0.02580000; ForShock32 = 0.05670000; ForShock33 = 0.22570000; % Fiscal parameters FisLag111 = 0.90000000; FisLag112 = 0.00000000; FisLag113 = 0.00000000; FisLag114 = 0.00000000; FisLag115 = 0.00000000; FisLag121 = 0.00000000; FisLag122 = 1.57450000; FisLag123 = 0.06400000; FisLag124 = 0.00000000; FisLag125 = -0.03950000; FisLag131 = 0.00000000; FisLag132 = 0.03660000; FisLag133 = 0.76230000; FisLag134 = 0.00000000; FisLag135 = 0.02860000; FisLag141 = 0.00000000; FisLag142 = 0.00000000; FisLag143 = 0.00000000; FisLag144 = 0.90000000; FisLag145 = 0.00000000; FisLag151 = 0.00000000; FisLag152 = -0.04850000; FisLag153 = 0.05380000; FisLag154 = 0.00000000; FisLag155 = 0.56210000; FisLag211 = 0.00000000; FisLag212 = 0.00000000; FisLag213 = 0.00000000; FisLag214 = 0.00000000; FisLag215 = 0.00000000; FisLag221 = 0.00000000; FisLag222 = -0.64620000; FisLag223 = 0.03710000; FisLag224 = 0.00000000; FisLag225 = -0.01780000; FisLag231 = 0.00000000; FisLag232 = -0.02950000; FisLag233 = 0.21200000; FisLag234 = 0.00000000; FisLag235 = -0.05260000; FisLag241 = 0.00000000; FisLag242 = 0.00000000; FisLag243 = 0.00000000; FisLag244 = 0.00000000; FisLag245 = 0.00000000; FisLag251 = 0.00000000; FisLag252 = 0.10510000; FisLag253 = -0.13950000; FisLag254 = 0.00000000; FisLag255 = 0.19930000; FisShock11 = 1.00000000; FisShock12 = 0.00000000; FisShock13 = 0.00000000; FisShock14 = 0.00000000; FisShock15 = 0.00000000; FisShock21 = 0.00000000; FisShock22 = 0.13240000; FisShock23 = 0.00000000; FisShock24 = 0.00000000; FisShock25 = 0.00000000; FisShock31 = 0.00000000; FisShock32 = 0.00000000; FisShock33 = 0.14300000; FisShock34 = 0.00000000; FisShock35 = 0.00000000; FisShock41 = 0.00000000; FisShock42 = 0.00000000; FisShock43 = 0.00000000; FisShock44 = 1.00000000; FisShock45 = 0.00000000; FisShock51 = 0.00000000; FisShock52 = 0.00000000; FisShock53 = 0.00000000; FisShock54 = 0.00000000; FisShock55 = 0.41480000; % shock autocorrelation parameters rho_Sh_E = 0.90900000; rho_Sh_MuZ = 0.72300000; rho_Sh_LaF = 0.97000000; rho_Sh_LaMC = 0.97800000; rho_Sh_LaMI = 0.96300000; rho_Sh_LaX = 0.88600000; rho_Sh_Upsilon = 0.75000000; rho_Sh_PiCpiTarget = 0.97500000; rho_Sh_ZetaC = 0.93500000; rho_Sh_ZetaH = 0.67500000; rho_Sh_ZetaQ = 1.00000000; rho_Sh_PhiTilde = 0.95500000; rho_Sh_ZTilde = 0.99300000; rho_Sh_R = 0.00000000; % shock variances sig_Sh_E = 0.51900000; sig_Sh_MuZ = 0.13700000; sig_Sh_LaF = 0.13200000; sig_Sh_LaMC = 2.58400000; sig_Sh_LaMI = 0.03540000; sig_Sh_LaX = 1.12400000; sig_Sh_Upsilon = 0.46900000; sig_Sh_PiCpiTarget = 0.05300000; sig_Sh_ZetaC = 0.15700000; sig_Sh_ZetaH = 0.09800000; sig_Sh_ZetaQ = 1.00000000; sig_Sh_PhiTilde = 0.18300000; sig_Sh_ZTilde = 0.21700000; sig_Sh_R = 0.13500000; model(linear); %% Domestic sticky price economy %% A.1) Monetary policy rule* R_t = rho_R*R_t(-1)+(1-rho_R)*(Sh_PiCpiTarget_t+psi_pi*(PiCpi_t(-1)-Sh_PiCpiTarget_t)+psi_y*Y_t(-1)+psi_x*X_t(-1)) + psi_dpi*(PiCpi_t - PiCpi_t(-1)) + psi_dy*(Y_t - Y_t(-1)) + Sh_R_t; %% A.2) Rental rate for capital* Rk_t = Sh_MuZ_t + W_t + Rf_t + L_t - Keff_t; %% A.3) interest paid by firms to finance wage bill in advance (friction excluded) Rf_t = nu*R/(nu*R+1-nu)*R_t(-1); %% A.4) Domestic Phillips Curve* Pi_t - Sh_PiCpiTarget_t = beta/(1+iota_d*beta)*(Pi_t(+1)-rho_pibar*Sh_PiCpiTarget_t) + iota_d/(1+iota_d*beta)*(Pi_t(-1)-Sh_PiCpiTarget_t)-(iota_d*beta*(1-rho_pibar)/(1+iota_d*beta))*Sh_PiCpiTarget_t+(((1-zeta_d)*(1-zeta_d*beta))/(zeta_d*(1+iota_d*beta)))*Mc_t + Sh_LaF_t; %% A.5) Domestic marginal costs* Mc_t = alpha*(Sh_MuZ_t+L_t-Keff_t) + W_t + Rf_t - Sh_E_t; %% A.6) Phillips Curve for domestic consumption good importing firms* PiMC_t - Sh_PiCpiTarget_t = (beta/(1+iota_mc*beta))*(PiMC_t(+1)-rho_pibar*Sh_PiCpiTarget_t) + (iota_mc/(1+iota_mc*beta))*(PiMC_t(-1)-Sh_PiCpiTarget_t)-(iota_mc*beta*(1-rho_pibar)/(1+iota_mc*beta))*Sh_PiCpiTarget_t+(((1-zeta_mc)*(1-zeta_mc*beta))/(zeta_mc*(1+iota_mc*beta)))*McMC_t + Sh_LaMC_t; %% A.7) Marginal costs of imported consumption goods* McMC_t = -McX_t - gamma_xstar - gamma_mcdhat; %% A.8) Phillips Curve for domestic investment good importing firms* PiMI_t - Sh_PiCpiTarget_t = (beta/(1+iota_mi*beta))*(PiMI_t(+1)-rho_pibar*Sh_PiCpiTarget_t) + (iota_mi/(1+iota_mi*beta))*(PiMI_t(-1)-Sh_PiCpiTarget_t)-(iota_mi*beta*(1-rho_pibar)/(1+iota_mi*beta))*Sh_PiCpiTarget_t+(((1-zeta_mi)*(1-zeta_mi*beta))/(zeta_mi*(1+iota_mi*beta)))*McMI_t + Sh_LaMI_t; %% A.9) Marginal costs of imported investment goods* McMI_t = -McX_t - gamma_xstar - gamma_midhat; %% A.10) Phillips Curve for exporting firms* PiX_t - Sh_PiCpiTarget_t = (beta/(1+iota_x*beta))*(PiX_t(+1)-rho_pibar*Sh_PiCpiTarget_t) + (iota_x/(1+iota_x*beta))*(PiX_t(-1)-Sh_PiCpiTarget_t)-(iota_x*beta*(1-rho_pibar)/(1+iota_x*beta))*Sh_PiCpiTarget_t+(((1-zeta_x)*(1-zeta_x*beta))/(zeta_x*(1+iota_x*beta)))*McX_t + Sh_LaX_t; %% A.11) Marginal costs of exported goods* McX_t = McX_t(-1) + Pi_t - PiX_t - dS_t; %% A.12) Relative prices* gamma_mcdhat = gamma_mcdhat(-1) + PiMC_t - Pi_t; %% A.13) Relative prices* gamma_midhat = gamma_midhat(-1) + PiMI_t - Pi_t; %% A.14) Relative prices* gamma_xstar = gamma_xstar(-1) + PiX_t - PiStar_t; %% A.15) CPI_Inflation PiCpi_t = ((1-omega_c)*(gamma_dc)^(1-eta_c))*Pi_t + ((omega_c)*(gamma_mcc)^(1-eta_c))*PiMC_t; %% A.16) Wage equation W_t = -(1/eta_1)*(eta_0*W_t(-1) + eta_2*W_t(+1) + eta_3*(Pi_t-Sh_PiCpiTarget_t) + eta_4*(Pi_t(+1)-rho_pibar*Sh_PiCpiTarget_t) + eta_5*(PiCpi_t(-1)-Sh_PiCpiTarget_t) + eta_6*(PiCpi_t-rho_pibar*Sh_PiCpiTarget_t) + eta_7*psi_zhat + eta_8*L_t + eta_9*TauY_t + eta_10*TauW_t) + Sh_ZetaH_t; %% A.17) Euler equation* C_t = -(1/(mu_z^2+b^2*beta))*(-b*beta*mu_z*C_t(+1) - b*mu_z*C_t(-1) + b*mu_z*(Sh_MuZ_t-beta*Sh_MuZ_t(+1)) + (mu_z-b*beta)*(mu_z-b)*psi_zhat + tau_c/(1+tau_c)*(mu_z-b*beta)*(mu_z-b)*TauC_t + (mu_z-b*beta)*(mu_z-b)*gamma_cdhat - (mu_z-b)*(-b*beta*Sh_ZetaC_t(+1))) + Sh_ZetaC_t; %% A.18) Optimal investment I_t = (1/((mu_z^2*S_tilde)*(1+beta)))*((mu_z^2*S_tilde)*(I_t(-1)+beta*I_t(+1) - Sh_MuZ_t+beta*Sh_MuZ_t(+1)) + Qk_t - gamma_idhat) + Sh_Upsilon_t; %% A.19) gamma_cdhat = omega_c*(gamma_mcc)^(1-eta_c)*gamma_mcdhat; %% A.20) gamma_idhat = omega_i*(gamma_mii)^(1-eta_i)*gamma_midhat; %% A.21) gamma_fhat = McX_t + gamma_xstar; %% A.22) Derivative w.r.t. real balances* -mu*psi_zhat + mu*psi_zhat(+1) - mu*Sh_MuZ_t(+1) + (mu-beta*tau_k)*R_t - mu*Pi_t(+1)+tau_k/(1-tau_k)*(beta-mu)*TauK_t(+1) = 0; %% A.23) Derivative w.r.t. capital* psi_zhat + Sh_MuZ_t(+1) - psi_zhat(+1) - beta*(1-delta)/mu_z*Qk_t(+1) + Qk_t - (mu_z-beta*(1-delta))/mu_z*Rk_t(+1) + tau_k/(1-tau_k)*(mu_z-beta*(1-delta))/mu_z*TauK_t(+1); %% A.24) UIP condition (B10)* dS_t(+1)-(R_t-RStar_t) - phi_a*a + Sh_PhiTilde_t; %% A.25) Aggregate resource constraint* (1-omega_c)*gamma_cd^eta_c*c/y_bar*(C_t+eta_c*gamma_cdhat) + (1-omega_i)*gamma_id^eta_i*i/y_bar*(I_t+eta_i*gamma_idhat) + gr*G_t + y_star/y_bar*(YStar_t-eta_f*gamma_xstar+Sh_ZTilde_t) = lambda_d*(Sh_E_t + alpha*(Keff_t-Sh_MuZ_t)+(1-alpha)*L_t) - (1-tau_k)*r_k*k_bar/(y_bar*mu_z)*(Keff_t-K_t(-1)); %% A.26) Law of motion for capital* K_t = (1-delta)*1/mu_z*K_t(-1)-(1-delta)*1/mu_z*Sh_MuZ_t+(1-(1-delta)*1/mu_z)*I_t + Sh_Upsilon_t; %% A.27) Deriative w.r.t. cash holding (without money demand shock) q_hat = 1/sigma_q*(tau_k/(1-tau_k)*TauK_t - psi_zhat - R/(R-1)*R_t(-1)); %% A.28) Money growth* mu_hat - m_barhat - Sh_MuZ_t - Pi_t + m_barhat(-1) = 0; %% A.29) Loan market clearing condition (without firm money demand shock)* nu*w_bar*H*(W_t+L_t) = mu*m_bar/(pi*mu_z)*(mu_hat + m_barhat(-1) - Pi_t - Sh_MuZ_t) - q*q_hat; %% A.30) net foreign assets a = -y_star*McX_t - eta_f*y_star*gamma_xstar + y_star*YStar_t + y_star*Sh_ZTilde_t + (c_m+i_m)*gamma_fhat - (c_m*(-eta_c*(1-omega_c)*(gamma_cd)^(-(1-eta_c))*gamma_mcdhat + C_t) + i_m*(-eta_i*(1-omega_i)*(gamma_id)^(-(1-eta_i))*gamma_midhat+I_t)) + R/(pi*mu_z)*a(-1); %% A.31) Deviation of output from SS Y_t = lambda_d*(Sh_E_t+alpha*(Keff_t-Sh_MuZ_t)+(1-alpha)*L_t); %% A.32) real exchange rate X_t = -omega_c*(gamma_cmc)^(-(1-eta_c))*gamma_mcdhat-gamma_xstar - McX_t; %% A.33) employment equation (B23) E_t = beta/(1+beta)*E_t(+1)+(1/(1+beta))*E_t(-1)+((1-zeta_e)*(1-beta*zeta_e))/((1+beta)*zeta_e)*(L_t-E_t); %% A.34) FOC w.r.t Capital utilization rate U_t = 1/sigma_a*Rk_t - 1/sigma_a*tau_k/(1-tau_k)*TauK_t; %% A.35) Capital utilization rate* U_t = Keff_t - K_t(-1); %% Observables %% B.1) Obs_Pi = 400*(pi-1)*pi + 4*pi*Pi_t; %% B.2) Obs_R = 400*(R-1)*R + 4*R*R_t; %% B.3) Obs_W= 100*log(mu_z)+(W_t-W_t(-1)) + Sh_MuZ_t; Obs_Y = 100*log(mu_z) + (Y_t - Y_t(-1)) + Sh_MuZ_t; %% B.4) Obs_RStar = 400*(R-1)*R + 4*R*RStar_t; %% B.5) Obs_PiStar = 400*(pi-1)*pi + 4*pi*PiStar_t; %% B.6) Obs_YStar = 100*log(mu_z) + (YStar_t - YStar_t(-1) + Sh_MuZ_t) + (Sh_ZTilde_t - Sh_ZTilde_t(-1)); %/ %% Foreign VAR %% C.1) YStar_t = ForLag111*YStar_t(-1) + ForLag112*PiStar_t(-1) + ForLag113*RStar_t(-1) + ForLag211*YStar_t(-2) + ForLag212*PiStar_t(-2) + ForLag213*RStar_t(-2) + ForLag311*YStar_t(-3) + ForLag312*PiStar_t(-3) + ForLag313*RStar_t(-3) + ForLag411*YStar_t(-4) + ForLag412*PiStar_t(-4) + ForLag413*RStar_t(-4) + ForShock11*eps_Sh_YStar + ForShock12*eps_Sh_PiStar + ForShock13*eps_Sh_RStar; %% C.2) PiStar_t = ForLag121*YStar_t(-1) + ForLag122*PiStar_t(-1) + ForLag123*RStar_t(-1) + ForLag221*YStar_t(-2) + ForLag222*PiStar_t(-2) + ForLag223*RStar_t(-2) + ForLag321*YStar_t(-3) + ForLag322*PiStar_t(-3) + ForLag323*RStar_t(-3) + ForLag421*YStar_t(-4) + ForLag422*PiStar_t(-4) + ForLag423*RStar_t(-4) + ForShock21*eps_Sh_YStar + ForShock22*eps_Sh_PiStar + ForShock23*eps_Sh_RStar; %% C.3) RStar_t = ForLag131*YStar_t(-1) + ForLag132*PiStar_t(-1) + ForLag133*RStar_t(-1) + ForLag231*YStar_t(-2) + ForLag232*PiStar_t(-2) + ForLag233*RStar_t(-2) + ForLag331*YStar_t(-3) + ForLag332*PiStar_t(-3) + ForLag333*RStar_t(-3) + ForLag431*YStar_t(-4) + ForLag432*PiStar_t(-4) + ForLag433*RStar_t(-4) + ForShock31*eps_Sh_YStar + ForShock32*eps_Sh_PiStar + ForShock33*eps_Sh_RStar; %% Fiscal VAR %% D.1) TauK_t = FisLag111*TauK_t(-1) + FisLag112*TauY_t(-1) + FisLag113*TauC_t(-1) + FisLag114*TauW_t(-1) + FisLag115*G_t(-1) + FisLag211*TauK_t(-2) + FisLag212*TauY_t(-2) + FisLag213*TauC_t(-2) + FisLag214*TauW_t(-2) + FisLag215*G_t(-2) + FisShock11*eps_Sh_TauK + FisShock12*eps_Sh_TauY + FisShock13*eps_Sh_TauC + FisShock14*eps_Sh_TauW + FisShock15*eps_Sh_G; %% D.2) TauY_t = FisLag121*TauK_t(-1) + FisLag122*TauY_t(-1) + FisLag123*TauC_t(-1) + FisLag124*TauW_t(-1) + FisLag125*G_t(-1) + FisLag221*TauK_t(-2) + FisLag222*TauY_t(-2) + FisLag223*TauC_t(-2) + FisLag224*TauW_t(-2) + FisLag225*G_t(-2) + FisShock21*eps_Sh_TauK + FisShock22*eps_Sh_TauY + FisShock23*eps_Sh_TauC + FisShock24*eps_Sh_TauW + FisShock25*eps_Sh_G; %% D.3) TauC_t = FisLag131*TauK_t(-1) + FisLag132*TauY_t(-1) + FisLag133*TauC_t(-1) + FisLag134*TauW_t(-1) + FisLag135*G_t(-1) + FisLag231*TauK_t(-2) + FisLag232*TauY_t(-2) + FisLag233*TauC_t(-2) + FisLag234*TauW_t(-2) + FisLag235*G_t(-2) + FisShock31*eps_Sh_TauK + FisShock32*eps_Sh_TauY + FisShock33*eps_Sh_TauC + FisShock34*eps_Sh_TauW + FisShock35*eps_Sh_G; %% D.4) TauW_t = FisLag141*TauK_t(-1) + FisLag142*TauY_t(-1) + FisLag143*TauC_t(-1) + FisLag144*TauW_t(-1) + FisLag145*G_t(-1) + FisLag241*TauK_t(-2) + FisLag242*TauY_t(-2) + FisLag243*TauC_t(-2) + FisLag244*TauW_t(-2) + FisLag245*G_t(-2) + FisShock41*eps_Sh_TauK + FisShock42*eps_Sh_TauY + FisShock43*eps_Sh_TauC + FisShock44*eps_Sh_TauW + FisShock45*eps_Sh_G; %% D.5) G_t = FisLag151*TauK_t(-1) + FisLag152*TauY_t(-1) + FisLag153*TauC_t(-1) + FisLag154*TauW_t(-1) + FisLag155*G_t(-1) + FisLag251*TauK_t(-2) + FisLag252*TauY_t(-2) + FisLag253*TauC_t(-2) + FisLag254*TauW_t(-2) + FisLag255*G_t(-2) + FisShock51*eps_Sh_TauK + FisShock52*eps_Sh_TauY + FisShock53*eps_Sh_TauC + FisShock54*eps_Sh_TauW + FisShock55*eps_Sh_G; %% shock processes %% E.1) Sh_E_t = rho_Sh_E*Sh_E_t(-1) + sig_Sh_E*eps_Sh_E; %% E.2) Sh_MuZ_t = rho_Sh_MuZ*Sh_MuZ_t(-1) + sig_Sh_MuZ*eps_Sh_MuZ; %% E.3) Sh_LaF_t = rho_Sh_LaF*Sh_LaF_t(-1) + sig_Sh_LaF*eps_Sh_LaF; %% E.4) Sh_LaMC_t = rho_Sh_LaMC*Sh_LaMC_t(-1) + sig_Sh_LaMC*eps_Sh_LaMC; %% E.5) Sh_LaMI_t = rho_Sh_LaMI*Sh_LaMI_t(-1) + sig_Sh_LaMI*eps_Sh_LaMI; %% E.6) Sh_LaX_t = rho_Sh_LaX*Sh_LaX_t(-1) + sig_Sh_LaX*eps_Sh_LaX; %% E.7) Sh_Upsilon_t = rho_Sh_Upsilon*Sh_Upsilon_t(-1) + sig_Sh_Upsilon*eps_Sh_Upsilon; %% E.8) Sh_PiCpiTarget_t = rho_Sh_PiCpiTarget*Sh_PiCpiTarget_t(-1) + sig_Sh_PiCpiTarget*eps_Sh_PiCpiTarget; %% E.9) Sh_ZetaC_t = rho_Sh_ZetaC*Sh_ZetaC_t(-1) + sig_Sh_ZetaC*eps_Sh_ZetaC; %% E.10) Sh_ZetaH_t = rho_Sh_ZetaH*Sh_ZetaH_t(-1) + sig_Sh_ZetaH*eps_Sh_ZetaH; %% E.11) Sh_ZetaQ_t = rho_Sh_ZetaQ*Sh_ZetaQ_t(-1) + sig_Sh_ZetaQ*eps_Sh_ZetaQ; %% E.12) Sh_PhiTilde_t = rho_Sh_PhiTilde*Sh_PhiTilde_t(-1) + sig_Sh_PhiTilde*eps_Sh_PhiTilde; %% E.13) Sh_ZTilde_t = rho_Sh_ZTilde*Sh_ZTilde_t(-1) + sig_Sh_ZTilde*eps_Sh_ZTilde; %% E.14) Sh_R_t = rho_Sh_R*Sh_R_t(-1) + sig_Sh_R*eps_Sh_R; end; shocks; % Domestic shocks var eps_Sh_E; stderr 1; var eps_Sh_MuZ; stderr 1; var eps_Sh_LaF; stderr 1; var eps_Sh_LaMC; stderr 1; var eps_Sh_LaMI; stderr 1; var eps_Sh_LaX; stderr 1; var eps_Sh_Upsilon; stderr 1; var eps_Sh_PiCpiTarget; stderr 1; var eps_Sh_ZetaC; stderr 1; var eps_Sh_ZetaH; stderr 1; var eps_Sh_ZetaQ; stderr 1; var eps_Sh_PhiTilde; stderr 1; var eps_Sh_ZTilde; stderr 1; var eps_Sh_R; stderr 1; var eps_Sh_RStar; stderr 1; var eps_Sh_YStar; stderr 1; var eps_Sh_PiStar; stderr 1; end; estimated_params; % syntax: name of variable, pior distribution, pior mean, pior standard Error /*rho_R , 0.800000, beta_pdf, 0.80000000, 0.10000000 ; psi_pi , normal_pdf, 1.70000000, 0.10000000; psi_y , normal_pdf, 0.12500000, 0.05000000; psi_x , -0.00900000, normal_pdf, 0.00000000, 0.05000000; psi_dpi , 0.31700000, normal_pdf, 0.30000000, 0.10000000; psi_dy , 0.11600000, normal_pdf, 0.06250000, 0.05000000; sig_Sh_LaF , 0.13200000, inv_gamma_pdf, 0.30000000, 2.00000000; sig_Sh_R , 0.13500000, inv_gamma_pdf, 0.15000000, 2.00000000;*/ rho_R , 0.8000000, beta_pdf, 0.80000000, 0.1000000; psi_pi , 1.73000000, normal_pdf, 1.70000000, 0.10000000; psi_y , 0.10400000, normal_pdf, 0.12500000, 0.05000000; psi_x , -0.00900000, normal_pdf, 0.00000000, 0.05000000; psi_dpi , 0.31000000, normal_pdf, 0.30000000, 0.10000000; psi_dy , 0.12800000, normal_pdf, 0.06250000, 0.05000000; zeta_w , 0.69000000, beta_pdf, 0.67500000, 0.05000000; zeta_d , 0.89100000, beta_pdf, 0.67500000, 0.05000000; zeta_mc , 0.44400000, beta_pdf, 0.50000000, 0.10000000; zeta_mi , 0.72100000, beta_pdf, 0.50000000, 0.10000000; zeta_x , 0.61200000, beta_pdf, 0.50000000, 0.10000000; zeta_e , 0.78700000, beta_pdf, 0.67500000, 0.10000000; iota_w , 0.49700000, beta_pdf, 0.50000000, 0.15000000; iota_d , 0.21700000, beta_pdf, 0.50000000, 0.15000000; iota_mc , 0.22000000, beta_pdf, 0.50000000, 0.15000000; iota_mi , 0.23100000, beta_pdf, 0.50000000, 0.15000000; iota_x , 0.18500000, beta_pdf, 0.50000000, 0.15000000; lambda_d , 1.22200000, inv_gamma_pdf, 1.20000000, 2.00000000; lambda_mi , 1.27500000, inv_gamma_pdf, 1.20000000, 2.00000000; lambda_mc , 1.63300000, inv_gamma_pdf, 1.20000000, 2.00000000; S_tilde , 8.67000000, normal_pdf, 7.69400000, 1.50000000; b , 0.70800000, beta_pdf, 0.65000000, 0.10000000; eta_i , 1.69600000, inv_gamma_pdf, 1.50000000, 4.00000000; eta_f , 1.48600000, inv_gamma_pdf, 1.50000000, 4.00000000; mu_z , 1.00500000, normal_pdf, 1.00600000, 0.00050000; phi_a , 0.25200000, inv_gamma_pdf, 0.01000000, 2.00000000; tau_k , 0.13500000, beta_pdf, 0.12000000, 0.05000000; tau_w , 0.19700000, beta_pdf, 0.20000000, 0.05000000; rho_Sh_E , 0.88600000, beta_pdf, 0.85000000, 0.10000000; rho_Sh_MuZ , 0.69800000, beta_pdf, 0.85000000, 0.10000000; rho_Sh_LaMC , 0.97000000, beta_pdf, 0.85000000, 0.10000000; rho_Sh_LaMI , 0.96300000, beta_pdf, 0.85000000, 0.10000000; rho_Sh_LaX , 0.88600000, beta_pdf, 0.85000000, 0.10000000; rho_Sh_Upsilon , 0.72000000, beta_pdf, 0.85000000, 0.10000000; rho_Sh_ZetaC , 0.89200000, beta_pdf, 0.85000000, 0.10000000; rho_Sh_ZetaH , 0.67600000, beta_pdf, 0.85000000, 0.10000000; rho_Sh_PhiTilde , 0.95500000, beta_pdf, 0.85000000, 0.10000000; rho_Sh_ZTilde , 0.99200000, beta_pdf, 0.85000000, 0.10000000; sig_Sh_E , 0.51900000, inv_gamma_pdf, 0.70000000, 2.00000000; sig_Sh_MuZ , 0.13700000, inv_gamma_pdf, 0.20000000, 2.00000000; sig_Sh_LaF , 0.13200000, inv_gamma_pdf, 0.30000000, 2.00000000; sig_Sh_LaMC , 2.88200000, inv_gamma_pdf, 0.30000000, 2.00000000; sig_Sh_LaMI , 0.35400000, inv_gamma_pdf, 0.30000000, 2.00000000; sig_Sh_LaX , 1.12400000, inv_gamma_pdf, 0.30000000, 2.00000000; sig_Sh_Upsilon , 0.46900000, inv_gamma_pdf, 0.20000000, 2.00000000; sig_Sh_PiCpiTarget , 0.05300000, inv_gamma_pdf, 0.05000000, 2.00000000; sig_Sh_ZetaC , 0.15700000, inv_gamma_pdf, 0.20000000, 2.00000000; sig_Sh_ZetaH , 0.09800000, inv_gamma_pdf, 0.20000000, 2.00000000; sig_Sh_ZetaQ , 1.00000000, inv_gamma_pdf, 0.20000000, 2.00000000; sig_Sh_PhiTilde , 0.18300000, inv_gamma_pdf, 0.05000000, 2.00000000; sig_Sh_ZTilde , 0.21700000, inv_gamma_pdf, 0.40000000, 2.00000000; sig_Sh_R , 0.13500000, inv_gamma_pdf, 0.15000000, 2.00000000; end; steady; check; estimation(datafile=VARDATA,first_obs=50,presample=0,mode_compute=4,mh_replic=0,mode_check); %stoch_simul(irf = 20);% Obs_Pi W_t C_t I_t X_t Obs_R E_t Y_t PiCpi_t; %dynare_sensitivity(identification=1);