%% Declaration of exogenous processes var z varphi_u varphi_r lambda_f_t mu bu br Gh eps_zeta; varexo eps_z eps_varphi_u eps_varphi_r eps_lambda eps_mu eps_bu eps_br eps_g nu_zeta eps_B eps_m eps_T; parameters rho_z rho_varphi rho_mu rho_b rho_g rho_zeta; %% Declaration of model variables parameters alpha beta_u beta_r betabar zeta_p lambda_f chi_pu delta gamma adp qu zeta Csi_ratio C_ratio h sigma_u sigma_r Cu_ss Cr_ss zeta_w nu chi_wu rk Sdp RL R kappa lambda_w coef1 coef2 G T B BL Y rho_B phi_T rho_r phi_pi phi_y zetaprime omega_u omega_r I KBAR lnPi mc_ss; var mc rhk wh Kh Lh Yh X_pnu X_pnr X_pdu X_pdr Csi_u Csi_r pi uh Kbh Ih Cu Cr zetah rL r X_wnu X_wnr X_wdu X_wdr Bh Bh_L Th qh; %% Calibration (mode of distribution of parameters) B = 0.16; G = 0.25; alpha = 0.33; delta = 0.025; lambda_f = 3.5; lambda_w = 3; Y = 1; gamma = 1.9922/400; lnPi = 2.2404/400; beta_u = 1/(1+0.4943/400); zeta = 0.4761/100; BL = B * 0.8222; Sdp = 4.4277; adp = 0.2093; h = 0.8370; sigma_u = 3.0151; sigma_r = 1.5635; zetaprime = 0.2420/100; omega_u = 0.9832; Csi_ratio = 0.7917; C_ratio = 0.7641; chi_wu = 0.5170; nu = 1.6814; zeta_w = 0.6860; zeta_p = 0.9260; phi_T = 1.2660; rho_r = 0.8547; phi_pi = 1.5644; phi_y = 0.2975; rho_z = 0.1286; rho_mu = 0.8293; rho_b = 0.9603; rho_varphi = 0.5200; rho_B = 0.9773; rho_zeta = 0.9614; rho_g = 0.7581; %% Steady-state values omega_r = 1 - omega_u; R = exp(lnPi)*exp(gamma)/beta_u; RL = (1+zeta) * R; beta_r = beta_u/(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); mc_ss = 1/(1+lambda_f); w_til = (1+lambda_f)^(-1/(1-alpha)) * alpha^(alpha/(1-alpha)) * (1-alpha); w_ss = w_til * rk^(-alpha/(1-alpha)); K_til = alpha/(1+lambda_f); K = K_til/rk; L = K^(-alpha/(1-alpha)); KBAR = exp(gamma) * K_til/rk; I = (exp(gamma)-(1-delta))*K_til/rk; Cr_ss = (1-I-G)/(omega_u*C_ratio + omega_r); Cu_ss = C_ratio * Cr_ss; %% Composite parameters kappa = RL - RL/30; 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 = (BL/B)/(RL-kappa); coef2 = ((1-exp(-gamma)*(exp(lnPi))^(-1)*kappa)*RL)/(RL-kappa); %Letting this here because of kappa... T = G - (1 - (1/beta_u))*B - ( (1/(RL-kappa)) - (RL/(RL-kappa))*(1/(exp(gamma)*exp(lnPi))) ) * BL; model; %Exogenous processes (A.46-A.52) z = rho_z*z(-1)+eps_z; varphi_u = rho_varphi * varphi_u(-1) + eps_varphi_u; varphi_r = rho_varphi * varphi_r(-1) + eps_varphi_r; lambda_f_t = eps_lambda; mu = rho_mu * mu(-1) + eps_mu; bu = rho_b * bu(-1) + eps_bu; br = rho_b * br(-1) + eps_br; Gh = rho_g * Gh(-1) + eps_g; eps_zeta = rho_zeta * eps_zeta(-1) + nu_zeta; %Log-linearized equations 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 + lambda_f_t + mc) + (beta_u*zeta_p)*EXPECTATION(0)((1+lambda_f)/lambda_f * pi(+1) + X_pnu(+1)); X_pnr = (1-beta_r*zeta_p)*(Csi_r + Yh + lambda_f_t + mc) + (beta_r*zeta_p)*EXPECTATION(0)((1+lambda_f)/lambda_f * pi(+1) + X_pnr(+1)); X_pdu = (1-beta_u*zeta_p)*(Csi_u + Yh) + (beta_u*zeta_p)*EXPECTATION(0)(pi(+1)/lambda_f + X_pdu(+1)); X_pdr = (1-beta_r*zeta_p)*(Csi_r + Yh) + (beta_r*zeta_p)*EXPECTATION(0)(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))*(mu+Ih); rhk = adp/rk * uh; qh = betabar*exp(-gamma)*EXPECTATION(0)(rk*rhk(+1)+(1-delta)*qh(+1)) - EXPECTATION(0)(z(+1)) + EXPECTATION(0)(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*EXPECTATION(0)(z(+1) + Ih(+1) - Ih); Csi_u = (1/(1-beta_u*h))* (bu - beta_u*h*EXPECTATION(0)(bu(+1)) - (sigma_u/(1-h))*((1+beta_u*h^2)*Cu - beta_u*h*EXPECTATION(0)(Cu(+1)) - h*Cu(-1))); Csi_r = (1/(1-beta_r*h))* (br - beta_r*h*EXPECTATION(0)(br(+1)) - (sigma_r/(1-h))*((1+beta_r*h^2)*Cr - beta_r*h*EXPECTATION(0)(Cr(+1)) - h*Cr(-1))); Csi_u = r + EXPECTATION(0)(Csi_u(+1)-z(+1)-pi(+1)); zetah + Csi_u = (RL/(RL-kappa))*rL + EXPECTATION(0)(Csi_u(+1) - z(+1) - pi(+1) - (kappa/(RL-kappa)) * rL(+1)); Csi_r = (RL/(RL-kappa))*rL + EXPECTATION(0)(Csi_r(+1) - z(+1) - pi(+1) - (kappa/(RL-kappa)) * rL(+1)); X_wnu = (1-zeta_w*beta_u) * (bu + varphi_u + (1+nu)*Lh + ((1+lambda_w)/lambda_w)*(1+nu)*wh) + (zeta_w*beta_u)*EXPECTATION(0)( ((1+lambda_w)/lambda_w)*(1+nu)*(pi(+1)+z(+1)) + X_wnu(+1) ); X_wnr = (1-zeta_w*beta_r) * (br + varphi_r + (1+nu)*Lh + ((1+lambda_w)/lambda_w)*(1+nu)*wh) + (zeta_w*beta_r)*EXPECTATION(0)( ((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)*EXPECTATION(0)((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)*EXPECTATION(0)((1/lambda_w)*(pi(+1)+z(+1)) + X_wdr(+1)); wh = (1-zeta_w)*(1+((1+lambda_w)/lambda_w)*nu)^(-1) * (chi_wu*(X_wnu-X_wdu)+(1-chi_wu)*(X_wnr-X_wdr)) + zeta_w *(wh(-1)-pi-z); Bh + coef1 * Bh_L = (1/beta_u)*(Bh(-1) + r(-1))+ coef1*(1/beta_r)*Bh_L(-1) + coef2 * coef1 * rL + G/B * Gh - Y/B * Th - ((1/beta_u) + coef1 * (1/beta_r))*(z+pi); Bh_L - (RL/(RL-kappa))*rL = rho_B * (Bh_L(-1) - (RL/(RL-kappa))*rL(-1)) + eps_B; (Th-G*Gh)/(T-G) = phi_T * ((Bh(-1) + coef1*Bh_L(-1) - (RL/(RL-kappa))*coef1* rL(-1))/(1+coef1)) + eps_T; r = rho_r * r(-1) + (1-rho_r)*(phi_pi * pi + phi_y*(Yh - Yh(-4) + z + z(-1) + z(-2) + z(-3))) + eps_m; zetah = zetaprime * Bh_L + eps_zeta; Yh = (omega_u*Cu_ss/Y)*Cu + (omega_r*Cr_ss/Y)*Cr + I/Y*Ih + G/Y*Gh + exp(-gamma)*rk*KBAR/Y*uh; end; resid(1); steady; check;