// Endogenous variables: var C_T // Tradable consumption C_N // Nontradable consumption I_T // Investment in capital for Tradable sector I_N // Investment in capital for Nontradable sector I_C // Investment in capital for Commodity sector L_T // Tradable sector Labor L_N // Nontradable sector Labor L_C // Commodity sector Labor lambda // Lagrange multiplier D // debt stock A_N // Productivity factor of Nontradable sector K_N // Capital for Nontradable sector Y_N // Output of Nontradable sector A_C // Productivity factor of Commodity sector K_C // Capital for Commodity sector Y_C // Output of Commodity sector TB_C // Trade balance of nontradable sector A_T // Productivity factor of Tradable sector K_T // Capital for Tradable sector CM_T // Demand for Commodity goods from Tradable sector Y_T // Output of tradable sector TB_T // Trade Balance of tradable sector I // Total Investment C // Consumption TB // Total Trade balance Y // Total Production P_N // Price of Nontradable good P_C // Price of commodity goods R // Interest rate of borrowing mu_T // rental rate of capital for Tradable sector mu_N // rental rate of capital for nontradable sector mu_C // rental rate of capital for Commodity sector W_T // Wage for Tradable sector W_N // Wage for Nontradable sector W_C; // Wage for Commodity sector // Exogenous variables: varexo eps_C // Shock in Commodity price process eps_R // Shock in Risk premium process eps_AT // Shock in productivity factor in Tradable sector eps_AN // Shock in productivity factor in Tradable sector eps_AC; // Shock in productivity factor in Tradable sector parameters betaa // Subjective discount factor varphi // Elasticity of substitution sigma // relative risk coeficient omega_T // Frisch elasticity of labor supply for Tradable sector omega_N // Frisch elasticity of labor supply for Nontradable sector omega_C // Frisch elasticity of labor supply for Commodity sector chi // a number between 0 and 1 used in the CES aggregator phi_T // parameter in the capital adjustment cost for Tradable sector phi_N // parameter in the capital adjustment cost for Nradable sector phi_C // parameter in the capital adjustment cost for Commodity sector delta // depreciation rate alpha_T // output elasticity of capital for Tradable sector alpha_N // output elasticity of capital for nontradable sector alpha_C // output elasticity of capital for Commodity sector gammaa_T // output elasticity of commodity goods for Tradable sector v_C // Coefficient used in the price commodity process v_D // Coefficient used in the price commodity process rho_C // autoregressive coefficient for commodity price process rho_AT // autoregressive coefficient for productivity factor process in the Tradable sector rho_AN // autoregressive coefficient for productivity factor process in the nontradable sector rho_AC // autoregressive coefficient for productivity factor process in the commodity sector Rss // Interest rate in the steady state used in the exogenous process Dss // Debt in the steady state used in the exogenous process Pss_C; // Commodity price in the steady state used in the exogenous process varphi = 0.5; sigma = 2; omega_T = 1.455; omega_N = 1.455; omega_C = 1.455; chi = 0.35; delta = 0.025; alpha_T = 0.35; alpha_N = 0.25; alpha_C = 0.35; gammaa_T = 0.05; phi_T = 4.6; phi_N = 9.3; phi_C =10.3; rho_C = 0.95; rho_AC = 0.88; rho_AT = 0.87; rho_AN = 0.84; v_D = 0.077; v_C = -0.014; Pss_C = 0.69; Dss = 0.12; Rss = 1.02; betaa = 1/Rss; model; // Households: // 1. Price of nontradable goods: P_N = ((1-chi)/chi)*((C_T/C_N)^(1/varphi)); // 2-4. Labor supply for each sector: (L_T^(omega_T - 1)) = chi*((C/C_T)^(1/varphi))*W_T; (L_N^(omega_N - 1)) = chi*((C/C_T)^(1/varphi))*W_N; (L_C^(omega_C - 1)) = chi*((C/C_T)^(1/varphi))*W_C; // 5. Euler equation: lambda = betaa*R*lambda(+1); // 6. CES aggregator: C = (chi*(C_T^((varphi-1)/varphi)) + (1-chi)*(C_N^((varphi - 1)/varphi)))^(varphi/(varphi-1)); // 7. Lagrange multiplier: lambda = ((C - ((L_T^omega_T)/omega_T) - ((L_N^omega_N)/omega_N) - ((L_C^omega_C)/omega_C))^(-sigma))*chi*((C/C_T)^(1/varphi)); // 8-10. Euler equation: lambda*(1 + phi_T*(K_T - K_T(-1))) = betaa*lambda(+1)*(1- delta + mu_T(+1) - phi_T*(K_T(+1) - K_T)); lambda*(1 + phi_N*(K_N - K_N(-1))) = betaa*lambda(+1)*(1- delta + mu_N(+1) - phi_N*(K_N(+1) - K_N)); lambda*(1 + phi_C*(K_C - K_C(-1))) = betaa*lambda(+1)*(1- delta + mu_C(+1) - phi_C*(K_C(+1) - K_C)); // 11-13. Law of motion of capital: K_T = I_T + (1-delta)*K_T(-1) - phi_T*(K_T - K_T(-1)); K_N = I_N + (1-delta)*K_N(-1) - phi_N*(K_N - K_N(-1)); K_C = I_C + (1-delta)*K_C(-1) - phi_C*(K_C - K_C(-1)); // Firms FOC: // 14-17. Tradable sector FOC: Y_T = A_T*(K_T(-1)^alpha_T)*(CM_T^gammaa_T)*(L_T^(1 - gammaa_T - alpha_T)); L_T = (1 - alpha_T - gammaa_T)*(Y_T/W_T); K_T(-1) = alpha_T*(Y_T/mu_T); CM_T = gammaa_T*(Y_T/P_C); // 18-20. Nontradable Sector: Y_N = A_N*(K_N(-1)^alpha_N)*(L_N^(1 - alpha_N)); L_N = (1-alpha_N)*(Y_N*P_N/W_N); K_N(-1) = alpha_N*(Y_N*P_N/mu_N); // 21-23. Commodity Sector: Y_C = A_C*(K_C(-1)^alpha_C)*(L_C^(1 - alpha_C)); L_C = (1 - alpha_C)*((Y_C*P_C)/W_C); K_C(-1) = alpha_C*((Y_C*P_C)/mu_C); // Market Clearing // 24. Nontradable Sector: C_N = Y_N; // 25. Tradable Sector: Y_T = C_T + I_T + I_N + I_C + TB_T; // 26. Commodity Sector: P_C*Y_C = P_C*CM_T + TB_C; // 27. Balance of payments: TB_T + TB_C = D(+1) + D*(R-2); // 28. Total trade balance: TB = TB_T + TB_C; // 29. Total Investment: I = I_T + I_N + I_C; // 30. Total Output: Y = Y_T + P_N*Y_N + P_C*Y_C; // Exogenous Process: // 31. Commodity Price ln(P_C) = rho_C*ln(P_C(-1)) + eps_C; // 32. Risk Premium: R = Rss + v_D*(exp(D - Dss) - 1) + v_C*(exp(P_C - Pss_C) - 1) + eps_R; // 33-35. Productivity sector: ln(A_T) = rho_AT*ln(A_T(-1)) + eps_AT; ln(A_N) = rho_AN*ln(A_N(-1)) + eps_AN; ln(A_C) = rho_AC*ln(A_C(-1)) + eps_AC; end; steady(solve_algo = 1, maxit=50000); check; shocks; var eps_C; stderr 0.01; //var eps_R; stderr 0.02; //var eps_AT; stderr ; //var eps_AN; stderr ; //var eps_AC; stderr ; end; stoch_simul(order=1,irf=40) Y I C TB P_N;