% Running the open economy with open economy parameter estimates %-------------------------------------------------------------------------- % 40 Endogenous variables %-------------------------------------------------------------------------- var uc_h ul_h y_h c_h i_h k_h q_i_h r_k_h R_h b_h l_h w_h v_h delv_h g_h z_h tk_h tl_h tc_h tau_k_h tau_l_h tau_c_h u_b_h u_l_h u_i_h u_a_h u_g_h u_tk_h u_tl_h u_tc_h u_z_h b_f b by_h by_f by tb_h tby_h cay_h risk_prem U welfare; %-------------------------------------------------------------------------- % Endogenous variable definitions %-------------------------------------------------------------------------- % uc_h : marginal utility of consumption % ul_h : marginal utility of hours worked % y_h : log of home output % c_h : log of home consumption % i_h : log of home investment % k_h : log of home capital stock % q_i_h : log of home investment price % l_h : log of home labour % w_h : log of the home real wage % b_h : log of the number of home bonds % v_h : log of the utilization level % delv_h : log of the depreciation rate % g_h : log of home government consumption % tk_h : log of home total capital tax revenue % tl_h : log of home total labour tax revenue % tc_h : log of home total consumption tax revenue % tau_k_h : log of home capital tax rate % tau_l_h : log of home labour tax rate % tau_c_h : log of home consumption tax rate % z_h : log of home government lump sum transfers % b_h : log of home debt % b_f : log of foreign debt % by_h : log of home debt to output ratio % by_f : log of foreign debt to output ratio % by : log of total debt to output ratio % b : log of total debt % R_h : log of debt elastic interest rate % tb_h : log of home trade balance % tby_h : log of home trade balance to output ratio % cay_h : log of home current account to output ratio % u_b_h : log of home general preference shock % u_l_h : log of home labour supply shock % u_i_h : log of home investment specific shock % u_a_h : log of home technology % u_g_h : log of home government spending shock % u_tk_h : log of home capital tax rate shock % u_tl_h : log of home labour tax rate shock % u_tc_h : log of home consumption tax rate shock % u_z_h : log of home government lump sum transfers shock %-------------------------------------------------------------------------- % 9 Exogenous shocks (error terms) %-------------------------------------------------------------------------- varexo e_u_b_h e_u_l_h e_u_i_h e_u_a_h e_u_g_h e_u_tk_h e_u_tl_h e_u_tc_h e_u_z_h; %-------------------------------------------------------------------------- % Parameters %-------------------------------------------------------------------------- parameters BETA GAMMA H DELTA0 DELTA1 DELTA2 ALPHA CHI ZETA UPS PSI2 R_w KAPPA TK_h_bar TL_h_bar TC_h_bar L_h_bar GY_h_bar BY_h_bar BY_f_bar G_h_bar Y_h_bar B_bar B_h_bar B_f_bar Z_h_bar TAU_K_h_bar TAU_L_h_bar TAU_C_h_bar EPSI_G EPSI_K EPSI_L EPSI_Z GAMMA_G GAMMA_K GAMMA_L GAMMA_Z PHI_KL PHI_KC PHI_LC RHO_B RHO_L RHO_I RHO_G RHO_A RHO_TK RHO_TL RHO_TC RHO_Z SIGMA_A_H SIGMA_B_H SIGMA_L_H SIGMA_I_H SIGMA_G_H SIGMA_Z_H SIGMA_TK_H SIGMA_TL_H SIGMA_TC_H ; %-------------------------------------------------------------------------- % Calibration %-------------------------------------------------------------------------- % We set BETA. This implies a value for steady state R. % From here we can work out steady state Rk, K, Y, I and finally C (in that order). % Parameter values are from Letendre (2007) and SGU (2003) BETA = 0.993; R_w = 1/BETA; PSI2 = 0.021; % 0.001 Letendre (2007) KAPPA = 0.57; DELTA0 = 0.025; ALPHA = 0.32; GAMMA = 1.27; H = 0.6; CHI = 5.09; UPS = 0.500; ZETA = 1.0; DELTA2 = 0.83; GY_h_bar = .23; BY_h_bar =0.56; BY_f_bar = .10; % Parameter values come from the mean of the respective series TAU_K_h_bar = 0.22; TAU_L_h_bar = 0.11; TAU_C_h_bar = 0.099; % Parameter values from Leeper (2010) GAMMA_G = 0.30; GAMMA_K = 0.02; GAMMA_L = 0.03; GAMMA_Z = 0.35; EPSI_K = 1.93; EPSI_L = 0.54; EPSI_G = 0.05; EPSI_Z = 0.15; PHI_KL = 0.11; PHI_KC = -0.05; PHI_LC = -0.04; %-------------------------------------------------------------------------- % Definitions of parameters %-------------------------------------------------------------------------- % BETA : discount factor % R_w : world interest rate % PSI2 : coefficient for debt elastic interest rate % KAPPA : inverse Frish elasticity % DELTA0 : % ALPHA : capital share % GY_h_bar : SS ratio of government spending to GDP % BY_h_bar : SS debt, Ratio of government (public held at home) debt to GDP % BY_f_bar : Ratio of government (public held abroad) debt to GDP % TAU_K_h_bar : Steady state capital tax rate % TAU_L_h_bar : Steady state labor tax rate % TAU_C_h_bar : Steady state consumption tax rate % GAMMA : Risk aversion % H : Habit formation % CHI : Investment adjustment cost parameters and is 0 <= CHI % UPS : Capital adjustment cost parameters and 0 < UPS <= 1 % Capital and/or Investment adjustment cost parameters and 0 <= ZETA <= 1 % ZETA =1 Pure investment adjustment costs as in Christiano and Eichenbaum %(2005) % ZETA =0 Pure capital adjustment costs as in Backus, Routledge and Zin (2007) % ZETA : Capital and/or Investment adjustment cost parameters % DELTA2 : Capital utilization % GAMMA_G : Government spending debt coefficient % GAMMA_K : Capital tax rate debt coefficient % GAMMA_L : Labor tax rate debt coefficient % GAMMA_Z : Transfers debt coefficient % EPSI_K : Capital tax rate output coefficient % EPSI_L : Labor tax rate output coefficient % EPSI_G : Government spending output coefficient % EPSI_Z : Transfers output coefficient % PHI_KL : Capital-Labor co-term % PHI_KC : Capital-Consumption co-term % PHI_LC : Labor-Consumption co-term %-------------------------------------------------------------------------- % Parameters for the exogenous shocks %-------------------------------------------------------------------------- RHO_A = 0.99; SIGMA_A_H = 0.59; RHO_B = 0.91; SIGMA_B_H = 0.76; RHO_L = 0.99; SIGMA_L_H = 2.15; RHO_I = 0.51; SIGMA_I_H = 1.61; RHO_G = 0.98; SIGMA_G_H = 2.12; RHO_TK = 0.98; SIGMA_TK_H = 2.23; RHO_TL = 0.95; SIGMA_TL_H = 1.95; RHO_TC = 0.86; SIGMA_TC_H = 2.78; RHO_Z = 0.99; SIGMA_Z_H = 3.05; %-------------------------------------------------------------------------- % Steady states %-------------------------------------------------------------------------- R_h_bar = 1/BETA; R_K_h_bar = (R_h_bar + DELTA0 - 1) / (1-TAU_K_h_bar); DELTA1 = R_K_h_bar * (1-TAU_K_h_bar); K_h_bar = ( ( ((1-H)*( (R_K_h_bar/ALPHA)*(1-GY_h_bar-BY_f_bar*(R_h_bar-1))-DELTA0) ))^(-GAMMA)* ((1-TAU_L_h_bar)*(1-ALPHA)/(1+TAU_C_h_bar))*(R_K_h_bar/ALPHA)^((ALPHA+KAPPA)/(ALPHA-1)) ) ^ (1/(GAMMA+KAPPA)) ; L_h_bar = (R_K_h_bar/ALPHA)^(1/(1-ALPHA)) * K_h_bar; Y_h_bar = K_h_bar^ALPHA * L_h_bar^(1-ALPHA); I_h_bar = DELTA0 * K_h_bar; G_h_bar = GY_h_bar * Y_h_bar; B_h_bar = BY_h_bar * Y_h_bar; W_h_bar = (1-ALPHA)* Y_h_bar / L_h_bar ; B_f_bar = BY_f_bar * Y_h_bar; C_h_bar = Y_h_bar - I_h_bar - G_h_bar - (R_h_bar-1)*B_f_bar; TB_h_bar = Y_h_bar - (C_h_bar+I_h_bar+G_h_bar); TBY_h_bar = TB_h_bar/Y_h_bar; CAY_h_bar = (-(R_h_bar-1) * B_f_bar + TB_h_bar) / Y_h_bar; BY_h_bar = B_h_bar/Y_h_bar; BY_f_bar = B_f_bar/Y_h_bar; B_bar = B_h_bar + B_f_bar; BY_bar = BY_h_bar + BY_f_bar; TK_h_bar = TAU_K_h_bar * ALPHA * Y_h_bar; TL_h_bar = TAU_L_h_bar * (1-ALPHA) * Y_h_bar; TC_h_bar = TAU_C_h_bar * C_h_bar; Z_h_bar = TK_h_bar + TL_h_bar + TC_h_bar - G_h_bar - (R_h_bar-1)*B_bar; Uc_h_bar = (C_h_bar-H*C_h_bar) ^(-GAMMA) ; Ul_h_bar = -(L_h_bar ^ KAPPA) ; disp('Steady state DELTA0'); disp(DELTA0); disp('Steady state DELTA1'); disp(DELTA1); disp('Steady state KAPPA'); disp(KAPPA); disp('====================='); disp('LEVELS'); disp('Steady state R_h_bar'); disp(R_h_bar); disp('Steady state R_K_h_bar'); disp(R_K_h_bar); disp('Steady state Uc_h_bar'); disp(Uc_h_bar); disp('Steady state Ul_h_bar'); disp(Ul_h_bar); disp('Steady state y_h'); disp(Y_h_bar); disp('Steady state c_h'); disp(C_h_bar); disp('Steady state i_h'); disp(I_h_bar); disp('Steady state l_h'); disp(L_h_bar); disp('Steady state w_h'); disp(W_h_bar); disp('Steady state k_h'); disp(K_h_bar); disp('Steady state g_h'); disp(G_h_bar); disp('Steady state b_h'); disp(B_h_bar); disp('Steady state b_f'); disp(B_f_bar); disp('Steady state by_h'); disp(BY_h_bar); disp('Steady state by_f'); disp(BY_f_bar); disp('Steady state b'); disp(B_bar); disp('Steady state by'); disp(BY_bar); disp('Steady state z_h'); disp(Z_h_bar); disp('Steady state tb_h'); disp(TB_h_bar); disp('Steady state tby_h'); disp(TBY_h_bar); disp('Steady state cay_h'); disp(CAY_h_bar); disp('Steady state tk_h'); disp(TK_h_bar); disp('Steady state tl_h'); disp(TL_h_bar); disp('Steady state tc_h'); disp(TC_h_bar); disp('Steady state tau_k_h'); disp(TAU_K_h_bar); disp('Steady state tau_l_h'); disp(TAU_L_h_bar); disp('Steady state tau_c_h'); disp(TAU_C_h_bar); disp('====================='); disp(' '); disp('====================='); disp('Convert to logs'); R_K_h_bar = log(R_K_h_bar); Y_h_bar = log(Y_h_bar); C_h_bar = log(C_h_bar); I_h_bar = log(I_h_bar); L_h_bar = log(L_h_bar); K_h_bar = log(K_h_bar); W_h_bar = log(W_h_bar); G_h_bar = log(G_h_bar); TK_h_bar = log(TK_h_bar); TL_h_bar = log(TL_h_bar); TC_h_bar = log(TC_h_bar); TAU_K_h_bar = log(TAU_K_h_bar); TAU_L_h_bar = log(TAU_L_h_bar); TAU_C_h_bar = log(TAU_C_h_bar); disp('Steady state R_K_h_bar'); disp(R_K_h_bar); disp('Steady state y_h'); disp(Y_h_bar); disp('Steady state c_h'); disp(C_h_bar); disp('Steady state i_h'); disp(I_h_bar); disp('Steady state l_h'); disp(L_h_bar); disp('Steady state w_h'); disp(W_h_bar); disp('Steady state k_h'); disp(K_h_bar); disp('Steady state g_h'); disp(G_h_bar); disp('Steady state tk_h'); disp(TK_h_bar); disp('Steady state tl_h'); disp(TL_h_bar); disp('Steady state tc_h'); disp(TC_h_bar); disp('Steady state tau_k_h'); disp(TAU_K_h_bar); disp('Steady state tau_l_h'); disp(TAU_L_h_bar); disp('Steady state tau_c_h'); disp(TAU_C_h_bar); disp('====================='); %-------------------------------------------------------------------------- % Model %-------------------------------------------------------------------------- model; U = (u_b_h) * ( ( c_h - H*c_h(-1) )^(1-GAMMA)/(1-GAMMA) - (u_l_h)* l_h^(1+KAPPA)/(1+ KAPPA)); welfare = U + BETA*welfare(+1); risk_prem = PSI2*(exp(b_f - B_f_bar) - 1); exp(R_h) = R_w + risk_prem ; by_h = b_h/exp(y_h); by_f = b_f/exp(y_h); b = b_h + b_f; by = by_h + by_f; tb_h = exp(y_h) - exp(c_h) - exp(i_h) - exp(g_h) ; tby_h = tb_h/exp(y_h); cay_h = tby_h - (exp(R_h(-1))-1)*b_f(-1)/exp(y_h); % MU of consumption (Habit is not internalized) uc_h = exp(u_b_h)*( exp(c_h) - H*exp(c_h(-1)) ) ^(-GAMMA) ; % MU of hours worked ul_h = -exp(u_b_h)*exp(u_l_h)*exp(l_h) ^ KAPPA ; % Equation 6: Endogenous depreciation rate of the capital stock exp(delv_h) = DELTA0 + DELTA1*(exp(v_h) - 1) + (DELTA2/2)*(exp(v_h) - 1)^2; % Equation 9: marginal product of labour exp(w_h) = (1-ALPHA) * exp(y_h)/exp(l_h) ; % Marginal product of capital exp(r_k_h) = ALPHA * exp(y_h)/(exp(v_h)*exp(k_h(-1))) ; % Equation (A.1): Euler equation - intertemporal condition uc_h/(1+exp(tau_c_h)) = BETA*exp(R_h)*uc_h(+1)/(1+exp(tau_c_h(+1))); % Equation (A.2): Intratemporal condition ul_h + uc_h * exp(w_h) * (1-exp(tau_l_h))/(1+exp(tau_c_h)) = 0; % Equation (A.3): marginal conditions for capital exp(q_i_h) = ( exp(q_i_h(+1))*(1-exp(delv_h(+1))) + (1-exp(tau_k_h(+1)))*ALPHA * exp(y_h(+1))/exp(k_h) + exp(q_i_h(+1))*( ( (1-ZETA)*(1-UPS)*DELTA0/UPS)*( ( exp(u_i_h(+1))*exp(i_h(+1))/exp(k_h))^UPS * DELTA0^(-UPS) - 1 ) ) ) /exp(R_h) ; % Equation (A.4): marginal conditions for intensity of capital exp(r_k_h)*(1-exp(tau_k_h)) = exp(q_i_h)*( DELTA1 + DELTA2*(exp(v_h) - 1) ) ; % Equation (A.5): marginal conditions for investment 1.0 = exp(q_i_h)* ( ZETA*( 1.0 - 0.5*CHI - 1.5*CHI*(exp(u_i_h)*exp(i_h)/exp(i_h(-1)))^2 + 2.0*CHI*(exp(u_i_h)*exp(i_h)/exp(i_h(-1))) ) + (1-ZETA)* ( (exp(u_i_h)*exp(i_h)/exp(k_h(-1)))^(UPS-1) * DELTA0^(1-UPS) ) ) + exp(q_i_h(+1)) *ZETA *CHI *( (exp(u_i_h(+1))*exp(i_h(+1))/exp(i_h))^3 -(exp(u_i_h(+1))*exp(i_h(+1))/exp(i_h))^2 ) / exp(R_h) ; % Equation (A.6): final goods market equilibrium LIKE SGU BUT ADJUSTMENT COSTS % ARE PUT IN CAPITAL ACCUMULATION PROCESS b_f = exp(R_h(-1)) * b_f(-1) - exp(y_h) + exp(c_h) + exp(i_h) + exp(g_h); %Equation : Household resource constraint (1+exp(tau_c_h))*exp(c_h) + exp(i_h) + b_h = exp(l_h)*exp(w_h)*(1-exp(tau_l_h)) + exp(r_k_h)*(1-exp(tau_k_h))*exp(k_h(-1)) + exp(R_h(-1))*b_h(-1) + z_h ; % Equation (A.7): Capital stock accumulation (adjusted to allow for either IAC % and/or CAC) % Note if ZETA=1 it is the same as Leeper et al (2009). exp(k_h) = (1-exp(delv_h))*exp(k_h(-1)) + ZETA *( (1 - 0.5 * CHI * (exp(u_i_h)*exp(i_h)/exp(i_h(-1))-1.0)^2) * exp(i_h) ) + (1-ZETA)*( ( (exp(u_i_h)*exp(i_h)/exp(k_h(-1)))^UPS * DELTA0^(1-UPS) - (1-UPS)* DELTA0 )*(exp(k_h(-1))/UPS) ); % Equation (A.9): Total capital tax revenue exp(tk_h) = exp(tau_k_h) * ALPHA * exp(y_h) ; % Equation (A.10): Total labour tax revenue exp(tl_h) = exp(tau_l_h) * (1-ALPHA) * exp(y_h) ; % Equation (A.11): Total consumption tax revenue exp(tc_h) = exp(tau_c_h) * exp(c_h) ; % Equation (A.12): Production function exp(y_h) = exp(u_a_h) * (exp(v_h)*exp(k_h(-1)))^ALPHA * exp(l_h)^(1-ALPHA); %-------------------------------------------------------------------------- % Fiscal rules where instruments respond to foreign debt %-------------------------------------------------------------------------- %Equation 11: Government spending policy rule g_h - G_h_bar = - EPSI_G*(y_h-Y_h_bar) - GAMMA_G*(b(-1)-B_bar) + (u_g_h) ; %Equation 12: Capital tax policy rule tau_k_h - TAU_K_h_bar = EPSI_K*(y_h-Y_h_bar) + GAMMA_K*(b(-1)-B_bar) + PHI_KL*u_tl_h + PHI_KC*u_tc_h + (u_tk_h) ; %Equation 13: Labour tax policy rule tau_l_h - TAU_L_h_bar = EPSI_L*(y_h-Y_h_bar) + GAMMA_L*(b(-1)-B_bar) + PHI_KL*u_tk_h + PHI_LC*u_tc_h + (u_tl_h) ; %Equation 14: Consumption tax policy rule tau_c_h - TAU_C_h_bar = PHI_KC*(u_tk_h) + PHI_LC*(u_tl_h) + (u_tc_h) ; %Equation 15: Transfers tax policy rule z_h - Z_h_bar = - EPSI_Z*(y_h-Y_h_bar) - GAMMA_Z*(b(-1)-B_bar) + (u_z_h) ; %-------------------------------------------------------------------------- % Exogenous shocks %-------------------------------------------------------------------------- % Equation 1: Taste shock u_b_h = RHO_B * u_b_h(-1) + e_u_b_h; % Equation 2: Leisure shock u_l_h = RHO_L * u_l_h(-1) + e_u_l_h; % Equation 5: Utilization shock u_i_h = RHO_I * u_i_h(-1) + e_u_i_h; % Equation 8: Technology shock u_a_h = RHO_A * u_a_h(-1) + e_u_a_h; u_g_h = RHO_G * u_g_h(-1) + e_u_g_h; u_tk_h = RHO_TK * u_tk_h(-1) + e_u_tk_h; u_tl_h = RHO_TL * u_tl_h(-1) + e_u_tl_h; u_tc_h = RHO_TC * u_tc_h(-1) + e_u_tc_h; u_z_h = RHO_Z * u_z_h(-1) + e_u_z_h; end; %-------------------------------------------------------------------------- % Computation/Initial Values %-------------------------------------------------------------------------- initval; U = 0; welfare = 0; R_h = log(R_h_bar); uc_h = Uc_h_bar; ul_h = Ul_h_bar; y_h = Y_h_bar; c_h = C_h_bar; i_h = I_h_bar; l_h = L_h_bar; k_h = K_h_bar; w_h = W_h_bar; g_h = G_h_bar; b = B_bar; b_h = B_h_bar; b_f = B_f_bar; by = BY_bar; by_h = BY_h_bar; by_f = BY_f_bar; tb_h = TB_h_bar; tby_h = TBY_h_bar; cay_h = CAY_h_bar; risk_prem = 0; z_h = Z_h_bar; r_k_h = R_K_h_bar; tk_h = TK_h_bar; tl_h = TL_h_bar; tc_h = TC_h_bar; tau_k_h = TAU_K_h_bar; tau_l_h = TAU_L_h_bar; tau_c_h = TAU_C_h_bar; v_h = 0; delv_h = log(DELTA0); q_i_h = 0; u_b_h = 0; u_l_h = 0; u_i_h = 0; u_a_h = 0; u_g_h = 0; u_tk_h = 0; u_tl_h = 0; u_tc_h = 0; u_z_h = 0; end; %-------------------------------------------------------------------------- % shocks block %-------------------------------------------------------------------------- shocks; var e_u_b_h = SIGMA_B_H ^2; var e_u_l_h = SIGMA_L_H ^2; var e_u_i_h = SIGMA_I_H ^2; var e_u_a_h = SIGMA_A_H ^2; var e_u_g_h = SIGMA_G_H ^2; var e_u_z_h = SIGMA_Z_H ^2; var e_u_tk_h = SIGMA_TK_H ^2; var e_u_tl_h = SIGMA_TL_H ^2; var e_u_tc_h = SIGMA_TC_H ^2; end; %-------------------------------------------------------------------------- % Simulation %-------------------------------------------------------------------------- steady(solve_algo=2); resid; check; %model_info; stoch_simul(order=2,pruning,periods=100000,nograph); %stoch_simul(order=1,hp_filter=1600,irf=40, conditional_variance_decomposition=1) y_h c_h i_h l_h b b_h b_f w_h r_k_h R_h risk_prem cay_h tby_h %g_h z_h tau_k_h tau_l_h tau_c_h tk_h tl_h tc_h;