%-------------------------------------------------------------------------- % ROT model with distortionary taxes and debt % All adjust where both agents receieve/pay transfers % Closed economy % Uniform wage and labour tax rate %-------------------------------------------------------------------------- %-------------------------------------------------------------------------- % 27 Endogenous variables %-------------------------------------------------------------------------- var y_h c_h c_h_o c_h_r l_h l_h_o l_h_r i_h k_h b_h w_h r_h r_k_h g_h tau_k_h tau_c_h tau_l_h z_h u_a_h u_g_h u_tk_h u_tc_h u_tl_h u_z_h tk_h tc_h tl_h; %-------------------------------------------------------------------------- % 7 Exogenous shocks (error terms) %-------------------------------------------------------------------------- varexo e_u_a_h e_u_g_h e_u_tk_h e_u_tc_h e_u_tl_h e_u_z_h; %-------------------------------------------------------------------------- % 45 parameters %-------------------------------------------------------------------------- parameters BETA DELTA ALPHA GAMMA KAPPA H THETA PHI Y_h_bar G_h_bar B_h_bar Z_h_bar TAU_K_h_bar TAU_C_h_bar TAU_L_h_bar TK_h_bar TC_h_bar TL_h_bar RHO_A RHO_G RHO_TK RHO_TC RHO_TL RHO_Z SIGMA_A_H SIGMA_G_H SIGMA_TK_H SIGMA_TC_H SIGMA_TL_H SIGMA_Z_H EPSI_G EPSI_K EPSI_L EPSI_Z GAMMA_G GAMMA_K GAMMA_L GAMMA_Z PHI_KL PHI_KC PHI_LC; BETA = 0.99; DELTA = 0.025; ALPHA = 0.30; GAMMA = 5.0; KAPPA = -7.047; H = 0.50; THETA = 0.50; PHI = 10.0; Y_h_bar = 0.956; B_h_bar = 0.324; G_h_bar = 0.088; Z_h_bar = 0.016; % Steady state capital tax rate TAU_K_h_bar = 0.184; % Steady state consumption tax rate TAU_C_h_bar = 0.028; % Steady state labour tax rate TAU_L_h_bar = 0.223; TK_h_bar = 0.058; TL_h_bar = 0.030; TC_h_bar = 0.019; % Government spending debt coefficient GAMMA_G = 0.23; % Capital tax rate debt coefficient GAMMA_K = 0.39; % Labour tax rate debt coefficient GAMMA_L = 0.049; % Transfers debt coefficient GAMMA_Z = 0.5; % Capital tax rate output coefficient EPSI_K = 1.7; % Labour tax rate output coefficient EPSI_L = 0.36; % Government spending output coefficient EPSI_G = 0.34; % Transfers output coefficient EPSI_Z = 0.13; % Capital-Labour co-term PHI_KL = 0.19; % Capital-Consumption co-term PHI_KC = 0.024; % Labour-Consumption co-term PHI_LC = -0.028; % Parameters for the exogenous shocks RHO_A = 0.9609; SIGMA_A_H = 0.6241; RHO_G = 0.9691; SIGMA_G_H = 3.0582; RHO_TK = 0.9349; SIGMA_TK_H = 4.3819; RHO_TC = 0.9321; SIGMA_TC_H = 4.0445; RHO_TL = 0.9725; SIGMA_TL_H = 3.0029; RHO_Z = 0.9437; SIGMA_Z_H = 3.3809; %-------------------------------------------------------------------------- % Model %-------------------------------------------------------------------------- model; % Aggregation exp(c_h) = THETA * exp(c_h_r) + (1-THETA) * exp(c_h_o) ; exp(l_h) = THETA * exp(l_h_r) + (1-THETA) * exp(l_h_o) ; % Production function exp(y_h) = exp(u_a_h)*(exp(k_h(-1)))^ALPHA * exp(l_h)^(1-ALPHA); % Law of motion exp(k_h) = (1-DELTA)*exp(k_h(-1)) + exp(i_h); % MPL and MPK exp(w_h) = (1-ALPHA)* exp(y_h)/exp(l_h) ; exp(r_k_h) = ALPHA * exp(y_h)/(exp(k_h(-1))) ; % intertemporal conditions (exp(c_h_o) - H*exp(c_h_o(-1)) )^(-GAMMA)/(1+exp(tau_c_h)) = BETA * (exp(c_h_o(+1))- H*exp(c_h_o) )^(-GAMMA) / (1+exp(tau_c_h(+1))) * exp(r_h(+1)); (exp(c_h_o) - H*exp(c_h_o(-1)) )^(-GAMMA)/(1+exp(tau_c_h)) = BETA * (exp(c_h_o(+1))- H*exp(c_h_o) )^(-GAMMA) / (1+exp(tau_c_h(+1))) *((1-exp(tau_k_h(+1))) * exp(r_k_h(+1)) + 1 - DELTA); % intratemporal conditions exp(w_h) = PHI*(1-exp(l_h_o))^ KAPPA /(1-exp(tau_l_h)) * (1+exp(tau_c_h))/ (exp(c_h_o) - H*exp(c_h_o(-1)) )^(-GAMMA); exp(w_h) = PHI*(1-exp(l_h_r))^ KAPPA /(1-exp(tau_l_h)) * (1+exp(tau_c_h))/ (exp(c_h_r) - H*exp(c_h_r(-1)) )^(-GAMMA); % GBC exp(b_h) + exp(tk_h) + exp(tc_h) + exp(tl_h) = exp(r_h(-1)) * exp(b_h(-1)) + exp(g_h) + exp(z_h); % Optimizing agents BC (1-exp(tau_l_h)) * exp(w_h) * exp(l_h_o) + (1-exp(tau_k_h)) * exp(r_k_h) * exp(k_h(-1)) + exp(r_h) * exp( b_h(-1)) + exp(z_h) = (1+exp(tau_c_h))*exp(c_h_o) + exp(i_h) + exp(b_h); % ROT constraint (1+exp(tau_c_h)) * exp(c_h_r) = (1 - exp(tau_l_h)) * exp(l_h_r)* exp(w_h) ; % Total capital tax revenue exp(tk_h) = exp(tau_k_h) * exp(r_k_h) * exp(k_h(-1)); % Total labor tax revenue exp(tl_h) = exp(tau_l_h) * exp(w_h) * exp(l_h_o); % Total consumption tax revenue exp(tc_h) = exp(tau_c_h) * exp(c_h); %-------------------------------------------------------------------------- % Fiscal rules %-------------------------------------------------------------------------- % Government spending policy rule g_h = - EPSI_G*y_h - GAMMA_G*b_h(-1) + u_g_h + ( EPSI_G*log(Y_h_bar) + GAMMA_G*log(B_h_bar) + log(G_h_bar) ) ; % Capital tax policy rule tau_k_h = EPSI_K*y_h + GAMMA_K*b_h(-1) + PHI_KL*u_tl_h + PHI_KC*u_tc_h + u_tk_h + (-EPSI_K*log(Y_h_bar) - GAMMA_K*log(B_h_bar) + log(TAU_K_h_bar) ) ; % Labour tax policy rule tau_l_h = EPSI_L*y_h + GAMMA_L*b_h(-1) + PHI_KL*u_tk_h + PHI_LC*u_tc_h + u_tl_h + (-EPSI_L*log(Y_h_bar) - GAMMA_L*log(B_h_bar) + log(TAU_L_h_bar) ) ; % Consumption tax policy rule tau_c_h = PHI_KC*u_tk_h + PHI_LC*u_tl_h + u_tc_h + log(TAU_C_h_bar) ; % Transfers tax policy rule z_h = - EPSI_Z*y_h - GAMMA_Z*b_h(-1) + u_z_h + ( EPSI_Z*log(Y_h_bar) + GAMMA_Z*log(B_h_bar) + log(Z_h_bar) ) ; %-------------------------------------------------------------------------- % Exogenous shocks %-------------------------------------------------------------------------- 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_tc_h = RHO_TC * u_tc_h(-1) + e_u_tc_h; u_tl_h = RHO_TL * u_tl_h(-1) + e_u_tl_h; u_z_h = RHO_Z * u_z_h(-1) + e_u_z_h; end; %-------------------------------------------------------------------------- % Initial values %-------------------------------------------------------------------------- initval; y_h = -0.046; c_h = -0.366; c_h_o = -0.009; c_h_r = -0.926; l_h = -1.109; l_h_o = -2.124; l_h_r = -0.615; i_h = -1.057; k_h = 2.806; b_h = -1.126; w_h = -0.030; r_h = 0.010; r_k_h = -3.267; u_a_h = 0; u_g_h = 0; u_tk_h = 0; u_tc_h = 0; u_tl_h = 0; u_z_h = 0; tk_h = -2.8; tc_h = -3.9; tl_h = -2.6; tau_k_h = log(TAU_K_h_bar); tau_l_h = log(TAU_L_h_bar); tau_c_h = log(TAU_C_h_bar); g_h = log(G_h_bar); z_h = log(Z_h_bar); end; %-------------------------------------------------------------------------- % shocks %-------------------------------------------------------------------------- shocks; 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; %-------------------------------------------------------------------------- % Compute %-------------------------------------------------------------------------- steady(solve_algo=1); resid; check; //model_info ; stoch_simul(order=1,hp_filter=1600,irf=0);