% Mod file to solve NK model with Ricardian and non-Ricardian HHs close all; %---------------------------------------------------------------- % 1. Defining variables %---------------------------------------------------------------- var Cr Cn C Nr Nn L W R Rk Lambda K MC Gamma_1 Gamma_2 Y Pstar_P Pi sp G B_P Pr eps_a eps_c eps_l eps_R G_Y B_Y; varexo eta_g eta_a eta_R eta_l eta_c; parameters delta eta zeta lambda theta_p theta_w PHI alpha beta rho_R phi_pi phi_y rho_a rho_r rho_l rho_c sigma_a sigma_g sigma_r sigma_l sigma_c GY_ss psi k upsilon tau_w rho_b rho_g tau_c tau_k tau_p nu Cr_ss Cn_ss C_ss Nr_ss Nn_ss L_ss W_ss R_ss Rk_ss Lambda_ss K_ss MC_ss Gamma_1_ss Gamma_2_ss Y_ss Pstar_P_ss Pi_ss sp_ss G_ss B_P_ss Pr_ss; %---------------------------------------------------------------- % 2. Calibration %---------------------------------------------------------------- load parameters; set_param_value('delta' , delta); set_param_value('nu',nu); set_param_value('eta' , eta); set_param_value('zeta' , zeta); set_param_value('lambda' , lambda); set_param_value('theta_p' , theta_p); set_param_value('theta_w' , theta_w); set_param_value('PHI' , PHI); set_param_value('alpha' , alpha); set_param_value('beta' , beta); set_param_value('rho_R' , rho_R); set_param_value('phi_pi' , phi_pi); set_param_value('phi_y' , phi_y); set_param_value('rho_a' , rho_a); set_param_value('rho_b' , rho_b); set_param_value('rho_r' , rho_r); set_param_value('rho_c' , rho_c); set_param_value('rho_l' , rho_l); set_param_value('rho_g',rho_g); set_param_value('sigma_a' , sigma_a); set_param_value('sigma_g' , sigma_g); set_param_value('sigma_r' , sigma_r); set_param_value('sigma_c' , sigma_c); set_param_value('sigma_l' , sigma_l); set_param_value('psi' , psi); set_param_value('k' , k); set_param_value('upsilon' , upsilon); set_param_value('tau_w',tau_w); set_param_value('tau_c',tau_c); set_param_value('tau_k',tau_k); set_param_value('tau_p',tau_p); set_param_value('GY_ss' , GY_ss); set_param_value('B_P_ss' , B_P_ss); set_param_value('Y_ss',Y_ss); set_param_value('C_ss',C_ss); set_param_value('L_ss',L_ss); set_param_value('K_ss',K_ss); set_param_value('W_ss',W_ss); set_param_value('R_ss',R_ss); set_param_value('Rk_ss',Rk_ss); set_param_value('MC_ss',MC_ss); set_param_value('Gamma_1_ss',Gamma_1_ss); set_param_value('Gamma_2_ss',Gamma_2_ss); set_param_value('Pr_ss',Pr_ss); set_param_value('Nr_ss',Nr_ss); set_param_value('Cr_ss',Cr_ss); set_param_value('Nn_ss',Nn_ss); set_param_value('Cn_ss',Cn_ss); set_param_value('Pi_ss',Pi_ss); set_param_value('Pstar_P_ss',Pstar_P_ss); set_param_value('sp_ss',sp_ss); set_param_value('Lambda_ss',Lambda_ss); set_param_value('G_ss' , G_ss); %---------------------------------------------------------------- % 3. Model %---------------------------------------------------------------- model; %----------- % Ricardian %----------- ((1-tau_w)/(1+tau_c))*W = (eps_l/eps_c)*Cr*(Nr)^upsilon; % 1. Ricardian HH Intratemporal EE 1 = beta*R(+1)*(1-tau_w)*(eps_c(+1)/eps_c)*(Cr/Cr(+1))*Pi(+1)^(-1); % 2. Ricardian HH EE 1 = beta*(1-tau_p)*(eps_c(+1)/eps_c)*(Cr/Cr(+1))*(1-delta+Rk(+1)); % 3. Ricardian HH, capital stock choice (interest rate determination) Lambda = beta*(eps_c(+1)/eps_c)*(Cr/Cr(+1)); % 4. Ricardian HH stochastic discount factor %-------------- % Non Ricardian %-------------- (1+tau_c)*Cn = (1-tau_w)*W*Nn; % 5. Non-Ricardian HH BC ((1-tau_w)/(1+tau_c))*W = (eps_l/eps_c)*Cn*(Nn)^upsilon; % 6. Non-Ricardian HH EE %-------- % Firms %-------- K(-1)/L = (alpha/(1-alpha))*W/Rk; % 7. Capital to labour ratio MC = eps_a*((Rk/alpha)^alpha)*(W/(1-alpha))^(1-alpha); % 8. Margina cost Gamma_1 = MC*Y + theta_p*Lambda(+1)*((Pi(+1))^zeta)*Gamma_1(+1); % 9 Gamma_2 = Y + theta_p*Lambda(+1)*((Pi(+1))^(zeta-1))*Gamma_2(+1); % 10 Pstar_P*Gamma_2 = (zeta/(zeta-1))*Gamma_1; % 11. Price setting Pr = Y - L*W - K(-1)*Rk; % 12. Profit %------------------------- % Aggregate Price Dynamics %------------------------- 1 = (1-theta_p)*(Pstar_P)^(1-zeta)+theta_p*Pi^(zeta-1); % 13. Inflation sp = (1-theta_p)*Pstar_P^(-zeta)+theta_p*Pi^(zeta)*sp(-1); % 14. Relative price dispersion %------------- %Government %------------- G + R*B_P(-1)/Pi = tau_w*W*L + tau_c*C + tau_k*Pr + tau_p*(1-delta+Rk)*K(-1) + B_P; % 15. Government BC log((G/Y)/GY_ss) = rho_b*log(B_P(-1)/B_P_ss) + eta_g; % 16. Government spending rule %------------- % Central Bank %------------- R/R_ss = (Pi^phi_pi)*eps_R; % 17. MP rule %--------------------------------- % Market clearing and feasibility %--------------------------------- Y = C+K-(1-delta)*K(-1)+G; % 18. Aggregate Resource constraint sp*Y = eps_a*K(-1)^(alpha)*L^(1-alpha); % 19. Goods market clearance L = nu*Nn + (1-nu)*Nr; % 20. Total labour C = nu*Cn + (1-nu)*Cr; % 21. Total Consumption G_Y = G/Y; % 22. Government spending as percentahe of Y B_Y = B_P/Y; % 23. Government debt as percentage of Y %-------- % Shocks %-------- log(eps_a) = rho_a*log(eps_a(-1))+eta_a; % 24. Technology shock log(eps_R) = rho_r*log(eps_R(-1))+eta_R; % 25. Monetary Policy log(eps_l) = rho_l*log(eps_l(-1))+eta_l; % 26. Labour log(eps_c) = rho_c*log(eps_c(-1))+eta_c; % 27. Consumption end; %---------------------------------------------------------------- % 4. Steady State %---------------------------------------------------------------- initval; Cr = Cr_ss; Cn = Cn_ss; C = C_ss; Nr = Nr_ss; Nn = Nn_ss; L = L_ss; W = W_ss; R = R_ss; Rk = Rk_ss; Lambda = Lambda_ss; K = K_ss; MC = MC_ss; Gamma_1 = Gamma_1_ss; Gamma_2 = Gamma_2_ss; Y = Y_ss; Pstar_P = Pstar_P_ss; Pi = Pi_ss; sp = sp_ss; G = G_ss; B_P = B_P_ss; Pr = Pr_ss; eps_a=1; eps_R=1; eps_l=1; eps_c=1; end; resid(1); steady(solve_algo=3,maxit=100000); check; %---------------------------------------------------------------- % 5. Shocks %---------------------------------------------------------------- shocks; var eta_g = sigma_g^2; var eta_a = sigma_a^2; var eta_R = sigma_r^2; var eta_l = sigma_l^2; var eta_c = sigma_c^2; end; %---------------------------------------------------------------- % 6. Solve %---------------------------------------------------------------- stoch_simul(hp_filter = 1600, order=1, irf=80); %---------------------------------------------------------------- % 7. Output %---------------------------------------------------------------- output = Y_eta_g;