%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % A .mod file for solving the DSGE model in Working Paper I (2012). % % % % Written for Matlab by % % ANDREW KEINSLEY % % DEPARTMENT OF ECONOMICS % % 415 SNOW HALL % % THE UNIVERSITY OF KANSAS % % LAWRENCE, KS 66045 % % akeinsley@ku.edu % % % % This Version: June 13, 2012 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Preamble % % Defining Variables and Parameters % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% var c, m_a, e_a, k, n, d, t, l, q, m, f, y, n_upsilon, m_s, h_s, h, h_g, h_b, h_d, h_k, h_upsilon, w, mm, r, r_upsilon, r_d, r_l, r_k, r_a, u_a, u_n, u_d, rr, xi, z, pi, upsilon_e, a, x_a, tau, lambda_1, lambda_2, lambda_3, lambda_4, g; varexo epsilon_e, epsilon_a, epsilon_z, epsilon_x, epsilon_r, epsilon_tau; parameters chi, beta, upsilon_es, upsilon_n, rho_e, rho_a, rho_x, rho_r, rho_pi, rho_g, rho_tau, theta_y, theta_e, theta_m, eta, z_s, g_s, phi, phi_upsilon, phi_k, pi_s, x_e, x_n, x_as, nu, alpha, tau_s, sigma_u, sigma_a, sigma_z, sigma_x, sigma_r, sigma_tau, omega, r_s; chi = 5.00; beta = 0.995; upsilon_es = 0.90; upsilon_n = 0.20; rho_e = 0.95; rho_a = 0.95; rho_x = 0.50; rho_r = 0.93; rho_pi = 0.11; rho_g = 0.09; rho_tau = 0.50; theta_y = 6.00; theta_e = 6.00; theta_m = 0.50; eta = 2.50; z_s = 1.005; g_s = 1.005; phi = 50; phi_upsilon = 0.000005; phi_k = 0.00005; % Will need to change this to cover both pi_s = 1.005; x_e = 0.71; % Will need to change this to cover both omega = 1; % Will need to change this to cover both x_n = 0.75; x_as = 65; nu = 0.25; alpha = 1.0; tau_s = 0.999375; sigma_u = 0.01; % This is 'sigma_e' in the paper. sigma_a = 0.01; sigma_z = 0.01; sigma_x = log(2); sigma_r = 0.000625; sigma_tau = 0.0003125; r_s = log(1.0151); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Model % % All equations in Dynare notation. % % Here all variables are now considered in log form. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% model; exp(h_s) = (1/chi)*(exp(upsilon_e+c-e_a))^chi; upsilon_e = ((1-rho_e)*STEADY_STATE(upsilon_e))+(rho_e*upsilon_e(-1))+ (epsilon_e); a = (rho_a)*a(-1)+(epsilon_a); exp(d) = exp(m(-1)-pi-z(-1))+exp(t)-exp(n)+exp(l); exp(e_a) = (((x_e)^(1/theta_e)*(exp(k)^((theta_e-1)/theta_e)))+ ((1-x_e)^(1/theta_e)*(exp(m_a)^((theta_e-1)/theta_e))))^ (theta_e/(theta_e-1)); exp(m_a) = (((upsilon_n)^(1/theta_m)*(exp(n)^((theta_m-1)/theta_m)))+ ((1-upsilon_n)^(1/theta_m)*(exp(d)^((theta_m-1)/theta_m))))^ (theta_m/(theta_m-1)); exp(m) = exp(n)+exp(w+h)+exp(r_d+d)+omega*exp(k)+exp(f)-exp(r_l+l)- omega*exp(r_k(-1)+k(-1)-pi-z(-1))-exp(c); exp(d) = (1-upsilon_n)*exp(m_a)*(exp(lambda_2)/(exp(lambda_1)- exp(r_d+lambda_3)))^theta_m; exp(n) = upsilon_n*exp(m_a)*(exp(lambda_2)/(exp(lambda_1)-exp(lambda_3)))^ theta_m; exp(lambda_1) = exp(r_l+lambda_3); exp(lambda_1-r) = beta*exp(lambda_1(+1)-pi(+1)-z); exp(lambda_1+q) = exp(lambda_3+f)+beta*exp(lambda_1(+1)+q(+1)); eta*exp(a) = exp(lambda_3+w); exp(lambda_3) = exp(a-c)*(1-eta*exp(upsilon_e+c-e_a)^chi); exp(lambda_4+e_a) = eta*exp(a)*exp(upsilon_e+c-e_a)^chi; exp(m_a) = (1-x_e)*exp(e_a)*exp(lambda_4-lambda_2)^theta_e; exp(lambda_3) = beta*exp(lambda_1(+1)-pi(+1)-z); omega*exp(lambda_3) = (beta*omega*exp(lambda_3(+1)+r_k-pi(+1)-z))- (x_e^(1/theta_e)*exp(lambda_4)*(exp(e_a-k)^ (1/theta_e))); exp(y) = exp(z+h_g); z = STEADY_STATE(z)+epsilon_z; %% Equation 20 %% exp(f) = (1-exp(w-z)-(phi/2)*((exp(pi)/pi_s)-1)^2)*exp(y); (exp(lambda_3)*(1-theta_y+(theta_y*exp(w-z))-(phi*((exp(pi)/pi_s)-1)* exp(pi)/pi_s))*exp(y))-((beta*phi/pi_s)*exp(lambda_3(+1)+pi(+1)+y(+1))* ((exp(pi)/pi_s)-1)) = 0; exp(x_a)*((x_n^(1/nu)*exp(n_upsilon)^((nu-1)/nu))+((1-x_n)^(1/nu)* exp(z+h_d)^((nu-1)/nu)))^(nu/(nu-1)) = exp(d); x_a = (1-rho_x)*STEADY_STATE(x_a)+rho_x*x_a(-1)+epsilon_x; exp(d) = exp(n_upsilon)+exp(l)+omega*exp(k); exp(z+h_upsilon) = phi_upsilon*exp(n_upsilon); exp(z+h_k) = phi_k*exp(k); exp(n_upsilon) = ((exp(r_l)-exp(r_d))^nu)*exp((nu-1)*x_a+d)*x_n* ((exp(r_l)-exp(r_upsilon)+(phi_upsilon*exp(w-z))) ^(-nu)); exp(h_d) = ((exp(r_l)-exp(r_d))^nu)*(exp(x_a)^(nu-1))*exp(d)*(1-x_n)* exp((nu-1)*z-nu*w); exp(r_k) = (exp(pi(+1))/beta)*(exp(r_l)+phi_k*exp(w-z)); exp(g) = exp(y+z-y(-1)); r-STEADY_STATE(r) = rho_r*(r(-1)-STEADY_STATE(r))+rho_pi*(pi(-1)- STEADY_STATE(pi))+rho_g*(g(-1)-STEADY_STATE(g)) +epsilon_r; r_upsilon = tau+alpha*r; tau = (1-rho_tau)*STEADY_STATE(tau)+rho_tau*tau(-1)+(epsilon_tau); exp(r)-exp(r_a) = ((upsilon_n*(exp(r)-1)^(1-theta_m))+((1-upsilon_n)* (exp(r)-exp(r_d))^(1-theta_m)))^(1/(1-theta_m)); exp(u_a) = (exp(r)-exp(r_a))/exp(r); exp(u_d) = (exp(r)-exp(r_d))/exp(r); exp(u_n) = (exp(r)-1)/exp(r); exp(m_s) = exp(n)+exp(d); exp(xi) = (exp(c)-omega*exp(k))/exp(c); exp(rr) = exp(n_upsilon-d); exp(m) = exp(m(-1)-pi-z(-1))+exp(t)+(exp(r_upsilon)-1)*exp(n_upsilon); exp(mm) = (exp(d)+exp(n))/(exp(n_upsilon)+exp(n)); exp(h) = exp(h_g)+exp(h_b); exp(h_b) = exp(h_upsilon)+exp(h_d)+exp(h_k); end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Initial Values/Steady States % % All steady state values are input in log form. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% initval; c = log(0.33091631); m_a = log(1.08503850344); e_a = log(0.863668523921); k = log(0.006487102412); n = log(0.107466707728); d = log(1.16486903679); t = log(0.000906258388654); l = log(1.10725831132); q = log(10.8664601346); m = log(0.165816990844); f = log(0.0551527457159); y = log(0.330916474296); n_upsilon = log(0.0511236230649); m_s = log(1.27233574452); h_s = log(0.000975209552239); h = log(0.332091925024); h_g = log(0.329270123677); h_b = log(0.00282180134641); h_d = log(0.00282122425861); h_k = log(0.000000322741413532); h_upsilon = log(0.000000254346383407); w = log(0.8375); mm = log(8.02278258808); r = log(1.01510050251); r_upsilon = log(1.0144660647); r_d = log(1.01304411448); r_l = log(1.01510050251); r_k = log(1.02534460304); r_a = log(1.01139720164); u_a = log(0.00364821105521); u_n = log(0.0148758694092); u_d = log(0.00202579747513); rr = log(0.0438878718981); xi = log(0.980396546752); lambda_1 = log(3.03015075377); lambda_2 = log(0.0110546294788); lambda_3 = log(2.98507462687); lambda_4 = log(0.0141143495049); g = log(1.0050); z = log(1.0050); pi = log(1.0050); a = log(1.0000); upsilon_e = log(0.9000); x_a = log(65); tau = log(0.999375); epsilon_e = (0); epsilon_x = (0); epsilon_a = (0); epsilon_z = (0); epsilon_r = (0); epsilon_tau = (0); end; resid; steady(solve_algo = 2); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Shocks to the Model % % The standard deviations are established in the Preamble % % so all we have to do is define the variances. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% shocks; var epsilon_e = sigma_u^2; var epsilon_a = sigma_a^2; var epsilon_z = sigma_z^2; var epsilon_x = sigma_x^2; var epsilon_r = sigma_r^2; var epsilon_tau = sigma_tau^2; end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Deriving Results % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% stoch_simul(irf = 100);