%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Dmitri Bogonos % dmitri.bogonos@rwi-essen.de % 05.08.2015 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Define variables, shocks and parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% var y c g p_k j i z_k z_y v_k v_y n_y a_k a_y h_k h_y x k l o_k o_y pi_k pi_y p_k_st p_k_et n_k j_y j_k i_s i_e lambda_y lambda_k p_k_bar chi Lambda; varexo eps sigma varrho eps_st; parameters mu_k_bar mu mu_k beta rho_lambda vartheta alpha delta theta gamma ksi_k ksi_y mu_w zeta u delta_der_u chi_k_bar chi_y_bar phi lambda_y_bar lambda_k_bar; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Give your parameters values %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% beta = 0.98; %Lambda = 1; delta = 0.015; alpha = 0.35; gamma = 1 - 0.17/alpha; zeta = 1; theta = 1.4; vartheta = 1.25; %theta_bar = 0.8; u = 0.9; mu = 1.1; mu_w = 1.2; mu_k = 1.15; mu_k_bar = (mu_k*theta)/(theta*gamma + 1 - gamma); chi_y_bar = 0.0202; chi_k_bar = 0.0304; phi = 0.99; rho_lambda = 0.9; ksi_k = 1; ksi_y = ksi_k*log((1 - phi)/chi_y_bar)/log((1 - phi)/chi_k_bar); lambda_y_bar = 0.1; lambda_k_bar = 0.1; %rho = 0.9; %eta = 0.9; %nu = 0.9; %rho_st = 0.85; delta_der_u = (1/beta + delta - 1)/u; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Define your model equations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% model; % Resource constraint y/mu = c + g + i*(2*mu_k - 1)/mu_k + (z_k - a_k)*h_k + (z_y - a_y)*h_y; %1 % aggregate production function y = x*((a_y)^(vartheta - 1))*((n_y)^(mu - 1))*((u*k(-1))^alpha)*(l^(1 - alpha)); %2 % capital accumulation k = (1 - delta)*k(-1) + (mu_k_bar*i)/p_k; %3 % product amount a_y(+1) = lambda_y*(z_y - a_y) + phi*a_y; %4 a_k(+1) = lambda_k*(z_k - a_k) + phi*a_k; %5 % stock of new technologies z_y(+1) = (chi_y_bar*(chi^ksi_y) + phi)*z_y; %6 z_k(+1) = (chi_k_bar*(chi^ksi_k) + phi)*z_k; %7 % factor market equilibria (1 - alpha)*y/l = mu*mu_w*(l^zeta)*c; %8 alpha*y/u = mu*delta_der_u*p_k*k(-1); %9 % new capital (p_k*j)/mu_k_bar = i; %10 (theta*i_e)/i_s = (1 - gamma)/gamma; %11 j = (mu_k_bar*i)/p_k; %12 % euler equation p_k = beta*Lambda(+1)*((alpha*y(+1))/(mu*k) + (1 - delta)*p_k(+1)); %13 Lambda(+1) = c/c(+1); %14 % optimal adoption 1 = phi*beta*Lambda*(v_y(+1) - j_y(+1))*lambda_y*rho_lambda/h_y; %15 1 = phi*beta*Lambda*(v_k(+1) - j_k(+1))*lambda_k*rho_lambda/h_k; %16 v_y = pi_y + phi*beta*(Lambda*v_y(+1)); %17 v_k = pi_k + phi*beta*(Lambda*v_k(+1)); %18 pi_k = ((theta - 1)/theta)*(1 - gamma)*(i/(a_k*mu_k)); %19 pi_y = ((vartheta - 1)/vartheta)*y/(a_y*mu); %20 j_y = -h_y + phi*beta*(Lambda*(lambda_y*v_y(+1) + (1 - lambda_y)*j_y(+1))); %21 j_k = -h_k + phi*beta*(Lambda*(lambda_k*v_k(+1) + (1 - lambda_k)*j_k(+1))); %22 lambda_y = lambda_y_bar*((a_y*h_y/o_y)^(rho_lambda)); %23 lambda_k = lambda_k_bar*((a_k*h_k/o_k)^(rho_lambda)); %24 ((mu - 1)/mu)*(y/n_y) = o_y; %25 ((mu_k - 1)/mu_k)*(i/n_k) = o_k; %26 p_k = mu_k*(n_k^(1 - mu_k))*(p_k_st^gamma)*(p_k_et^(1 - gamma)); %27 p_k_et = theta*(a_k^(1-theta)); %28 p_k_bar = (theta^(1 - gamma))*(a_k^((gamma - 1)*(theta - 1)))*(p_k_st^gamma); %29 i = theta*i_e + i_s; %30 % stochastic processes log(chi) = log(chi(-1)) + eps; %31 log(x) = log(x(-1)) + sigma; %32 log(g) = log(g(-1)) + varrho; %33 log(p_k_st) = log(p_k_st(-1)) + eps_st; %34 end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Set initial values for some variables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %steady_state_model; initval; Lambda = 1; k = 1; j = delta*k; lambda_k = 0.05; lambda_y = 0.05; z_k = 10; z_y = 10; a_y = (lambda_y*z_y)/(1 - phi + lambda_y); a_k = (lambda_k*z_k)/(1 - phi + lambda_k); chi = (chi_y_bar/chi_k_bar)^(1/(ksi_k - ksi_y)); y = (phi*beta*Lambda*rho_lambda*lambda_k*u*delta_der_u*mu_k_bar*mu*a_k*theta*mu_k*(vartheta-1)*(lambda_k_bar^(1/rho_lambda)))/((1 - phi*beta*Lambda*(1 - lambda_k))*(mu-1)*(theta-1)*(1-gamma)*vartheta*alpha*delta*(lambda_k^(1/rho_lambda))); i = alpha*y*delta*k/(u*mu*delta_der_u*k*mu_k_bar); pi_y = (y*(vartheta - 1))/(vartheta*a_y*mu); pi_k = ((theta-1)*(1-gamma)*i)/(a_k*mu_k*theta); v_k = pi_k/(1 - phi*beta*Lambda); v_y = pi_y/(1 - phi*beta*Lambda); h_k = ((1 - phi*beta*Lambda)*phi*beta*Lambda*rho_lambda*lambda_k*v_k)/(1 - phi*beta*Lambda + phi*beta*Lambda*lambda_k*(1 - rho_lambda)); h_y = ((1 - phi*beta*Lambda)*phi*beta*Lambda*rho_lambda*lambda_y*v_y)/(1 - phi*beta*Lambda + phi*beta*Lambda*lambda_y*(1 - rho_lambda)); o_k = (h_k*a_k*(lambda_k_bar^(1/rho_lambda)))/(lambda_k^(1/rho_lambda)); o_y = (h_y*a_y*(lambda_y_bar^(1/rho_lambda)))/(lambda_y^(1/rho_lambda)); j_k = (-h_k + phi*beta*Lambda*lambda_k*v_k)/(1 - phi*beta*Lambda*(1 - lambda_k)); j_y = (-h_y + phi*beta*Lambda*lambda_y*v_y)/(1 - phi*beta*Lambda*(1 - lambda_y)); n_k = (i*(mu_k-1)*(lambda_k^(1/rho_lambda)))/(a_k*h_k*mu_k*(lambda_k_bar^(1/rho_lambda))); n_y = (y*(mu-1)*(lambda_y^(1/rho_lambda)))/(a_y*h_y*mu*(lambda_y_bar^(1/rho_lambda))); p_k_et = theta*((a_k)^(1 - theta)); p_k = alpha*y/(u*mu*delta_der_u*k); p_k_st = (p_k*(n_k^(mu_k - 1))*(p_k_et^(gamma - 1))/mu_k)^(1/gamma); i_s = gamma*i; i_e = (i - i_s)/theta; p_k_bar = (p_k_et^(1 - gamma))*(p_k_st^gamma); l = ((1 - alpha)/((1/mu - 0.2 - ((i*(2*mu_k - 1)/mu_k + (z_k - a_k)*h_k + (z_y - a_y)*h_y)/(y)))*mu*mu_w))^(1/(zeta + 1)); c = ((1 - alpha)*y)/(mu*mu_w*(l^(zeta + 1))); g = y/5; x = y*(a_y^(1 - vartheta))*(n_y^(1 - mu))*((u*k)^(-alpha))*(l^(alpha - 1)); end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Calculate the steady state, check for existence %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% resid; steady(maxit = 5000); model_diagnostics; check(qz_zero_threshold = 1e-50); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Add shocks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% shocks; var eps = 0.07^2; var sigma = 0; var varrho = 0; var eps_st = 0; end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Start simulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% options_.debug=1; stoch_simul(order=1,irf=20,periods = 200,nograph);