%Dynare code %Author: Manuel CG %-------------------% % Description % %-------------------% % The following code replicates the paper of Carvalho and Ferrero "What %Explains Japan's Persistent Deflation?"(2014). All the variables are expressed %in efficiency units due to detrending %------------------------------------------------------------------------------% % Endogenous variables % %------------------------------------------------------------------------------% var %-------------------% % Households % %-------------------% psi %1 Dependency ratio c_r %2 Retirees consumption c_w %3 Workers consumption c %4 Total consumption xi_r %5 Marginal propensity of comsume for retirees xi_w %6 Marginal propensity of comsume for workers epsilon %7 Ratio of marginal propensities to consume (xi_r/xi_w) Omega %8 Adjustment factor a_r %9 Assets holding by the retirees a_w %10 Assets holding by the workers a %11 Total amount of assets v_r %12 Retirees welfare v_w %13 Workers welfare v %14 Retirees Welfare lambda %15 Distribution of wealth h %16 Aggregate value of human wealth %-------------------% % Firms % %-------------------% y %17 Gross Domestic Product i %18 Investment k %19 Capital w %20 Real wage R_k %21 Rental rate of capital mc %22 Marginal cost p_F %23 Price of intermediate firm shares d_F %24 Profits of intermediate good producers %-------------------% % Government % %-------------------% pi %25 Inflation rate g_g %26 Government consumption b_g %27 Government bonds R_b %28 Bond interest rate t; %29 Lump-sum taxes %------------------------------------------------------------------------------% % Exogenous variables % %------------------------------------------------------------------------------% varexo n %1 Growth rate of labor force omega %2 Probability of remain in the labor force gamma %3 Probability of survive x %4 Productivity growth rate g %5 Government spending (% of GDP) b; %6 Governemtn debt (% of GDP) %------------------------------------------------------------------------------% % Parameters % %------------------------------------------------------------------------------% parameters alpha %1 Labor share beta %2 Individual discount factor delta %3 Depreciation rate of physical capital theta %4 Elasticity of substititution among varieties phi_P %5 Price adjustment cost sigma %6 Elasticity of intertemporal susbstitution phi_pi; %7 Inflation response coefficient %------------------% % Calibration % %------------------% alpha = 0.623; beta = 0.9982; delta = 0.025; theta = 12; phi_P = 133; sigma = 0.5; phi_pi = 2; %------------------------------------------------------------------------------% % Equations of the model % %------------------------------------------------------------------------------% model; %[1] Dependency ratio (1 + n)*psi = (1 - omega) + gamma*psi(-1); %[2] Agreggate consumption for retirees c_r = xi_r*(R_b(-1)/pi)*a_r(-1); %[3] Marginal propensity to consume for retirees xi_r = 1 - gamma(+1)*(beta^sigma)*((R_b/pi(+1))^(sigma - 1))*(xi_r/xi_r(+1)); %[4] Retirees welfare v_r = ((xi_r)^(sigma/(1 - sigma)))*c_r; %[5] Aggregate consumption for workers c_w = xi_w*((R_b(-1)/pi)*a_w(-1) + h); %[6] Marginal propensity to consume for workers xi_w = 1 - (beta^sigma)*(((Omega(+1)*R_b)/pi(+1))^(sigma - 1))*(xi_w/xi_w(+1)); %[7] Workers welfare v_w = ((xi_w)^(sigma/(1 - sigma)))*c_w; %[8] Aggregate value of human wealth h = (w - t) + ((1 + x(+1))*omega(+1)*h(+1))/(Omega(+1)*R_b/pi(+1)); %[9] Adjustment factor Omega = omega + (1 - omega)*(epsilon^(1/(1 - sigma))); %[10] Ratio of marginal propensities to consume epsilon = xi_r/xi_w; %[11] Aggregate consumption c = xi_w*((1 - lambda(-1))*(R_b(-1)/pi)*a(-1) + h + epsilon*lambda(-1)*(R_b(-1)/pi)*a(-1)); %[12] Distribution of wealth (1 + x(+1) + n(+1))*(lambda - (1 - omega))*a = omega*(1 - xi_r)*lambda(-1)* (R_b(-1)/pi)*a(-1); %[13] Retirees assests a_r/a = lambda; %[14] Workers assets a_w/a = 1 - lambda; %[15] & [16] No arbitrage conditions R_b/(pi(+1)) = R_k(+1) + (1 - delta); R_b/(pi(+1)) = (1 + x(+1) + n(+1))*((p_F(+1) + d_F(+1))/p_F); %[17] Aggregate welfare v = ((xi_w^(sigma/(1 - sigma)))* (c_w + psi*(epsilon^(sigma/(1 - sigma)))*c_r))/(1 + psi); %[18] Real wage w = mc*alpha*y; %[19] Rental rate of capital R_k = mc*(((1 - alpha)*y)/k(-1)); %[20] Marginal cost mc = ((w^alpha)*(R_k^(1 - alpha)))/((alpha^alpha)*((1 - alpha)^(1 - alpha))); %[21] Phillips curve (pi - 1)*pi = ((theta - 1)/phi_P)*((theta/(theta - 1))*mc - 1) + (1 + x(+1) + n(+1))*(1/(R_b/pi(+1)))*(y(+1)/y)*(pi(+1) - 1)*pi(+1); %[22] Government budget constraint (1 + x(+1) + n(+1))*b_g = (R_b/pi)*b_g(-1) + g_g - t; %[23] Fiscal rule (1 + x(+1) + n(+1))*b_g = b*y; %[24] Government consumption g_g = g*y; %[25] Monetary policy rule pi*((y/y(-4))^phi_pi) = 1; %[26] Aggregate assets a = k + b + p_F; %[27] Profits of intermediate good produces d_F = (1 - mc - (phi_P/2)*((pi - 1)^2))*y; %[28] Capital law of motion (1 + x(+1) + n(+1) )*k = (1 - delta)*k(-1) + i; %[29] Resource constraint (1 - (phi_P/2)*((pi - 1)^2))*y = c + i + g_g; end; %------------------------------------------------------------------------------% % Steady State Model % %------------------------------------------------------------------------------% steady_state_model; psi = (1 - omega)/(1 + n - gamma); pi = 1^phi_pi; mc = (theta - 1)/theta; end; %Initial values initval; %-------------------% % Households % %-------------------% psi = 0.327; c_r = 0.5; c_w = 0.2; c = 0.4; xi_r = 0.7; xi_w = 0.3; epsilon = 2.3; Omega = 1; a_r = 1; a_w = 0.5; a = 1.5; v_r = 0.2; v_r = 0.2; v = 2; lambda = 0.8; h = 0.2; %-------------------% % Firms % %-------------------% y = 1; i = 0.29; k = 3; w = 0.55; R_k = 0.15; mc = 0.9; p_F = 0.2; d_F = 0.1; %-------------------% % Government % %-------------------% pi = 1; g_g = 0.17; R_b = 0.012; b_g = 3.5; t = 0.2; %---------------------------% % Exogenous variables % %---------------------------% n = 0.008; omega = 0.9948; gamma = 0.9907; x = 0.0027; g = 0.17; b = 4; end; %Calculating the steady state steady; %Check the Blanchard-Khan conditions check;