%This file replicates CEE2005 (without implementing the lag expectations everywhere). %Roberto Croce, Ohio State University %Columbus, Ohio %April 2009 %a * indicates that the variable was present in the 13 variable system from the paper var pi %inflation * s %real marginal cost qbar %transaction money / m1 * q %real transaction money r %nominal interest rate * m %total money supply / m2 * mu %money growth rate psi %marginal utility of consumption * c %consumption * wbar %wage w %real wage p_ki %marginal product of capital in marginal utility terms * l %labor * h %habit * kbar %capital stock * k %capital services * i %capital investment * y %output u %capacity utilization rk %return to capital ; varexo eR; parameters R %steady state nominal ir beta %discount rate alph %labor share of production delt %capital depreciation rate b_w %simplifying parameter xi_p %price stickiness xi_w %wage stickiness lam_w %household labor market power mubar %steady state money growth rate mbar %steady state m2 qbar_ss %steady state m1 wbar_ss %steady state wage lbar %steady state labor supply b %habit parameter 1 chi %habit parameter 2 sig_c %simplies labor supply decision Euler sig_a %relates capacity utilization to return on capital sig_q %relates cash holding and the interest rate mc %steady state marginal cost (1/markup) K_Y %steady state capital-ouput ratio K_H %steady state capital-labor ratio Y_H %steady state output-labor ratio C_Y %steady state consumption output ratio rho_r %interest rate smooting policy parameter rho_pi %taylor rule inflation response rho_y %taylor rule output response X %reciprocal of the elasticity of investment wrt current price of installed capital ; %------------------------------------------------------------------------------------------% % PARAMETERS % %------------------------------------------------------------------------------------------% %1)PREFERENCES %(intertemporal elasticity of sub. in C = 1) b =0.63; % degree of habit persistence beta = 1.03^(-1/4); % subjective discount factor R = 1/beta; % steady state nominal rate psi0 =1; % marginal disutility of hours chi = 0.0; % habit parameter 2 %2)TECHNOLOGY alph = 0.36; % share of capital delt = 0.025; % depreciation rate %3)CALVO PARAMETERS xi_w = 0.70; %on wages xi_p = 0.50; %on prices %4)INDEXATION lam_w =1.05; %household labor market power lam_f =1.45; %firm market power %5)ELASTICITIES OF SUBSTITUTIONS eta = 6; % price-elasticity of demand for a differianted good mc = (eta-1)/eta; % marginal cost %6) OTHER CALIBRATIONS lbar = 1; % steady state labor supplied by households sig_a = 0.01; % mubar = 1.017; % steady state money growth rate, calibrated post ww2 qbar_ss = mubar*(1-0.36/(beta*(1-alph))); % steady state M1 mbar = (1/0.44)*qbar_ss; % steady state M2 sig_q = 9.966; X = (1/0.28); %------------------------------------------------------------------------------------------% % STEADY STATE RATIOS and VALUES % %------------------------------------------------------------------------------------------% %underscore denotes a ratio %2)ENDOGENOUS VALUES rk_bar = (1/beta-1+delt); %steady state capital rental rate K_H = mc^(1/(alph*(1-alph)))*(rk_bar/alph)^(1/(alph-1)); %capital-labor ratio Y_H = (K_H)^alph; %output-labor ratio K_Y = K_H/Y_H; %capital-output ratio C_Y = 1-delt*K_Y; %consumption_output ratio I_Y = delt*K_Y; %investment over output //wbar_ss = (1-alph)/alph*(K_H)*rk_bar; wbar_ss = mc^(1/(1-alph))*(1-alph)*alph^(alph/(1-alph))*rk_bar^(alph/(alph-1))/R; %steady state wage %------------------------------------------------------------------------------------------% % Simplifying Parameters % %------------------------------------------------------------------------------------------% b_w = (2*lam_w - 1)/((1-xi_w)*(1-beta*xi_w)); sig_c = (1-chi)/(1-chi-b)*(1-beta*chi)/(1-beta*chi-beta*b); %------------------------------------------------------------------------------------------% % MONETARY RULE % %------------------------------------------------------------------------------------------% rho_pi = 1.5; % monetary rule parameter (on inflation) rho_y = 0.5; % monetary rule parameter (on output) rho_r = 0.8; % monetary rule parameter (on lagged interest rate) model(linear); %inflation Euler pi = (1/(1+beta))*pi(-1) + (beta/(1+beta))*pi(+1) + ((1-beta*xi_p)*(1-xi_p)/((1+beta)*xi_p))*s; %money demand q = (-1/sig_q)*(R/(R-1)*r + psi); %household labor decision 0=w(-1) - ((b_w*(1+beta*xi_w^2)-lam_w)/(b_w*xi_w))*w + beta*w(+1) + (beta*(pi(+1) - pi) - (pi - pi(-1))) + ((1-lam_w)/(b_w*xi_w))*(psi-l); %household borrowing/lending Euler psi(+1) + r(+1) - pi(+1) - psi = 0; %def of capacity utilization u = k(-1) - kbar(-1); %return on capital rk = w + r + l - k; %household consumption Euler 0 = -p_ki - psi + psi(+1) + (1-beta*(1-delt))*(rk(+1)) + beta*(1-delt)*p_ki(+1); (1/beta - (1-delt))*(K_Y/C_Y)*u + c + delt*(K_Y/C_Y)*i = (alph/C_Y)*k + ((1-alph)/C_Y)*l; %loan market clearing mubar*mbar*(mu + m) - qbar_ss*q - wbar_ss*lbar*(w + l)=0; %money growth relationship to the inflation rate m - m(-1) - mu(-1) + pi= 0; %habit formation h - chi*h(-1) - (1-chi)*c(-1) = 0; -beta*chi*psi(+1) + sig_c*(c - h*b/(1-chi)) - (b+chi)*beta*sig_c*(c(+1) - h(+1)*b/(1-chi)) + psi=0; p_ki = X*(i - i(-1) - beta*(i(+1)-i)); kbar = (1-delt)*kbar(-1) + delt*i; u -(1/sig_a)*rk = 0; r = (1-rho_r)*(rho_pi*pi(-1) + rho_y*y(-1)) +rho_r*r(-1) - eR; s = alph*rk + (1-alph)*(w + r); y = alph*k(-1) + (1-alph)*l; qbar = q + pi; wbar = w + pi; end; steady; check; shocks; var eR; stderr 0.6; end; stoch_simul(linear,irf=20); dyngraph