%Porto 2012, Replication of Greenwood and Wright 'Frontiers of Business cycle Research - chapter 6', 1995 %code by Joćo Ricardo M. G. costa Filho close all; %---------------------------------------------------------------------------------------------------------------------------------------------------------- % 1. Defining variables %---------------------------------------------------------------------------------------------------------------------------------------------------------- var c cm ch y km hm kh hh w l r xm xh x zm zh; varexo em eh; parameters beta th tk deltam deltah theta eta hmbar hhbar rhom rhoh sigmam sigmah e rbar kmbar ybar xmbar wbar lbar khbar xhbar xbar cmbar chbar phi psi kappa omega a cbar b; %---------------------------------------------------------------------------------------------------------------------------------------------------------- % 2. Calibration/Steady State %---------------------------------------------------------------------------------------------------------------------------------------------------------- beta=.9898; %discount factor th=0.35; %tax rate on labor income tk=0.70; %tax rate on capital income deltam=0.235; %market capital depreciation rate deltah=0.235; %home capital depreciation rate theta=0.2944; % eta=0.3245; %exponent of home consumption function hmbar=0.33; %market hours hhbar=0.25; %home hours rhom=0.95; %ar coefficient of market technology rhoh=0.95; %ar coefficient of home technology sigmam=0.7; %market innovation standard deviation sigmah=0.7; %home innovation standard deviation e=2/3; gamma=2/3; %model 2 %e=0.4; gamma=0; %model 3 rbar=(1/beta+deltam-1-tk*deltam)/(1-tk); %equilibrium interest rate kmbar=hmbar*(theta/rbar)^(1/(1-theta)); %equilibrium market capital stock ybar=kmbar*(rbar/theta); %equilibrium output xmbar=deltam*kmbar; %equilibrium market investment wbar=(ybar/hmbar)*(1-theta); %equilibrium wage lbar=1-hmbar-hmbar; %equilibrium leisure khbar=((1/(hhbar^(2-eta))*wbar)*((1-eta)/(1-th))*((1-beta*(1-deltah))/(eta+beta*eta)))^(1/(eta-1)); %equilibrium home capital stock xhbar=deltah*khbar; %equilibrium home investment xbar=xmbar+xhbar; %equilibrium total investment cmbar=ybar-xbar; %equilibrium market consumption chbar=(khbar^eta)*(hhbar^(1-eta)); %equilibrium home-produced-goods consumption phi=(cmbar^(e-1))*wbar*(1-th); %auxiliary variable psi=1/lbar; %auxiliary variable kappa=(chbar^(e-1))*(1-eta); %auxiliary variable omega= hhbar/lbar; %auxiliary variable a=kappa*psi/(phi*omega+kappa*psi); %market consumption weight on total consumption cbar=(a*cmbar^e+(1-a)*chbar^e)^(1/e); %equilibrium total consumption b=(psi*cbar^e)/(a*phi+psi*cbar^e); % %---------------------------------------------------------------------------------------------------------------------------------------------------------- % 3. Model %---------------------------------------------------------------------------------------------------------------------------------------------------------- model(linear); c=(cbar^-e)*(a*(cmbar^e)*cm+(1-a)*(chbar^e)*ch); y=theta*km(-1)+(1-theta)*zm+(1-theta)*hm; ch=eta*kh(-1)+(1-eta)*zh+(1-eta)*hh; zm=rhom*zm(-1)+em; zh=rhoh*zh(-1)+eh; ybar*y=cmbar*cm+xbar*x; xmbar*xm=kmbar*(km-(1-deltam)*km(-1)); xhbar*xh=khbar*(kh-(1-deltah)*kh(-1)); xbar*x=xmbar*xm+xhbar*xh; (e-1)*cm+w-e*c=-l; (e-1)*ch-e*c=hh-l; beta*((rbar*(1-tk)+tk*deltam+(1-deltam))*((e-1)*cm(+1)-e*c(+1))+(1-tk)*rbar*r(+1))=(e-1)*cm-e*c; -e*((1-a)*(chbar^e)*eta/khbar-a*(cmbar^(e-1)))*c+(1-a)*e*(ch^e)*(eta/khbar)*(ch-kh)-a*(e-1)*(cmbar^(e-1))*cm=beta*(e*c(+1)*(a*(cmbar^(e-1))*(1-deltah)+(1-a)*(chbar^e)*eta/khbar)-(1-deltah)*a*(e-1)*(cmbar^(e-1))*cm(+1)-(((1-a)*e*eta*chbar^e)/khbar)*(kh-eta*ch(+1))); y-km(-1)=r; y-hm=w; lbar*l=-(hmbar*hm+hhbar*hh); end; %---------------------------------------------------------------------------------------------------------------------------------------------------------- shocks; var em=sigmam^2; var eh=sigmah^2; corr em, eh=gamma; end; steady; stoch_simul(ar=1,irf=100) y cm ch hh hm; %---------------------------------------------------------------- % 5. Some Results %---------------------------------------------------------------- %statistic1 = sqrt(diag(oo_.var(1:6,1:6)))./sqrt(oo_.var(1,1)); %table('Relative standard deviations in %',strvcat('VARIABLE','REL. S.D.'),var_list_(1:6,:),statistic1,10,8,4)