% Endogenous variables var AFhat AHhat ANhat ANhatstar bhat CA CCstar Chat Chatstar Deltas ihat ihatstar kFhatstar kHhat kNhat kNhatstar lFhatstar lhat lhatstar lHhat lNhat lNhatstar pi piH piF pistar Rhat Rhatstar RShat That what whatstar xFhatstar xHhat xNhat xNhatstar Yhat Yhatstar; % Exogenous variables varexo muH; varexo muF; varexo muN; varexo muNstar; % Parameters parameters abar alpha b beta delta gammabar epsilon eta kappa l nu nustar rho omega omegastar theta xHbar_Ybar xNbar_Ybar Cbar_Ybar xFbar_Ybarstar xNbarstar_Ybarstar lNbar_lbar lHbar_lbar lNbarstar_lbar lFbarstar_lbar Cbarstar_Ybarstar; abar = 0.000; alpha = 0.585; b = 1.000; beta = 0.960; delta = 0.100; gammabar = 1.000; epsilon = 0.004; eta = 3.170; kappa = 0.440; l = 0.200; nu = 0.700; nustar = 0.700; rho = 2.000; omega = 0.400; omegastar = 0.400; theta = 1.000; xHbar_Ybar = delta*gammabar*(1-alpha)/(1/beta - (1-delta)); xNbar_Ybar = delta*(1-omega)*(1-alpha)/(1/beta - (1-delta)); Cbar_Ybar = 1 - xHbar_Ybar - xNbar_Ybar; xFbar_Ybarstar = delta*((1-alpha)/(1/beta-(1-delta)))*(omega*(1-nu)*omegastar*nustar + omegastar*(1-nustar)*(gammabar-nu*omega))/(gammabar-nu*omega); xNbarstar_Ybarstar = delta*(1-omegastar)*(1-alpha)/(1/beta - (1-delta)); Cbarstar_Ybarstar = 1 - xFbar_Ybarstar - xNbarstar_Ybarstar; lNbar_lbar = (1-omega)/(1+abar*(beta-1)); lHbar_lbar = (omega + abar*(beta-1))/(1+abar*(beta-1)); lNbarstar_lbar = (1-omegastar)*((1-nu)*omega + abar*(beta-1))/((1-omegastar*nustar)*((1-nu)*omega + abar*(beta-1)) + omega*(1-nu)*nustar*omegastar); lFbarstar_lbar = 1 - (1-omegastar)*((1-nu)*omega + abar*(beta-1))/((1-omegastar*nustar)*((1-nu)*omega + abar*(beta-1)) + omega*(1-nu)*nustar*omegastar); % Model equations model(linear); % Home and foreign Euler equations (1-2) rho*Chat(+1) + eta*(1/(1-l))*lhat(+1) = rho*Chat + eta*(1/(1-l))*lhat + ihat - pi(+1); rho*Chatstar(+1) + eta*(1/(1-l))*lhatstar(+1) = rho*Chatstar + eta*(1/(1-l))*lhatstar + ihatstar - pistar(+1); % UIP (3) Deltas(+1) = ihat - ihatstar + epsilon*bhat; % Home and foreign consumption-labor effort trade-off(4-5) -Chat + what = eta*(l/(1-l))*lhat; -Chatstar + whatstar = eta*(1/(1-l))*lhatstar; % Current account (6) beta*(1+abar*epsilon)*bhat = bhat(-1) + abar*(beta*ihatstar + Deltas - pi) + (1-theta)*(nu-1)*gammabar*That + theta*(gammabar-nu*omega)*RShat + omega*(nu-1)*Yhat + (gammabar-nu*omega)*Yhatstar + (omega-1)*((1-kappa)*omega*(nu-1) + (1-theta)*(gammabar-nu*omega))*Rhat + (theta-kappa)*(omegastar-1)*(gammabar - nu*omega)*Rhatstar; % The …firms ’optimality conditions for investment, capital and labor input in traded and non-traded sectors home (7-12) rho*Chat(+1) + eta*(l/(1-l))*lhat(+1) = rho*Chat + eta*(1/(1-l))*lhat + (1 + beta*(delta-1))*(what(+1) + lHhat(+1) - kHhat) - b*delta*(xHhat - kHhat(-1)) + b*delta*beta*(xHhat(+1) - kHhat); rho*Chat(+1) + eta*(l/(1-l))*lhat(+1) = rho*Chat + eta*(1/(1-l))*lhat + (1 + beta*(delta-1))*(what(+1) + lNhat(+1) - kNhat) - b*delta*(xNhat - kNhat(-1)) + b*delta*beta*(xNhat(+1) - kNhat); kHhat = (1-delta)*kHhat(-1) + delta*xHhat; kNhat = (1-delta)*kNhat(-1) + delta*xNhat; what = (nu-1)*That + (omega-1)*Rhat + alpha*AHhat + (alpha-1)*lHhat + (1-alpha)*kHhat(-1); what = omega*Rhat + alpha*ANhat + (alpha-1)*lNhat + (1-alpha)*kNhat(-1); % The …firms ’optimality conditions for investment, capital and labor input in traded and non-traded sectors foreign (13-18) rho*Chatstar(+1) + eta*(l/(1-l))*lhatstar(+1) = rho*Chatstar + eta*(1/(1-l))*lhatstar + (1 + beta*(delta-1))*(whatstar(+1) + lFhatstar(+1) - kFhatstar) - b*delta*(xFhatstar - kFhatstar(-1)) + b*delta*beta*(xFhatstar(+1) - kFhatstar); rho*Chatstar(+1) + eta*(l/(1-l))*lhatstar(+1) = rho*Chatstar + eta*(1/(1-l))*lhatstar + (1 + beta*(delta-1))*(whatstar(+1) + lNhatstar(+1) - kNhatstar) - b*delta*(xNhatstar - kNhatstar(-1)) + b*delta*beta*(xNhatstar(+1) - kNhatstar); kFhatstar = (1-delta)*kFhatstar(-1) + delta*xFhatstar; kNhatstar = (1-delta)*kNhatstar(-1) + delta*xNhatstar; whatstar = nu*That - RShat + (omega-1)*Rhat + alpha*AFhat + (alpha-1)*lFhatstar + (1-alpha)*kFhatstar(-1); whatstar = omegastar*Rhatstar + alpha*ANhatstar + (alpha-1)*lNhatstar + (1-alpha)*kNhatstar(-1); % Production constraint home (19-20) -theta*(nu-1)*That + (omega*nu/gammabar)*Yhat + ((gammabar-nu*omega)/gammabar)*(theta*RShat + Yhatstar) + ((omega*nu/gammabar)*kappa*(1-omega) + ((gammabar-nu*omega)/gammabar)*theta*(1-omega))*Rhat + ((gammabar-nu*omega)/gammabar)*(theta-kappa)*(omegastar-1)*Rhatstar = ((1-alpha)*kHhat(-1) + alpha*lHhat + alpha*AHhat); -kappa*omega*Rhat + Yhat = ((1-alpha)*kNhat(-1) + alpha*lNhat + alpha*ANhat); % Production constraint foreign (21-22) -nu*theta*That + ((1-nu)*nustar*omega/(omega*(1-nu)*nustar + (1-nustar)*(gammabar - nu*omega)))*(-kappa*(omega-1)*Rhat + Yhat) + ((1-nustar)*(gammabar - nu*omega)/(omega*(1-nu)*nustar + (1-nustar)*(gammabar - nu*omega)))*((theta-kappa)*(omegastar-1)*Rhatstar - theta*(omega-1)*Rhat + theta*RShat + Yhatstar) = ((1-alpha)*kFhatstar(-1) + alpha*lFhatstar + alpha*AFhat); -kappa*omegastar*Rhatstar + Yhatstar = ((1-alpha)*kNhatstar(-1) + alpha*lNhatstar + alpha*ANhatstar); % Resource constraint (23-26) Yhat = (Cbar_Ybar)*Chat + (xHbar_Ybar)*xHhat + (xNbar_Ybar)*xNhat; Yhatstar = (Cbarstar_Ybarstar)*Chatstar + (xFbar_Ybarstar)*xFhatstar + (xNbarstar_Ybarstar)*xNhatstar; lhat = (lHbar_lbar)*lHhat + (lNbar_lbar)*lNhat; lhatstar = (lFbarstar_lbar)*lFhatstar + (lNbarstar_lbar)*lNhatstar; % RER and ToT (27-28) RShat = (nu-nustar)*That + (omega-1)*Rhat + (1-omegastar)*Rhatstar; That = That(-1) + Deltas + piF - piH; % Monetary policy - set inflation to zero (29-32) pi = omega*(1-nu)*piF + omega*(1-nu)*(Deltas); pistar = omegastar*nustar*piH - omegastar*nustar*Deltas; piH = -((1-omega)/(omega*nu + (1-omega)))*(AHhat - ANhat); piF = -((1-omegastar)/(omegastar*(1-nustar)+1-omegastar))*(AFhat - ANhatstar); % Relative consumption and current account (33-34) CCstar = Chat - Chatstar; CA = bhat - bhat(-1); % shocks (35-38) AFhat = 0.154*AFhat(-1) + muF; AHhat = 0.154*AHhat(-1) + muH; ANhat = 0.154*ANhat(-1) + muN; ANhatstar = 0.9*ANhatstar(-1) + muNstar; end; shocks; var muF; stderr 0.01; corr muF,muH = 1.21; end; stoch_simul(order=1,irf=100);