diff --git a/examples/agtrend.mod b/examples/agtrend.mod index 619e5421b995f7449fab4f308b2b5a259cef4113..8fb600b4feede07265a590a873662e0a5c527839 100644 --- a/examples/agtrend.mod +++ b/examples/agtrend.mod @@ -1,15 +1,27 @@ /* * This file replicates the model studied in: * Aguiar, Mark and Gopinath, Gita (2004): "Emerging Market Business Cycles: - * The Cycle is the Trend" (NBER WP 10734) + * The Cycle is the Trend" (NBER WP 10734). It is different from version published + * in the Journal of Political Economy. + * + * This model file is intended to show the capabilities of the Dynare macro + * languange. It is not intended to provide a full replication of the original + * paper due to some differences in model calibration. In + * particular, this mod-file does not calibrate the share of debt to GDP + * to 0.1 as this would require the use of a steady state file. Rather, the + * absolute value of debt is set to 0.1. Given that output is close to 1 in + * the benchmark specification, this results in only a small difference to + * the working paper. + * The mod-file reproduces Figure 4 of the working paper, which displays the + * model response to 1 percent shock to trend and cyclical TFP. * - * This implementation was written by Sébastien Villemot. Please note that the - * following copyright notice only applies to this Dynare implementation of the - * model. + * This implementation was written by S�bastien Villemot and Johannes Pfeifer. + * Please note that the following copyright notice only applies to this Dynare + * implementation of the model. */ /* - * Copyright (C) 2012 Dynare Team + * Copyright (C) 2012-13 Dynare Team * * This file is part of Dynare. * @@ -54,7 +66,7 @@ sigma = 2; delta = 0.03; beta = 0.98; psi = 0.001; -b_star = 0.1; +b_star = 0.1; //taken here as the steady state value of debt; in the original paper, this is the share of debt to GDP // Estimated parameters (table 4) @#if mexico == 1 @@ -98,8 +110,8 @@ r_star = mu_g^sigma/beta - 1; r_star = mu_g^(1-gamma*(1-sigma))/beta - 1; @#endif -model; -y=exp(z)*k(-1)^(1-alpha)*l^alpha; // Production technology (1) +model; //equation numbers refer to numbers in the working paper version +y=exp(z)*k(-1)^(1-alpha)*(g*l)^alpha; // Production technology (1) z = rho_z*z(-1)+sigma_z*eps_z; // Transitory shock (2) log(g) = (1-rho_g)*log(mu_g)+rho_g*log(g(-1))+sigma_g*eps_g; // Trend shock @#if ghh == 1 @@ -115,13 +127,14 @@ f = beta*g^(gamma*(1-sigma)); @#endif c+g*k=y+(1-delta)*k(-1)-phi/2*(g*k/k(-1)-mu_g)^2*k(-1)-b(-1)+q*g*b; // Resource constraint (5) 1/q = 1+r_star+psi*(exp(b-b_star)-1); // Price of debt (6) -uc*(1+phi*(g*k/k(-1)-mu_g))*g=f*uc(+1)*(1-delta+(1-alpha)*y(+1)/k+phi/2*(g(+1)*k(+1)/k-mu_g)*(g(+1)*k(+1)/k+mu_g)); // FOC wrt to capital (10) +uc*(1+phi*(g*k/k(-1)-mu_g))*g=f*uc(+1)*(1-delta+(1-alpha)*y(+1)/k+phi/2*(g(+1)*k(+1)/k-mu_g)*(g(+1)*k(+1)/k+mu_g)); // FOC wrt to capital (10) with envelope condition plugged in ul+uc*alpha*y/l=0; // Leisure-consumption arbitrage (11) uc*g*q=f*uc(+1); // Euler equation (12) -tb_y = (b(-1)-g*q*b)/y; // Trade balance to GDP ratio -c_y = c/y; // Consumption to GDP ratio -i_y = (g*k-(1-delta)*k(-1))/y; // Investment to GDP ratio +//definition of auxilary variables to be plotted +tb_y = (b(-1)-g*q*b)/y; // Trade balance to GDP ratio, not logged as it can be negative +c_y = log(c/y); // Consumption to GDP ratio, logged to be in percent +i_y = log((g*k-(1-delta)*k(-1)+phi/2*(g*k/k(-1)-mu_g)^2*k(-1))/y); // Investment to GDP ratio, logged to be in percent end; initval; @@ -153,13 +166,13 @@ i_y = (g*k-(1-delta)*k)/y; end; shocks; -var eps_g = 1; -var eps_z = 1; +var eps_g; stderr 1/sigma_g/100; // use a 1 percent shock +var eps_z; stderr 1/sigma_z/100; // use a 1 percent shock end; steady; check; -// Plot impulse response functions (figure 4) -stoch_simul tb_y c_y i_y; +// Plot impulse response functions (Figure 4) +stoch_simul(order=1) tb_y c_y i_y;