diff --git a/doc/dynare.texi b/doc/dynare.texi index 3edecb3186e03cbb8bb374e4591063c39b52b363..56da4a6f098ea7e5f094fe22c3df7ed3b9113936 100644 --- a/doc/dynare.texi +++ b/doc/dynare.texi @@ -6958,11 +6958,19 @@ Multi-country RBC model with time to build, presented in @cite{Backus, Kehoe and Kydland (1992)}. @end table +@item agtrend.mod +Small open economy RBC model with shocks to the growth trend, presented +in @cite{Aguiar and Gopinath (2004)}. + @node Bibliography @chapter Bibliography @itemize +@item +Aguiar, Mark and Gopinath, Gita (2004): ``Emerging Market Business +Cycles: The Cycle is the Trend,'' @i{NBER Working Paper}, 10734 + @item Backus, David K., Patrick J. Kehoe, and Finn E. Kydland (1992): ``International Real Business Cycles,'' @i{Journal of Political diff --git a/examples/agtrend.mod b/examples/agtrend.mod new file mode 100644 index 0000000000000000000000000000000000000000..a50748707b74391f8fb2e91275d99bffe5167815 --- /dev/null +++ b/examples/agtrend.mod @@ -0,0 +1,165 @@ +/* + * 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) + * + * This implementation was written by Sébastien Villemot. Please note that the + * following copyright notice only applies to this Dynare implementation of the + * model. + */ + +/* + * Copyright (C) 2012 Dynare Team + * + * This file is part of Dynare. + * + * Dynare is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * Dynare is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with Dynare. If not, see <http://www.gnu.org/licenses/>. + */ + + +// Set the following variable to 0 to get Cobb-Douglas utility +@#define ghh = 1 +// Set the following variable to 0 to get the calibration for Canada +@#define mexico = 1 + +var c k y b q g l u z uc ul f c_y tb_y i_y; + +varexo eps_z eps_g; + +parameters mu_g sigma rho_g sigma_g delta phi psi b_star alpha rho_z sigma_z r_star beta; + +// Benchmark parameter values (table 3) +@#if ghh == 1 +parameters tau nu; +tau = 1.4; +nu = 1.6; +@#else +parameters gamma; +gamma = 0.36; +@#endif + +alpha = 0.68; +sigma = 2; +delta = 0.03; +beta = 0.98; +psi = 0.001; +b_star = 0.1; + +// Estimated parameters (table 4) +@#if mexico == 1 +@# if ghh == 1 +mu_g = 1.006; +sigma_z = 0.0041; +rho_z = 0.94; +sigma_g = 0.0109; +rho_g = 0.72; +phi = 3.79; +@# else +mu_g = 1.005; +sigma_z = 0.0046; +rho_z = 0.94; +sigma_g = 0.025; +rho_g = 0.06; +phi = 2.82; +@# endif +@#else +// Canada +@# if ghh == 1 +mu_g = 1.007; +sigma_z = 0.0057; +rho_z = 0.88; +sigma_g = 0.0014; +rho_g = 0.94; +phi = 2.63; +@# else +mu_g = 1.007; +sigma_z = 0.0072; +rho_z = 0.96; +sigma_g = 0.0044; +rho_g = 0.50; +phi = 3.76; +@# endif +@#endif + +@#if ghh == 1 +r_star = mu_g^(-sigma)/beta - 1; +@#else +r_star = mu_g^(1-gamma*(1-sigma))/beta - 1; +@#endif + +model; +y=exp(z)*k(-1)^(1-alpha)*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 +u = (c-tau*l^nu)^(1-sigma)/(1-sigma); // GHH utility (3) +uc = (c - tau*l^nu)^(-sigma); +ul = -tau*nu*l^(nu-1)*(c - tau*l^nu)^(-sigma); +f = beta*g^(1-sigma); +@#else +u = (c^gamma*(1-l)^(1-gamma))^(1-sigma)/(1-sigma); // Cobb-Douglas utility (4) +uc = gamma*u/c*(1-sigma); +ul = -(1-gamma)*u/(1-l)*(1-sigma); +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) +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 +end; + +initval; +q = 1/(1+r_star); +b = b_star; +z = 0; +g = mu_g; + +c = 0.583095; +k = 4.02387; +y = 0.721195; +l = 0.321155; + +@#if ghh == 1 +u = (c-tau*l^nu)^(1-sigma)/(1-sigma); +uc = (c - tau*l^nu)^(-sigma); +ul = -tau*nu*l^(nu-1)*(c - tau*l)^(-sigma); +f = beta*g^(1-sigma); +@#else +u = (c^gamma*(1-l)^(1-gamma))^(1-sigma)/(1-sigma); +uc = gamma*u/c*(1-sigma); +ul = -(1-gamma)*u/(1-l)*(1-sigma); +f = beta*g^(gamma*(1-sigma)); +@#endif + +tb_y = (b-g*q*b)/y; +c_y = c/y; +i_y = (g*k-(1-delta)*k)/y; +end; + +shocks; +var eps_g = 1; +var eps_z = 1; +end; + +steady; + +check; + +// Plot impulse response functions (figure 4) +stoch_simul tb_y c_y i_y;