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Created a new 'examples' subdirectory with a (still small) example da…
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Sébastien Villemot
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| Original file line number | Diff line number | Diff line change |
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| /* | ||
| * This file implements the multi-country RBC model with time to build, | ||
| * described in Backus, Kehoe and Kydland (1992): "International Real Business | ||
| * Cycles", Journal of Political Economy, 100(4), 745-775. | ||
| * | ||
| * The notation for the variable names are the same in this file than in the paper. | ||
| * However the timing convention is different: we had to taken into account the | ||
| * fact that in Dynare, if a variable is denoted at the current period, then | ||
| * this variable must be also decided at the current period. | ||
| * Concretely, here are the differences between the paper and the model file: | ||
| * - z_t in the model file is equal to z_{t+1} in the paper | ||
| * - k_t in the model file is equal to k_{t+J} in the paper | ||
| * - s_t in the model file is equal to s_{J,t}=s_{J-1,t+1}=...=s_{1,t+J-1} in the paper | ||
| * | ||
| * The macroprocessor is used in this file to create a loop over countries. | ||
| * Only two countries are used here (as in the paper), but it is easy to add | ||
| * new countries in the corresponding macro-variable and completing the | ||
| * calibration. | ||
| * | ||
| * The calibration is the same than in the paper. The results in terms of | ||
| * moments of variables are very close to that of the paper (but not equal | ||
| * since the authors a different solution method). | ||
| * | ||
| * This implementation was written by Sebastien Villemot. Please note that the | ||
| * following copyright notice only applies to this Dynare implementation of the | ||
| * model. | ||
| */ | ||
|
|
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| /* | ||
| * Copyright (C) 2010 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/>. | ||
| */ | ||
|
|
||
| @#define countries = [ "H", "F" ] | ||
| @#define J = 4 | ||
|
|
||
| @#for co in countries | ||
| var C_@{co} L_@{co} N_@{co} A_@{co} K_@{co} Z_@{co} X_@{co} LAMBDA_@{co} S_@{co} NX_@{co} Y_@{co}; | ||
|
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| varexo E_@{co}; | ||
|
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| parameters beta_@{co} alpha_@{co} eta_@{co} mu_@{co} gamma_@{co} theta_@{co} nu_@{co} sigma_@{co} delta_@{co} phi_@{co} psi_@{co} rho_@{co}_@{co}; | ||
| @#endfor | ||
|
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| // Lagrange multiplier of aggregate constraint | ||
| var LGM; | ||
|
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| parameters rho_@{countries[1]}_@{countries[2]} rho_@{countries[2]}_@{countries[1]}; | ||
|
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| model; | ||
| @#for co in countries | ||
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| Y_@{co} = ((LAMBDA_@{co}*K_@{co}(-@{J})^theta_@{co}*N_@{co}^(1-theta_@{co}))^(-nu_@{co}) + sigma_@{co}*Z_@{co}(-1)^(-nu_@{co}))^(-1/nu_@{co}); | ||
| K_@{co} = (1-delta_@{co})*K_@{co}(-1) + S_@{co}; | ||
| X_@{co} = | ||
| @# for lag in (-J+1):0 | ||
| + phi_@{co}*S_@{co}(@{lag}) | ||
| @# endfor | ||
| ; | ||
|
|
||
| A_@{co} = (1-eta_@{co})*A_@{co}(-1) + N_@{co}; | ||
| L_@{co} = 1 - alpha_@{co}*N_@{co} - (1-alpha_@{co})*eta_@{co}*A_@{co}(-1); | ||
|
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| // Utility multiplied by gamma | ||
| # U_@{co} = (C_@{co}^mu_@{co}*L_@{co}^(1-mu_@{co}))^gamma_@{co}; | ||
|
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| // FOC with respect to consumption | ||
| psi_@{co}*mu_@{co}/C_@{co}*U_@{co} = LGM; | ||
|
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| // FOC with respect to labor | ||
| // NOTE: this condition is only valid for alpha = 1 | ||
| psi_@{co}*(1-mu_@{co})/L_@{co}*U_@{co}*(-alpha_@{co}) = - LGM * (1-theta_@{co})/N_@{co}*(LAMBDA_@{co}*K_@{co}(-@{J})^theta_@{co}*N_@{co}^(1-theta_@{co}))^(-nu_@{co})*Y_@{co}^(1+nu_@{co}); | ||
|
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||
| // FOC with respect to capital | ||
| @# for lag in 0:(J-1) | ||
| +beta_@{co}^@{lag}*LGM(+@{lag})*phi_@{co} | ||
| @# endfor | ||
| @# for lag in 1:J | ||
| -beta_@{co}^@{lag}*LGM(+@{lag})*phi_@{co}*(1-delta_@{co}) | ||
| @# endfor | ||
| = beta_@{co}^@{J}*LGM(+@{J})*theta_@{co}/K_@{co}*(LAMBDA_@{co}(+@{J})*K_@{co}^theta_@{co}*N_@{co}(+@{J})^(1-theta_@{co}))^(-nu_@{co})*Y_@{co}(+@{J})^(1+nu_@{co}); | ||
|
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| // FOC with respect to stock of inventories | ||
| LGM=beta_@{co}*LGM(+1)*(1+sigma_@{co}*Z_@{co}^(-nu_@{co}-1)*Y_@{co}(+1)^(1+nu_@{co})); | ||
|
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| // Shock process | ||
| @# if co == countries[1] | ||
| @# define alt_co = countries[2] | ||
| @# else | ||
| @# define alt_co = countries[1] | ||
| @# endif | ||
| (LAMBDA_@{co}-1) = rho_@{co}_@{co}*(LAMBDA_@{co}(-1)-1) + rho_@{co}_@{alt_co}*(LAMBDA_@{alt_co}(-1)-1) + E_@{co}; | ||
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| NX_@{co} = (Y_@{co} - (C_@{co} + X_@{co} + Z_@{co} - Z_@{co}(-1)))/Y_@{co}; | ||
|
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| @#endfor | ||
|
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| // World ressource constraint | ||
| @#for co in countries | ||
| +C_@{co} + X_@{co} + Z_@{co} - Z_@{co}(-1) | ||
| @#endfor | ||
| = | ||
| @#for co in countries | ||
| +Y_@{co} | ||
| @#endfor | ||
| ; | ||
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| end; | ||
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| @#for co in countries | ||
| beta_@{co} = 0.99; | ||
| mu_@{co} = 0.34; | ||
| gamma_@{co} = -1.0; | ||
| alpha_@{co} = 1; | ||
| eta_@{co} = 0.5; // Irrelevant when alpha=1 | ||
| theta_@{co} = 0.36; | ||
| nu_@{co} = 3; | ||
| sigma_@{co} = 0.01; | ||
| delta_@{co} = 0.025; | ||
| phi_@{co} = 1/@{J}; | ||
| psi_@{co} = 0.5; | ||
| @#endfor | ||
|
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| rho_H_H = 0.906; | ||
| rho_F_F = 0.906; | ||
| rho_H_F = 0.088; | ||
| rho_F_H = 0.088; | ||
|
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| initval; | ||
| @#for co in countries | ||
| LAMBDA_@{co} = 1; | ||
| NX_@{co} = 0; | ||
| Z_@{co} = 1; | ||
| A_@{co} = 1; | ||
| L_@{co} = 0.5; | ||
| N_@{co} = 0.5; | ||
| Y_@{co} = 1; | ||
| K_@{co} = 1; | ||
| C_@{co} = 1; | ||
| S_@{co} = 1; | ||
| X_@{co} = 1; | ||
|
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| E_@{co} = 0; | ||
| @#endfor | ||
|
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| LGM = 1; | ||
| end; | ||
|
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| shocks; | ||
| var E_H; stderr 0.00852; | ||
| var E_F; stderr 0.00852; | ||
| corr E_H, E_F = 0.258; | ||
| end; | ||
|
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||
| steady; | ||
| check; | ||
|
|
||
| stoch_simul(order=1, hp_filter=1600, nograph); |
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,68 @@ | ||
| /* | ||
| * Example 1 from F. Collard (2001): "Stochastic simulations with DYNARE: | ||
| * A practical guide" (see "guide.pdf" in the documentation directory). | ||
| */ | ||
|
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| /* | ||
| * Copyright (C) 2001-2010 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/>. | ||
| */ | ||
|
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| var y, c, k, a, h, b; | ||
| varexo e, u; | ||
|
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| parameters beta, rho, alpha, delta, theta, psi, tau; | ||
|
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| alpha = 0.36; | ||
| rho = 0.95; | ||
| tau = 0.025; | ||
| beta = 0.99; | ||
| delta = 0.025; | ||
| psi = 0; | ||
| theta = 2.95; | ||
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| phi = 0.1; | ||
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| model; | ||
| c*theta*h^(1+psi)=(1-alpha)*y; | ||
| k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1))) | ||
| *(exp(b(+1))*alpha*y(+1)+(1-delta)*k)); | ||
| y = exp(a)*(k(-1)^alpha)*(h^(1-alpha)); | ||
| k = exp(b)*(y-c)+(1-delta)*k(-1); | ||
| a = rho*a(-1)+tau*b(-1) + e; | ||
| b = tau*a(-1)+rho*b(-1) + u; | ||
| end; | ||
|
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| initval; | ||
| y = 1.08068253095672; | ||
| c = 0.80359242014163; | ||
| h = 0.29175631001732; | ||
| k = 11.08360443260358; | ||
| a = 0; | ||
| b = 0; | ||
| e = 0; | ||
| u = 0; | ||
| end; | ||
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| shocks; | ||
| var e; stderr 0.009; | ||
| var u; stderr 0.009; | ||
| var e, u = phi*0.009*0.009; | ||
| end; | ||
|
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| stoch_simul; |
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