174 lines
5.1 KiB
Modula-2
174 lines
5.1 KiB
Modula-2
/*
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* This file implements the multi-country RBC model with time to build,
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* described in Backus, Kehoe and Kydland (1992): "International Real Business
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* Cycles", Journal of Political Economy, 100(4), 745-775.
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*
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* The notation for the variable names are the same in this file than in the paper.
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* However the timing convention is different: we had to taken into account the
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* fact that in Dynare, if a variable is denoted at the current period, then
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* this variable must be also decided at the current period.
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* Concretely, here are the differences between the paper and the model file:
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* - z_t in the model file is equal to z_{t+1} in the paper
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* - k_t in the model file is equal to k_{t+J} in the paper
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* - 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
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*
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* The macroprocessor is used in this file to create a loop over countries.
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* Only two countries are used here (as in the paper), but it is easy to add
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* new countries in the corresponding macro-variable and completing the
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* calibration.
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*
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* The calibration is the same than in the paper. The results in terms of
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* moments of variables are very close to that of the paper (but not equal
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* since the authors a different solution method).
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*
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* This implementation was written by Sebastien Villemot. Please note that the
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* following copyright notice only applies to this Dynare implementation of the
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* model.
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*/
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/*
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* Copyright © 2010 Dynare Team
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*
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* This file is part of Dynare.
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*
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* Dynare is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Dynare is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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*/
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@#define countries = [ "H", "F" ]
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@#define J = 4
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@#for co in countries
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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};
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@#endfor
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// Lagrange multiplier of aggregate constraint
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var LGM;
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parameters rho_@{countries[1]}_@{countries[2]} rho_@{countries[2]}_@{countries[1]};
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model;
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@#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});
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K_@{co} = (1-delta_@{co})*K_@{co}(-1) + S_@{co};
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X_@{co} =
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@# for lag in (-J+1):0
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+ phi_@{co}*S_@{co}(@{lag})
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@# endfor
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;
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A_@{co} = (1-eta_@{co})*A_@{co}(-1) + N_@{co};
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L_@{co} = 1 - alpha_@{co}*N_@{co} - (1-alpha_@{co})*eta_@{co}*A_@{co}(-1);
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// Utility multiplied by gamma
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# U_@{co} = (C_@{co}^mu_@{co}*L_@{co}^(1-mu_@{co}))^gamma_@{co};
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// FOC with respect to consumption
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psi_@{co}*mu_@{co}/C_@{co}*U_@{co} = LGM;
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// FOC with respect to labor
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// NOTE: this condition is only valid for alpha = 1
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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
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@# for lag in 0:(J-1)
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+beta_@{co}^@{lag}*LGM(+@{lag})*phi_@{co}
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@# endfor
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@# for lag in 1:J
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-beta_@{co}^@{lag}*LGM(+@{lag})*phi_@{co}*(1-delta_@{co})
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@# endfor
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= 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
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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
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@# if co == countries[1]
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@# define alt_co = countries[2]
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@# else
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@# define alt_co = countries[1]
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@# endif
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(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
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@#for co in countries
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+C_@{co} + X_@{co} + Z_@{co} - Z_@{co}(-1)
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@#endfor
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=
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@#for co in countries
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+Y_@{co}
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@#endfor
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;
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end;
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@#for co in countries
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beta_@{co} = 0.99;
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mu_@{co} = 0.34;
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gamma_@{co} = -1.0;
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alpha_@{co} = 1;
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eta_@{co} = 0.5; // Irrelevant when alpha=1
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theta_@{co} = 0.36;
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nu_@{co} = 3;
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sigma_@{co} = 0.01;
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delta_@{co} = 0.025;
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phi_@{co} = 1/@{J};
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psi_@{co} = 0.5;
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@#endfor
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rho_H_H = 0.906;
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rho_F_F = 0.906;
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rho_H_F = 0.088;
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rho_F_H = 0.088;
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initval;
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@#for co in countries
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LAMBDA_@{co} = 1;
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NX_@{co} = 0;
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Z_@{co} = 1;
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A_@{co} = 1;
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L_@{co} = 0.5;
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N_@{co} = 0.5;
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Y_@{co} = 1;
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K_@{co} = 1;
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C_@{co} = 1;
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S_@{co} = 1;
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X_@{co} = 1;
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E_@{co} = 0;
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@#endfor
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LGM = 1;
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end;
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shocks;
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var E_H; stderr 0.00852;
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var E_F; stderr 0.00852;
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corr E_H, E_F = 0.258;
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end;
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steady;
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check;
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stoch_simul(order=1, hp_filter=1600, nograph);
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