140 lines
4.3 KiB
Modula-2
140 lines
4.3 KiB
Modula-2
/*
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* This file shows how to solve an RBC model with two occasionally binding constraints:
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* 1. The INEG constraint implements quadratic capital adjustment costs if investment
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* falls below its steady state. If investment is above steady state, there are no
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* adjustment costs
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* 2. The IRR constraint implements irreversible investment. Investment cannot be lower
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* than a factor phi of its steady state.
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*
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* Notes:
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* - This mod-file is based on an example originally provided by Luca Guerrieri
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* and Matteo Iacoviello provided at https://www.matteoiacoviello.com/research_files/occbin_20140630.zip
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* - The INEG constraint should theoretically be log_Invest-log(steady_state(Invest))<0, but this will lead
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* to numerical issues. Instead we allow for a small negative value of <-0.000001
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*
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* Please note that the following copyright notice only applies to this Dynare
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* implementation of the model.
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*/
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/*
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* Copyright © 2021 Dynare Team
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*
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* This 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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* It 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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* For A copy of the GNU General Public License,
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* see <https://www.gnu.org/licenses/>.
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*/
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var A $A$ (long_name='TFP')
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C $C$ (long_name='consumption')
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Invest $I$ (long_name='investment')
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K $K$ (long_name='capital')
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Lambda $\lambda$ (long_name='Lagrange multiplier')
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log_K ${\hat K}$ (long_name='log capital')
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log_Invest ${\hat I}$ (long_name='log investment')
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log_C ${\hat C}$ (long_name='log consumption')
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;
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varexo epsilon $\varepsilon$ (long_name='TFP shock');
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parameters alpha $\alpha$ (long_name='capital share')
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delta $\delta$ (long_name='depreciation')
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beta $\beta$ (long_name='discount factor')
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sigma $\sigma$ (long_name='risk aversion')
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rho $\rho$ (long_name='autocorrelation TFP')
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phi $\phi$ (long_name='irreversibility fraction of steady state investment')
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psi $\psi$ (long_name='capital adjustment cost')
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;
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beta=0.96;
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alpha=0.33;
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delta=0.10;
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sigma=2;
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rho = 0.9;
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phi = 0.975;
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psi = 5;
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model;
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// 1.
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[name='Euler', bind = 'INEG']
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-C^(-sigma)*(1+2*psi*(K/K(-1)-1)/K(-1))+ beta*C(+1)^(-sigma)*((1-delta)-2*psi*(K(+1)/K-1)*
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(-K(+1)/K^2)+alpha*exp(A(+1))*K^(alpha-1))= -Lambda+beta*(1-delta)*Lambda(+1);
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[name='Euler', relax = 'INEG']
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-C^(-sigma) + beta*C(+1)^(-sigma)*(1-delta+alpha*exp(A(+1))*K^(alpha-1))= -Lambda+beta*(1-delta)*Lambda(+1);
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// 2.
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[name='Budget constraint',bind = 'INEG']
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C+K-(1-delta)*K(-1)+psi*(K/K(-1)-1)^2=exp(A)*K(-1)^(alpha);
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[name='Budget constraint',relax = 'INEG']
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C+K-(1-delta)*K(-1)=exp(A)*K(-1)^(alpha);
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// 3.
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[name='LOM capital']
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Invest = K-(1-delta)*K(-1);
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// 4.
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[name='investment',bind='IRR,INEG']
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(log_Invest - log(phi*steady_state(Invest))) = 0;
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[name='investment',relax='IRR']
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Lambda=0;
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[name='investment',bind='IRR',relax='INEG']
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(log_Invest - log(phi*steady_state(Invest))) = 0;
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// 5.
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[name='LOM TFP']
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A = rho*A(-1)+epsilon;
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// Definitions
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[name='Definition log capital']
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log_K=log(K);
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[name='Definition log consumption']
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log_C=log(C);
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[name='Definition log investment']
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log_Invest=log(Invest);
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end;
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occbin_constraints;
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name 'IRR'; bind log_Invest-log(steady_state(Invest))<log(phi); relax Lambda<0;
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name 'INEG'; bind log_Invest-log(steady_state(Invest))<-0.000001; %not exactly 0 for numerical reasons
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end;
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steady_state_model;
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K = ((1/beta-1+delta)/alpha)^(1/(alpha-1));
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C = -delta*K +K^alpha;
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Invest = delta*K;
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log_K = log(K);
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log_C = log(C);
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log_Invest = log(Invest);
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Lambda = 0;
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A=0;
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end;
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shocks;
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var epsilon; stderr 0.015;
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end;
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steady;
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shocks(surprise);
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var epsilon;
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periods 1:9, 10, 50, 90, 130, 131:169;
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values -0.0001, -0.01,-0.02, 0.01, 0.02, 0;
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end;
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occbin_setup;
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occbin_solver(simul_periods=200,simul_check_ahead_periods=200);
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occbin_graph log_C epsilon Lambda log_K log_Invest A;
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