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