Equilibrium models with heterogeneous agents under rational expectations and its numerical solution
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- GI-M2NICA - Artigos [74]
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Equilibrium models with heterogeneous agents under rational expectations and its numerical solutionData
2021-05Cita bibliográfica
J. Ráfales, and C. Vázquez, "Equilibrium models with heterogeneous agents under rational expectations and its numerical solution", Communications in Nonlinear Science and Numerical Simulation, Vol. 96, article number 105673, May 2021, doi: 10.1016/j.cnsns.2020.105673
Resumo
[Abstract]: In this work we assume rational expectations to pose general equilibrium models with heterogeneous firms that can enter or exit the industry. More precisely, we assume a general Ito process for the dynamics of the agents productivity, including the main dynamics in the literature. A Hamilton-Jacobi-Bellman (HJB) formulation models the endogenous decision of firms to remain or exit the industry. All firms that exit are immediately replaced by a group of new ones, so that the probability density function of firms satisfies an appropriate Kolmogorov-Fokker-Plank (KFP) equation with source term. Equilibrium models are completed with the household problem formulation and the feasibility conditions. In the evolutive and general stationary settings, analytical or semi-analytical formulas are not available, so that appropriate numerical methods are required. We propose a Crank-Nicolson scheme for the time discretization of the evolutive problems. Moreover, we use an augmented Lagrangian active set (ALAS) method combined with a finite difference discretization for the HJB formulation and a suitable finite differences discretization for the KFP problem. For the global equilibrium problem we propose a Steffensen algorithm. Numerical examples illustrate the performance of the proposed numerical methodologies as well as the expected behaviours of the computed economic variables.
Palabras chave
Augmented Lagrangian active set
Complementarity problems
Economic equilibrium models
Finite differences methods
Heterogeneous agents
HJB-KFP PDE system
Complementarity problems
Economic equilibrium models
Finite differences methods
Heterogeneous agents
HJB-KFP PDE system
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Atribución-NoComercial-SinDerivadas 3.0 España
ISSN
1007-5704