Estimation of Multilevel Simultaneous Equation Models through Genetic Algorithms

• Main Authors: Rocío Hernández-Sanjaime, Martín González, Jose J. López-Espín
• Format: Article
• Language: English
• Published: MDPI AG 2020-11-01
• Series: Mathematics
• Subjects: multilevel simultaneous equation model; maximum likelihood estimation; genetic algorithms; optimization
• Online Access: https://www.mdpi.com/2227-7390/8/12/2098

Problems in estimating simultaneous equation models when error terms are not intertemporally uncorrelated has motivated the introduction of a new multivariate model referred to as Multilevel Simultaneous Equation Model (MSEM). The maximum likelihood estimation of the parameters of an MSEM has been set forth. Because of the difficulties associated with the solution of the system of likelihood equations, the maximum likelihood estimator cannot be obtained through exhaustive search procedures. A hybrid metaheuristic that combines a genetic algorithm and an optimization method has been developed to overcome both technical and analytical limitations in the general case when the covariance structure is unknown. The behaviour of the hybrid metaheuristic has been discussed by varying different tuning parameters. A simulation study has been included to evaluate the adequacy of this estimator when error terms are not serially independent. Finally, the performance of this estimation approach has been compared with regard to other alternatives.