[:es]Rocío Hernández-Sanjaime (University Miguel Hernández of Elche), Martín González (University Miguel Hernández of Elche) and Jose J. López-Espín (University Miguel Hernández of Elche)

Abstract: Conventional simultaneous equation models assume that the error terms are serially independent. In some situations, data may present hierarchical or grouped structure and this assumption may be invalid. A new multivariate model referred as to Multilevel Simultaneous Equation Model (MSEM) is developed under this motivation. The maximum likelihood estimation of the parameters of an MSEM is considered. A matrix-valued distribution, namely, the matrix normal distribution, is introduced to incorporate an among-row and an among-column covariance matrix structure in the specification of the model. In the absence of an analytical solution of the system of likelihood equations, a general-purpose optimization solver is employed to obtain the maximum likelihood estimators. In a first approach to the solution of the problem, the adequacy of the matrix normal distribution is evaluated empirically in the case in which the double covariance structure is known. Using simulated data under the model assumptions, the performance of the maximum likelihood estimator (MLE) is assessed with regard to other conventional alternatives such as two-stage least squares estimator (2SLS).

Keywords: Multilevel simultaneous equation model; Maximum likelihood estimation; Matrix normal distribution; Simultaneous equation model; Multilevel model