Bayesian Information Criterion Developed Using Unbiased Estimator for Simultaneous Equations Model
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Abstract
This article introduces a new criterion for selecting a simultaneous equations model based on the Bayesian information criterion. The simultaneous equations model (SEM) is widely used in Statistics and Economics. The main characteristic of SEM is that the dependent variable of one equation can be the independent variable of the remaining equations. The new criterion performs the estimation of the error contemporaneous covariance matrix using the unbiased estimator (UE) instead of the maximum likelihood estimator (MLE) in the system of Bayesian information criterion (SBIC), and the new criterion is called SBIC(UE). The performances of SBIC(UE) and SBIC are compared using the extensive simulation study and the observed L2 performance. It is found that SBIC(UE) is more efficient than SBIC, with a higher percentage of correct model selections, a higher average of the observed L2 performance, and a lower standard deviation of the observed L2 performance. SBIC is more negatively biased than SBIC(UE) because the estimate of the error contemporaneous covariance matrix when using MLE is less than the estimate when using UE, i.e., it is underestimated. For this reason, the efficiency of the SBIC is lower than the SBIC(UE).
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