Model Selection Criterion Based on Kullback-Leibler’s Symmetric Divergence for Simultaneous Equations Model

Abstract

Moving average in the errors of simultaneous equations model (SEM) is a crucial problem making the estimators from the ordinary least squares (OLS) method inefficient. For this reason, we proposed the transformation matrix in order to correct the first-order moving average, MA(1), that generates in the fitted model and to recover the one lost observation in a SEM. After the errors are transformed to be independent, the Kullback information criterion for selecting the appropriate SEM, called SKIC, is derived where the problem of contemporaneous correlation still be considered. SKIC is constructed based on the symmetric divergence which is obtained by sum of the two directed divergences. The symmetric divergence is arguably more sensitive than either of its individual components. The performance of selection of the order of the model from the proposed criterion, SKIC, is examined relative to SAIC proposed by Keerativibool (2009). The results of simulation study show that the errors of the model after transformation are independent and SKIC convincingly outperformed SAIC because SAIC has a tendency to overfit the order of the model more so than does SKIC.