New Criteria for Selection in Simultaneous Equations Model

Abstract

When the errors of statistical models are not independent, such as in the existence of the autocorrelation (AR) and/or moving average (MA) problems, the values of the standard model selection criteria are not correct and hence may affect the acquisition of the true model. This paper attempts to modify the Bayesian information criterion (BIC) in order to select the most appropriate simultaneous equations model (SEM). The first criterion, a system of simultaneous equation BIC (SBIC), is constructed after correcting the second-order autocorrelation, AR(2), problem. The second criterion is the adjusted BIC when the AR(2) problem is ignored. If there is no AR(2) problem in the errors, SBIC reduces to BIC. Using an extensive simulation study, SBIC and BIC are compared with SAIC and AIC, the measures of model selection in SEM that were introduced by Keerativibool et al. (2011). From the simulation study we conclude that SBIC convincingly outperformed the other criteria and the rest of the criteria can be ordered according to their performance by BIC, SAIC, and AIC.