Akaike Information Criterion for a Simultaneous Equations Model using Unbiased Estimator

Warangkhana  Riansut

Authors

Warangkhana Riansut Department of Mathematics and Statistics, Faculty of Science and Digital Innovation, Thaksin University, Phatthalung, Thailand

Keywords:

Model selection criterion, performance, simultaneous equations model, unbiased estimator, maximum likelihood estimator

Abstract

This article introduces a novel approach in the fields of econometrics and statistics. A new criterion for selection in a simultaneous equation model (SEM) based on the Akaike information criterion using an unbiased estimator (UE) called SAIC(UE). This innovative method replaces the traditional maximum likelihood estimator (MLE) with UE, offering a fresh perspective on model selection. A comparison of the effectiveness of SAIC(UE) with SAIC (Keerativibool et al. 2011) by the extensive simulation study and the observed L₂ performance found that SAIC(UE) is the best criterion because it had the maximum percentage of correct model selections, the maximum average of the observed L₂ performance, and the minimum standard deviation of the observed L₂ performance in all situations of the simulation study. SAIC has a more negative bias than SAIC(UE) because the contemporaneous covariance matrix of error terms obtained from MLE is smaller than that obtained from UE or underestimated. This reason causes the correct order of the model from SAIC to be less than SAIC(UE).

References

This article introduces a novel approach in the fields of econometrics and statistics. A new criterion for selection in a simultaneous equation model (SEM) based on the Akaike information criterion using an unbiased estimator (UE) called SAIC(UE). This innovative method replaces the traditional maximum likelihood estimator (MLE) with UE, offering a fresh perspective on model selection. A comparison of the effectiveness of SAIC(UE) with SAIC (Keerativibool et al. 2011) by the extensive simulation study and the observed L2 performance found that SAIC(UE) is the best criterion because it had the maximum percentage of correct model selections, the maximum average of the observed L2 performance, and the minimum standard deviation of the observed L2 performance in all situations of the simulation study. SAIC has a more negative bias than SAIC(UE) because the contemporaneous covariance matrix of error terms obtained from MLE is smaller than that obtained from UE or underestimated. This reason causes the correct order of the model from SAIC to be less than SAIC(UE).