Model Selection of Simultaneous Equations Model Based on Kullback Information Criterion for Small Sample Case
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Abstract
This paper introduces a new criterion called SKICc, designed specifically for selecting simultaneous equations models (SEM) in small sample cases. The efficiency of SKICc was compared to that of SAIC, SBIC, and SKIC, considering the percentage of correct model selection and the L2 efficiency. The study’s scope was defined under the assumption that the independent variables were normally distributed, had a mean of zero, a variance of one, and no issues of multicollinearity. Additionally, the errors in the model had a mean of zero but exhibited contemporaneous correlations among the equations. The small sample sizes examined in the study included 15, 20, and 25 units, with 1,000 simulated data sets generated for each size. The results of the study indicated that the SKICc created had the following formula:
The efficiency comparison revealed that SKICc demonstrated the highest efficiency for small sample sizes. It achieved the best performance in terms of correct model selection and had the highest mean and lowest standard deviation of the L2 efficiency. However, as the sample size increased, SKIC exhibited the best efficiency. Furthermore, the research findings indicated that SAIC and SBIC tended to select models with too many variables due to their low penalty function values. In contrast, SKIC often selects models with too few variables because of its high penalty function value. Overall, SKICc effectively addressed the issue of selecting models with either too many or too few variables, outperforming the other criteria studied.
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