Ranking of Simultaneous Equation Techniques to Small Sample Properties and Correlated Random Deviates

Problem statement: All simultaneous equation estimation methods have some desirable asymptotic properties and these properties become effective in large samples. This study is relevant since samples available to researchers are mostly small in practice and are often plagued with the problem of mutual correlation between pairs of random deviates which is a violation of the assumption of mutual independence between pairs of such random deviates. The objective of this research was to study the small sample properties of these estimators when the errors are correlated to determine if the properties will still hold when available samples are relatively small and the errors were correlated. Approach: Most of the evidence on the small sample properties of the simultaneous equation estimators was studied from sampling (or Monte Carlo) experiments. It is important to rank estimators on the merit they have when applied to small samples. This study examined the performances of five simultaneous estimation techniques using some of the basic characteristics of the sampling distributions rather than their full description. The characteristics considered here are the mean, the total absolute bias and the root mean square error. Results: The result revealed that the ranking of the five estimators in respect of the Average Total Absolute Bias (ATAB) is invariant to the choice of the upper (P₁) or lower (P₂) triangular matrix. The result of the FIML using RMSE of estimates was outstandingly best in the open-ended intervals and outstandingly poor in the closed interval (-0.05<0.05) when P₁ and P₂ was re-combined. Conclusion: (i) The ranking of the various simultaneous estimation methods considered based on their small sample properties differs according to the correlation status of the error term, the identifiability status of the equation and the assumed triangular matrix. (ii) The nature of the relationship under study also determined which of the criteria for judging the performances of the estimators could be said to perform best when compared with others.