ASSESSING THE PERFOMANCES OF SIMULTANEOUS EQUATION ESTIMATORS UNDER THE INFLUENCE OF OUTLIERS

Abstract

The real life data available to researchers are mostly small in practice and are often plagued with outliers. This study examined the performances of simultaneous equation estimators when outliers are present in the observations using Monte Carlo method. Four estimators were considered: Ordinary Least Squares (OLS), Two Stage Least Squares (2SLS), Limited Information Maximum Likelihood (LIML) and Three Stage Least Squares (3SLS). Outliers of various degrees (0%, 5% and 10%) were introduced into the observations of sample sizes n=20, 25 and 30. The experiment was replicated 1000 times for each of the sample sizes. The performances of the estimators were judged using total absolute bias (TAB), variance and root mean square error (RMSE). It was deduced that OLS is the most efficient estimator under the influence of outliers and also performed best under this condition using RMSE, though inconsistent. The performance of OLS using upper triangular matrix 1P was better than that of lower triangular matrix 2P . Using TAB as criterion for comparison, 2SLS and 3SLS (i.e. 2,3SLS) were the best estimators for the over-identified equations as they are consistent across sample sizes and posed the minimum TAB as level of contamination increases. The estimates obtained using 2 P for 2,3SLS were better than that obtained using 1P as were depicted by all criteria employed. 2,3SLS and LIML produced identical estimates for the just identified equation as both sample size and contamination level increases from n=20 to 30 and from 0% to 10% respectively. In most of the cases considered, LIML's performance was the poorest for both equations.