Ranking of simultaneous equation estimators to outliers from heavy-tailed quasi-uniform distribution

Abstract

In this work, the ranking of the performances of two-equation simultaneous models when outliers are presumed present in a convoluted exogenous variable is carried out. The exogenous variable is a convolution of normal and uniform distribution. Monte Carlo experiment was carried out to investigate the performances of four estimators namely: Ordinary Least Squares (OLS), Two Stage Least Squares (2SLS), Limited Information Maximum Likelihood (LIML) and Three Stage Least Squares (3SLS). Five sample sizes were used to allow for measure of asymptotic properties of these estimators. The experiment was replicated 1000 limes and the results were evaluated using Total Absolute Bias (TAB), Variance and Root Mean Squared Error (RMSE). It is observed that the performances of the estimators when lower triangular matrix is used are better than that of upper triangular matrix. OLS using TAB as evaluation criterion is better than the other estimators when an exogenous variable is convoluted for the just-identified equation. The performance of 2SLS is best for the over-identified equation. OLS possesses the least variance for both equations and both matrices while LIML has the worst variance in most crises. OLS possesses the smallest RMSE for both matrices and equations except with the over-identified equation using lower triangular matrix when an exogenous variable is convoluted