Panel Data Estimators in the Presence of Quadratic and Exponential Functional Forms of Heteroscedasticity

Abstract

The problem of heteroscedasticity in panel data has been widely discussed in literature and has continued to attract
the attention of researchers particularly in applied econometrics. In this study, we explore two functional forms of
heteroscedasticity: Quadratic Heteroscedasticity Functional Form (QHFF) and Exponential Heteroscedasticity
Functional Form (EHFF) in a random error component model. We use one-way error component model to evaluate
these two forms of heteroscedasticity on individual effect of one error components model. In this paper, we design a
Monte Carlo experiment to investigate the relative sensitivity of the following estimators: Pooled Ordinary Least
Square (POLS), Between Group (BG), Within Group (WG) and Panel Generalize Least Square (PGLS) estimators,
in the presence QHFF and EHFF on individual effect. The Monte Carlo experiments follow closely that of [1] and
[2]. Using purposedly cross-sectional units, N ?10,30,50
and time periods T ? 5,15,20 and replication of 2500 for
various combinations of N and T dataset were generated. R Version 2.15.2 Statistical software is used for our
analyses. The relative performances of these estimators were assessed using Bias (BIAS) and Root Mean Squared
Error (RMSE). The estimators were then ranked according to their performances. The performance of estimators in
the presence QHFF and EHFF were investigated under the finite sampling properties of Bias and RMSE, for the two
experiments set up and estimators were ranked as follows in ascending order of their performances: PGLS, BG, WG
and POLS. This result will helps in the choice of estimator in empirical work when there is presence of
heteroscedasticity.