Page 277 - Contributed Paper Session (CPS) - Volume 4

CPS2224 Habshah Midi et al.

The robustness of two step estimation
against heteroskedasticity and outliers in
panel data
1,2
1
Habshah Midi , Nor Mazlina Abu Bakar
1 Institute of Mathematical Research, Universiti Putra Malaysia
2 Centre of Management Sciences, Faculty of Economics and Management Sciences,
Universiti Sultan Zainal Abidin, Terengganu, Malaysia.

Abstract
Robust methods in the literature are mainly proposed to withstand
heteroscedasticity or outlying values separately. However, when abnormal
data or outliers are present together with heteroskedasticity, two important
least square assumptions are simultaneously violated and requires immediate
solutions. In this study, Two Step Heteroscedasticity- and Outlier-robust or
TSHO is proposed to withstand the influence of outliers and at the same time
able to counter the heteroskedastic condition. TSHO assigned lower weights
to outlying observations and able to produce more reliable fixed effect
estimates than existing methods. This is confirmed by empirical evidence
provided in the study via application on numerical data.

Keywords
panel data; heteroscedasticity, outliers; robust

1. Introduction
Robustness with respect to outliers is widely discussed for non-panel data
regression where a large body of literature can be found in estimating robust
parameters. On the contrary, robustness in the econometric literature is
mainly discussed with respect to heteroskedasticity. Very little attention is
given in developing robust estimators against outliers for panel data
regression in the presence of heteroskedasticity. Feasible Generalized Least
Square or FGLS is the conventional method used to protect against the effects
of heteroskedasticity for fixed effect panel data model (Stock and Watson,
2008). In the presence of heteroskedastic errors, regression using Feasible
Generalized Least Squares (FGLS) offers potential efficiency gains over
Ordinary Least Squares (OLS) (Miller and Startz, 2018). However, the method
is a modified version of OLS and very much affected towards outliers. Bias
values will be produced and hence, the breakdown of FGLS. To the best of
our knowledge, a study regarding both problems of heteroskedasticity and
outlying values in panel data is non-existent. Thus, this study is considered to
be among the first (if not the first) in solving simultaneous problems of
heteroskedastic and non-normal errors. Therefore, this study is carried
forward to achieve two main objectives. The first objective is to propose Two

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