Investigation of Finite Sample Properties and Efficiency of Some Estimators for Panel Data Model with Normal and Non-Normal Error Structure

Abstract

The study investigates efficiency of some estimators for panel data model
with non-normal error structure and varying sample sizes. It considers
one-stage and two-stage error component models with three exogenous
and one endogenous variable. The efficiency of four estimators of panel
data model based on one-step and two-step error component models across
varying finite samples were investigated under normal and non-normal
error structures. The data set used for the panel linear model (PLM) and
the general feasible generalized least squares (GFGLS) model for
investigating efficiency of the four estimators in this study were simulated
using R software. Three predictors were simulated from normal
distributions at the various samples sizes and variances. The error
structures were simulated from Gaussian distribution with mean 0 and
variance 1 and Exponential distribution with lambda 1 in the plm library
of the R software. The four estimators were utilized to estimate the fixed
parameters that form the models and their efficiencies were assessed based
on absolute bias, coefficient of multiple determination and root mean
square error (RMSE) of parameter estimates. The results of the study
indicated that the Within Ordinary Least Squares (WOLS) estimator is
the most stable and most efficient estimator of panel data model parameters
than the Pooling, Between (BTW) and the First Difference (FD)
estimators with both one-stage and two-stage normal and non-normal
error structures. It is evident from this study that the four estimators
have increasing and the FD estimator is the next most stable while
both pooling and BTW are worse but pooling is more stable under varying
samples sizes (dimension).