Investigating the Asymptotic Properties of Some Estimators for Panel Data Regression Model with Individual Effects

Abstract

The panel data models are becoming more common in relation to cross-section and time series models for innumerable present advantages, in addition to the computational advance that facilitated theirs utilization. A primary advantage of these models is the ability to control for time invariant omitted variables that may bias observed relationships. This paper considers estimation of linear panel data models with fixed effects and random effects when the equation of interest contains unobserved heterogeneity as well as endogenous explanatory variables. This paper examines the asymptotic properties of the two-stage least square (2SLS), generalized (GLS) estimators and the Hausman test for panel data models with large numbers of cross-section (N) and fixed time-series (T) observations. In particular, consistency and asymptotic normality of the two standard panel data estimators are studied. We find that both estimators are consistent and asymptotically normal and have different convergence rates dependent on the assumptions of the regressors and the remainder disturbances. The asymptotic Hausman statistic, which is essentially a distance measure between the two estimators, is well defined and asymptotically chi-square distributed under the random effects assumptions.