Large-N and Large-T Properties of Panel Data Estimators and the Hausman Test

Large-N and Large-T Properties of
Panel Data Estimators and the

Hausman Test*

Seung Chan Ahn^           Hyungsik Roger Moon

Department of Economics Department of Economics
Arizona State University University of Southern California

This Version: August 2001

Abstract

This paper examines the asymptotic properties of the popular within,
GLS estimators and the Hausman test for panel data models with both
large numbers of cross-section (N) and time-series (T) observations. The
model we consider includes the regressors with deterministic trends in
mean as well as time invariant regressors. If a time-varying regressor
is correlated with time invariant regressors, the time series of the time-
varying regressor is not ergodic. Our asymptotic results are obtained con-
sidering the dependence of such non-ergodic time-varying regressors. We
find that the within estimator is as efficient as the GLS estimator. Despite
this asymptotic equivalence, however, the Hausman statistic, which is es-
sentially a distance measure between the two estimators, is well defined
and asymptotically χ²-distributed under the random effects assumption.

* We would like to thank Geert Ridder for helpful discussions. We also appreciate the com-
ments of seminar participants at Arizona State University, the University of British Columbia,
and the University of California, Davis.

t Corresponding Author: Seung C. Ahn, Department of Economics, Arizona State Univer-
sity, Tempe, AZ 85287; tel) 480-965-6574; email) [email protected].

* The first author gratefully acknowledges the financial support of the College of Business
and Dean’s Council of 100 at Arizona State University, the Economic Club of Phoenix, and
the alumni of the College of Business.

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