© 2017 The Department of Economics, University of Oxford and John Wiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 80, 2 (2018) 0305–9049
To Pool or Not to Pool: Revisited*
M. Hashem Pesaran† and Qiankun Zhou‡
†Department of Economics, USC Dornsife INET, University of Southern California, and
Trinity College, Cambridge, UK (e-mail: firstname.lastname@example.org)
‡Department of Economics, Lousiana State University, Baton Rouge, LA, 70803,
USA (e-mail: email@example.com)
This paper provides a new comparative analysis of pooled least squares and ﬁxed effects
(FE) estimators of the slope coefﬁcients in the case of panel data models when the time
dimension (T) is ﬁxed while the cross section dimension (N ) is allowed to increase without
bounds. The individual effects are allowed to be correlated with the regressors, and the
comparison is carried out in terms of an exponent coefﬁcient, , which measures the degree
of pervasiveness of the FE in the panel. The use of allows us to distinguish between
poolability of small N dimensional panels with large T from large N dimensional panels
with small T . It is shown that the pooled estimator remains consistent so long as < 1, and
is asymptotically normally distributed if < 1/ 2, for a ﬁxed T and as N →∞. It is further
shown that when < 1/ 2, the pooled estimator is more efﬁcient than the FE estimator. We
also propose a Hausman type diagnostic test of < 1/ 2 as a simple test of poolability, and
propose a pretest estimator that could be used in practice. Monte Carlo evidence supports
the main theoretical ﬁndings and gives some indications of gains to be made from pooling
when < 1/ 2.
This paper re-examines the issue of pooling in standard panel data models with exogenous
regressors in terms of an exponent coefﬁcient, 0
1, which measures the degree of
pervasiveness of correlated individual effects, deﬁned by
where N is the cross-section dimension of the panel, and
is the mean zero random part of
the individual effects. The use of exponent allows us to distinguish between poolability
of small N dimensional panels with large T from large N dimensional panels with small
T . A set of coefﬁcients could be heterogeneous for a ﬁnite N , nevertheless can be deemed
JEL Classiﬁcation numbers: C01, C23, C33.
*We thank the editor, two anonymous referees, Ron Smith and Carlos Lamarche for helpful comments.