A Principal Components Approach to Cross-Section Dependence in Panels



1 Introduction

In the panel time-series literature, where both the number of groups, N,
and the number of time periods T are both large, it is usual to assume
the absence of cross section dependence or uncorrelated disturbances across
groups. This seems restrictive for many applications in macroeconomics and
finance and neglecting it may be far from innocuous for empirical issues such
as purchasing power parity (PPP) or whether real exchange rates display
reversion towards a long run value (Bai and Ng 2001a; O’Connell 1998; Moon
and Perron 2001; Pedroni 1997).1 In addition, many theoretical panel results
have been derived under the assumption of cross section independence (
Baltagi and Kao 2000; Phillips and Moon 2000). As Phillips and Moon
(1999: p1092) put it “... quite commonly in panel data theory, cross section
independence is assumed in part because of the di
fficulties of characterizing
and modelling cross section dependence.”

In the presence of cross section dependence, traditional OLS-based esti-
mators are ine
fficient and the estimated standard errors are biased producing
misleading inference. The traditional remedy, SURE-GLS, is not however
feasible when the cross section dimension
N is of the same order of mag-
nitude as the time series dimension
T because the disturbance covariance
matrix is rank de
ficient. Robertson and Symons (1999) propose an innova-
tive method in this context which imposes a factor structure on the residuals
to provide a full-rank estimator of the covariance matrix. However, when
the non-zero covariances between the errors of di
fferent cross section units
are due to common omitted variables, it is not obvious that SURE-GLS is
always the correct response. If these common omitted variables — say oil
prices or global political events in the case where the units are countries —
are correlated with the country-speci
fic regressors, both traditional pooled
estimators and GLS estimators will be biased and inconsistent. If there is just
one common omitted variable to which all cross-section units react homoge-
neously and if the slope parameters in the model are identical across units,
then a two-way
fixed effects (FE) estimator may be appropriate. However
these conditions are very restrictive.

This paper, in common with a number of recent contributions in panel

1 While Banerjee, Marcellino and Osbat (2001) do not examine PPP directly, their
discussion of the issue of cross unit cointegrating relations is also germane to this debate.
Pedroni (1997) also stresses long run cross section dependence.



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