A Principal Components Approach to Cross-Section Dependence in Panels

methods, employs a factor analysis framework.² Suppose the parameters of
interest are a set of slope coefficients in a baseline regression (RI), the es-
timates of which will be biased and inconsistent if there are omitted global
variables correlated with each country regressor. We propose extracting the
largest factors of the RI residuals as proxies for the global unobservable vari-
ables. These factors are then included in an augmented regression (RII) to
seek to reduce the bias in the RI coefficient estimators. Established panel
estimators such as the pooled OLS (POLS), fixed effects (FE) or the Pesaran
and Smith (1995) mean group (MG) procedures can be used in each stage.
We show analytically for a simple DGP that the POLS estimator of the RII
slope coefficient has substantially smaller bias than that from the baseline
regression. In addition, it is shown to be consistent using sequential limit
asymptotics, as T converges to infinity with a fixed N and then N converges
to infinity.

This suggests that the proposed method is especially suited to many large
dimension datasets typically used for macroeconomic and financial analysis.
This is confirmed by Monte Carlo simulations for the finite sample perfor-
mance of the method and the choice of the number of factors included. The
bias reduction is confirmed using panel dimensions typical of annual and
monthly PPP datasets. Simulations show that information criteria based
on Bai and Ng (2002) are quite accurate in our context where the factors
are extracted from estimated disturbances rather than observed variables.
Finally when the method is applied to a PPP data set there is evidence of
cross section dependence and handling it with the proposed method seems
to reinforce the support for PPP. Throughout this paper we assume that the
omitted variables are I(0) and that the regressors and dependent variable are
either I(0) or cointegrate. The interesting case of an I(1) omitted variable is
a topic for further research.

The proposed estimation method is outlined in §2 and theoretical results
for a simple case are given in §3. The Monte Carlo simulations are pre-
sented in §4 and an empirical PPP application follows in §5. A final section
concludes.

² Factor structures for panels are used by Hall, Lazarova and Urga (1999) to test for the
number of common stochastic trends and by Bai and Ng (2001a,b) and Moon and Perron
(2001) to test for unit roots and cointegration.

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