Paul Johnson, Steven Durlauf and Jonathan Temple 1163test statistic is based on earlier work by Breusch and Pagan (1980) and appears to
possess good finite sample properties in comparison to this earlier work. Using a
country-level panel, Pesaran (2004) strongly rejects the null of no cross-section
dependence for the world as a whole, and within several geographic groupings.
The CD test need not be consistent for some alternatives of interest, however.
With this in mind, Pesaran, Ullah and Yamagata (2008) develop a bias-adjusted
version of the Breusch and Pagan Lagrange multiplier (LM) test statistic for cross-
section error independence, for panels with strictly exogenous regressors and
normally distributed errors. This approach retains some power in some circum-
stances where the CD test does not, but is less robust to departures from normality
and the presence of regressors that are only weakly exogenous.
The second strand of research on cross-section error dependence has constructed
empirical models that take it explicitly into account. One approach relies on for-
mulating a statistical model of the dependence. Phillips and Sul (2003) model the
error term in a growth panel as:
εi,t=δiθt+ui,t, (24.39)whereθtandui,tare independent random variables andui,tis assumed to be i.i.d.
across countries and across time. Pesaran (2006) develops an alternative estimation
strategy based on a generalized form of this error structure, one in whichθtmay be
a vector. While Phillips and Sul consider how to account for error dependence in a
generalized least squares (GLS)-type structure, Pesaran considers ways to filter the
individual observations in order to eliminate the dependence. From the perspective
of growth dynamics, (24.39) suffers from the problem that it does not account for
aspects of the error process associated with growth. In order to account for cross-
section dependence in convergence analysis, Phillips and Sul (2007a, 2007b) study
the case whereδiis replaced withδi,tin (24.39), arguing that transition dynamics
produce time varying coefficients of this type as less advanced economies catch up
to more advanced ones.
Another possibility when analyzing error dependence is to treat the problem as
one of spatial correlation. This issue has been much studied in the regional science
literature, and statisticians in this field have developed spatial analogues of many
time series concepts (see Anselin, 2001, 2006, for an overview). Spatial methods
may yet have an important role to play in growth econometrics. However, when
these methods are adapted from the spatial statistics literature, they raise the prob-
lem of identifying the appropriate notion of space. One can imagine many reasons
for cross-section correlation. If one is interested in technological spillovers, it may
well be the case that in the space of technological proximity, the United King-
dom is closer to the United States than is Mexico. Put differently, unlike the time
series and spatial cases, there is no natural cross-section ordering to elements in the
standard growth datasets. Following language due to Akerlof (1997), countries are
perhaps best thought of as occupying some general socioeconomic-political space
defined by a range of factors; spatial methods then require a means to identify their
locations.