1162 The Methods of Growth Econometrics
errors are consistent but not unbiased, which suggests that alternative solutions to
the problem may be desirable. For datasets of the size found in cross-country empir-
ical work, the alternative estimators developed by MacKinnon and White (1985)
are likely to have better finite sample properties, as discussed in Davidson and
MacKinnon (1993) and supported by simulations in Long and Ervin (2000).
There are at least two other concerns with the routine application of White’s
heteroskedasticity correction as the only response to heteroskedasticity. The first is
that by exploiting any structure in the variance of the disturbances, using weighted
least squares, it may be possible to obtain efficiency gains. The second and more
fundamental objection is that heteroskedasticity can often arise from serious model
misspecification, such as omitted variables or neglected parameter heterogeneity.
Evidence of heteroskedasticity should then prompt revisions of the model for the
conditional mean, rather than mechanical adjustments to the standard errors. See
Zietz (2001) for further discussion and references.
24.7.5 Cross-section error dependence
An unresolved issue in growth econometrics is the treatment of cross-section
dependence in model errors. This dependence may have important consequences
for inference. As noted by DeLong and Summers (1991) in the growth context,
failure to account for cross-sectional error correlation can lead to inaccurate stan-
dard errors. Furthermore, there are several reasons to expect cross-sectional error
dependence to be present when studying growth. For example, countries that
are geographically close together, or trading partners, may well experience com-
mon shocks. Output growth may often be related to the growth of large, leading
countries within a particular region or world.
The general issue of error dependence has been a focus of recent research, in the
context of panel data and panel time series estimators in particular. Whether the
effect of dependence is sizeable in practice remains an open question, but one that
might be addressed using ideas developed in Baltagi, Song and Koh (2003) and
Driscoll and Kraay (1998), among others.
In the context of growth regressions, work on cross-section dependence may
be divided into two strands. One concerns tests to identify the presence of cross-
section dependence. Pesaran (2004) develops tests that do not rely on any prior
ordering; this framework in essence sums the cross-section sample error correla-
tions in a panel and evaluates whether they are consistent with the null hypothesis
that the population correlations are zero. Specifically, and recalling thatNdenotes
the cross-section dimension andTthe time dimension, he proposes a cross-section
dependence statisticCD:
CD=√
2 TN(N− (^1) )
⎛
⎝
N∑− 1
i= 1
∑N
j=i+ 1
ρˆi,j
⎞
⎠, (24.38)
whereρˆi,jis the sample correlation betweenεi,tandεj,t. Pesaran gives conditions
under which this statistic converges to a Normal (0,1) random variable (asNand
Tbecome infinite) under the null hypothesis of no cross-section correlation. This