  In this paper we consider the properties of the Pesaran (2004, 2015a) CD test
for cross-section correlation when applied to residuals obtained from panel
data models with many estimated parameters. We show that the presence of
period-specific parameters leads the CD test statistic to diverge as length of
the time dimension of the sample grows. This result holds even if cross-section
dependence is correctly accounted for and hence constitutes an example of the
Incidental Parameters Problem. The relevance of this problem is investigated
both for the classical Time Fixed Effects estimator as well as the Common
Correlated Effects estimator of Pesaran (2006). We suggest a weighted CD test
statistic which re-establishes standard normal inference under the null
hypothesis. Given the widespread use of the CD test statistic to test for
remaining cross-section correlation, our results have far reaching implications
for empirical researchers.
