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In this paper we consider the properties of the Pesaran (2004, 2015a) CD testfor cross-section correlation when applied to residuals obtained from paneldata models with many estimated parameters. We show that the presence ofperiod-specific parameters leads the CD test statistic to diverge as length ofthe time dimension of the sample grows. This result holds even if cross-sectiondependence is correctly accounted for and hence constitutes an example of theIncidental Parameters Problem. The relevance of this problem is investigatedboth for the classical Time Fixed Effects estimator as well as the CommonCorrelated Effects estimator of Pesaran (2006). We suggest a weighted CD teststatistic which re-establishes standard normal inference under the nullhypothesis. Given the widespread use of the CD test statistic to test forremaining cross-section correlation, our results have far reaching implicationsfor empirical researchers.

The Incidental Parameters Problem in Testing for Remaining Cross-section Correlation