Incidental Parameters Problem in Testing: A Case of Cross-section Dependence Tests with Common Components

In this paper we consider the properties of Pesaran (2004, 2015a) CD test for crosssection correlation when applied to residuals obtained from panel data models with many estimated parameters. We show that, if applied to test for the presence of remaining crosssection dependence in the residuals, the CD test will always reject the null hypothesis, even if residuals are obtained using a consistent estimator. We show that this result is valid both in the classical Fixed Effects estimator with early dummies, as well as the Common Correlated Effects estimator of Pesaran (2006), and as such is an example of the Incidental Parameters Problem. For the former estimator we propose a modified version of the test statistic, while for the CCE estimator there exists no easy fix. Given the widespread use of the CD test statistic, our results have far reaching implications for empirical researchers.