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

TL;DR

This paper demonstrates that the Pesaran CD test for cross-section correlation diverges when applied to residuals from panel data models with many estimated parameters, due to the incidental parameters problem, affecting empirical testing.

Contribution

It reveals the incidental parameters problem in the Pesaran CD test and proposes a weighted version to restore valid inference in panel data models with many parameters.

Findings

Standard CD test diverges with many parameters

Weighted CD test restores normal inference

Implications for empirical cross-section dependence testing

Abstract

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.