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

In this article, we consider the properties of the Pesaran 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 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 for both the classical two-way fixed-effects estimator and the Common Correlated Effects estimator of Pesaran. 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.

Automated summary

In this article, we examine the properties of the Pesaran CD test when applied to residuals from panel data models with many estimated parameters. We find that the CD test statistic diverges as the time dimension of the sample grows due to the presence of period-specific parameters, even if cross-section dependence is correctly considered. We propose a weighted CD test statistic to restore standard normal inference under the null hypothesis.