A method to evaluate the rank condition for CCE estimators

Abstract

Copyright © 2023 The Author(s). We develop a binary classifier to evaluate whether the rank condition (RC) is satisfied or not for the Common Correlated Effects (CCE) estimator. The RC postulates that the number of unobserved factors, m, is not larger than the rank of the unobserved matrix of average factor loadings, ϱ. When this condition fails, the CCE estimator is inconsistent, in general. Despite its importance, to date this rank condition could not be verified. The difficulty lies in the fact that factor loadings are unobserved, such that ϱ cannot be directly determined. The key insight in this article is that ϱ can be consistently estimated with existing techniques through the matrix of cross-sectional averages of the data. Similarly, m can be estimated consistently from the data using existing methods. Thus, a binary classifier, constructed by comparing estimates of m and ϱ, correctly determines whether the RC is satisfied or not as (N,T)→∞. We illustrate the practical relevance of testing the RC by studying the effect of the Dodd-Frank Act on bank profitability. The RC classifier reveals that the rank condition fails for a subperiod of the sample, in which case the estimated effect of bank size on profitability appears to be biased upwards.