A method for evaluating the rank condition for CCE estimators

This paper proposes a binary classifier to evaluate the so-called rank condition (RC), which is required for consistency of the Common Correlated Effects (CCE) estimator of Pesaran (2006). The RC postulates that the number of unobserved factors, m, is not larger than the rank of the unobserved matrix of average factor loadings, rho. When this condition fails, the CCE estimator is generally inconsistent. Despite the obvious importance of the RC, to date this condition could not be verified. The difficulty lies in that since the factor loadings are unobserved, rho cannot be evaluated or estimated directly. The key insight in the present paper is that rho can be established from the rank of the matrix of cross-sectional averages of observables. As a result, rho can be estimated consistently using procedures already available for determining the true rank of an unknown matrix. Similarly, m can be estimated consistently from the data using existing methods. A binary classifier that evaluates the RC is constructed by comparing the estimates of m and rho. The classifier correctly determines whether the RC is satisfied or not, with probability 1 as (N,T) grow to infinity.