Working Paper

Abstract

This paper studies the asymptotic power for the sphericity test in a fixed effect panel data model proposed by Professors Badi H. Baltagi, Fa Feng and Chihwa Kao (2011), (JBFK). This is done under the alternative hypotheses of weak and strong factors. By weak factors, we mean that the Euclidean norm of the vector of the factor loadings is O(1). By strong factors, the authors mean that the Euclidean norm of the vector of factor loadings is O(pn), where n is the number of individuals in the panel. To derive the limiting distribution of JBFK under the alternative, the authors first derive the limiting distribution of its raw data counterpart. Their results show that, when the factor is strong, the test statistic diverges in probability to infinity as fast as Op(nT). However, when the factor is weak, its limiting distribution is a rightward mean shift of the limit distribution under the null. Second, the authors derive the asymptotic behavior of the difference between JBFK and its raw data counterpart. Our results show that when the factor is strong this difference is as large as Op(n). In contrast, when the factor is weak, this difference converges in probability to a constant. Taken together, these results imply that when the factor is strong, JBFK is consistent, but when the factor is weak, JBFK is inconsistent even though its asymptotic power is nontrivial.