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Asymptotic Power of the Sphericity Test Under Weak and Strong Factors in a Fixed Effects Panel Data Model

Badi Baltagi (), Chihwa Kao () and Fa Wang ()
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Fa Wang: Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244

No 189, Center for Policy Research Working Papers from Center for Policy Research, Maxwell School, Syracuse University

Abstract: This paper studies the asymptotic power for the sphericity test in a fixed effect panel data model proposed by Baltagi, Feng and 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, we 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, we first derive the limiting distribution of its raw data counterpart. Our 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, we 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.

Keywords: Asymptotic power; Sphericity; John Test; Weak Factor; Strong Factor; High Dimensional Inference; Panel Data (search for similar items in EconPapers)
JEL-codes: C12 C33 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2016-03
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Journal Article: Asymptotic power of the sphericity test under weak and strong factors in a fixed effects panel data model (2017) Downloads
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