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Asymptotic power of the sphericity test under weak and strong factors in a fixed effects panel data model

Baltagi, B. H., Kao, C. and Wang, F. (2017). Asymptotic power of the sphericity test under weak and strong factors in a fixed effects panel data model. Econometric Reviews, 36(6-9), pp. 853-882. doi: 10.1080/07474938.2017.1307580

Abstract

This paper studies the asymptotic power for the sphericity test in a Öxed e§ect 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(√n), where n is the number of individuals in the panel. To derive the limiting distribution of JBFK under the alternative, we Örst 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 inÖnity 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 di§erence 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 di§erence 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.

Publication Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Econometric Reviews on 24 Mar 2017, available online: http://www.tandfonline.com/10.1080/07474938.2017.1307580.
Publisher Keywords: Asymptotic power, high dimensional inference, John test, panel data, sphericity, strong factor, weak factor
Subjects: H Social Sciences > HB Economic Theory
Departments: Cass Business School > Finance
URI: http://openaccess.city.ac.uk/id/eprint/20450
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