Document Type

Working Paper

Date

Spring 3-2016

Keywords

Asymptotic power, Sphericity, John Test, Weak Factor, Strong Factor, High Dimensional Inference, Panel Data

Language

English

Disciplines

Econometrics | Economic Policy | Economics | Public Affairs, Public Policy and Public Administration

Description/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.

ISSN

1525-3066

Additional Information

Working paper no. 189

The authors dedicate this paper in honor of Esfandiar Maasoumi’s many contributions to econometrics. We would like to thank the editors Aman Ullah and Peter Phillips and two anonymous referees for useful comments and suggestions.

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Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

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