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.
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
Series
Working Papers Series
Disciplines
Econometrics | Economic Policy | Economics | Public Affairs, Public Policy and Public Administration
ISSN
1525-3066
Recommended Citation
Baltagi, Badi H.; Kao, Chihwa; and Wang, Fa, "Asymptotic Power of the Sphericity Test Under Weak and Strong Factors in a Fixed Effects Panel Data Model" (2016). Center for Policy Research. 218.
https://surface.syr.edu/cpr/218
Accessible PDF version
Source
Local input
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
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.