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

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.

wp189.pdf (862 kB)
Accessible PDF version

Source

Local input

Creative Commons License

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

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.