# 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*

*Econometric Reviews*, 2017, vol. 36, issue 6-9, 853-882

**Abstract:**
This paper studies the asymptotic power for the sphericity test in a fixed effect panel data model proposed by Baltagi et al. (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 \begin{equation}O(\sqrt{n})\end{equation}O(n), 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.

**Date:** 2017

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

http://hdl.handle.net/10.1080/07474938.2017.1307580 (text/html)

Access to full text is restricted to subscribers.

**Related works:**

Working Paper: Asymptotic Power of the Sphericity Test Under Weak and Strong Factors in a Fixed Effects Panel Data Model (2016)

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:853-882

**Ordering information:** This journal article can be ordered from

http://www.tandfonline.com/pricing/journal/LECR20

Access Statistics for this article

Econometric Reviews is currently edited by *Dr. Essie Maasoumi*

More articles in Econometric Reviews from Taylor & Francis Journals

Bibliographic data for series maintained by ().