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Asymptotic Power of the Sphericity Test Under Weak and Strong Factors in a Fixed Effects Panel Data Model

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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.

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  • Badi Baltagi & Chihwa Kao & Fa wang, 2016. "Asymptotic Power of the Sphericity Test Under Weak and Strong Factors in a Fixed Effects Panel Data Model," Center for Policy Research Working Papers 189, Center for Policy Research, Maxwell School, Syracuse University.
  • Handle: RePEc:max:cprwps:189
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    Cited by:

    1. Peng, Bin & Shen, Xinyuan & Ye, Jinqi, 2019. "Testing for sphericity in a fixed effects panel data model with time-varying variances," Economics Letters, Elsevier, vol. 181(C), pages 85-89.
    2. Zhaoyuan Li & Jianfeng Yao, 2021. "Extension of the Lagrange multiplier test for error cross-section independence to large panels with non normal errors," Papers 2103.06075, arXiv.org.

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    More about this item

    Keywords

    Asymptotic power; Sphericity; John Test; Weak Factor; Strong Factor; High Dimensional Inference; Panel Data;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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