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A simple, robust test for choosing the level of fixed effects in linear panel data models

Author

Listed:
  • Leslie E. Papke

    (Michigan State University)

  • Jeffrey M. Wooldridge

    (Michigan State University)

Abstract

For the panel data case where cross-sectional units are nested within higher-level groups, and there are many such groups, we propose a test that allows one to determine whether controlling for fixed effects at the more aggregate level is sufficient. The alternative is that one should allow for fixed effects at the unit level. The regression-based test is simple to carry out, even for unbalanced panels. In addition, the test is easily made robust to arbitrary heteroskedasticity, serial correlation across time, and even cluster correlation at the group level. We also show how to modify the traditional Hausman test of a single coefficient to be fully robust to serial correlation and cluster correlation. The tests work well in terms of size and power in a small simulation study. We apply the test to choosing between a fixed effects analysis at the school district level and the disaggregated school level.

Suggested Citation

  • Leslie E. Papke & Jeffrey M. Wooldridge, 2023. "A simple, robust test for choosing the level of fixed effects in linear panel data models," Empirical Economics, Springer, vol. 64(6), pages 2683-2701, June.
    • Handle: RePEc:spr:empeco:v:64:y:2023:i:6:d:10.1007_s00181-022-02337-y
    DOI: 10.1007/s00181-022-02337-y
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    References listed on IDEAS

    as
    1. Wooldridge, Jeffrey M., 2019. "Correlated random effects models with unbalanced panels," Journal of Econometrics, Elsevier, vol. 211(1), pages 137-150.
    2. Hausman, Jerry A & Taylor, William E, 1981. "Panel Data and Unobservable Individual Effects," Econometrica, Econometric Society, vol. 49(6), pages 1377-1398, November.
    3. Alberto Abadie & Susan Athey & Guido W Imbens & Jeffrey M Wooldridge, 2023. "When Should You Adjust Standard Errors for Clustering?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(1), pages 1-35.
    4. Papke, Leslie E. & Wooldridge, Jeffrey M., 2008. "Panel data methods for fractional response variables with an application to test pass rates," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 121-133, July.
    5. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    6. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    7. Papke, Leslie E., 2005. "The effects of spending on test pass rates: evidence from Michigan," Journal of Public Economics, Elsevier, vol. 89(5-6), pages 821-839, June.
    8. Jeffrey M. Wooldridge, 2003. "Cluster-Sample Methods in Applied Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 133-138, May.
    9. Riju Joshi & Jeffrey M. Wooldridge, 2019. "Correlated Random Effects Models with Endogenous Explanatory Variables and Unbalanced Panels," Annals of Economics and Statistics, GENES, issue 134, pages 243-268.
    10. Guggenberger, Patrik, 2010. "The impact of a Hausman pretest on the size of a hypothesis test: The panel data case," Journal of Econometrics, Elsevier, vol. 156(2), pages 337-343, June.
    11. Guggenberger, Patrik, 2010. "The Impact Of A Hausman Pretest On The Asymptotic Size Of A Hypothesis Test," Econometric Theory, Cambridge University Press, vol. 26(2), pages 369-382, April.
    12. Yang, Yimin & Schmidt, Peter, 2021. "An econometric approach to the estimation of multi-level models," Journal of Econometrics, Elsevier, vol. 220(2), pages 532-543.
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    Cited by:

    1. Claudia Pigini & Alessandro Pionati & Francesco Valentini, 2023. "Specification testing with grouped fixed effects," Papers 2310.01950, arXiv.org.

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    More about this item

    Keywords

    Panel data; Fixed effects; Correlated random effects; Hausman test;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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