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On the Proper Computation of the Hausman Test Statistic in Standard Linear Panel Data Models: Some Clarifications and New Results

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  • Julie Le Gallo

    (Center of Economics and Sociology Applied to Rural Areas, UMR1041, l’Institut Agro Dijon, INRAE, University Bourgogne Franche-Comté, 21000 Dijon, France
    These authors contributed equally to this work.)

  • Marc-Alexandre Sénégas

    (Bordeaux School of Economics, UMR CNRS6060, University of Bordeaux, 33000 Bordeaux, France
    These authors contributed equally to this work.)

Abstract

We provide new analytical results for the implementation of the Hausman specification test statistic in a standard panel data model, comparing the version based on the estimators computed from the untransformed random effects model specification under Feasible Generalized Least Squares and the one computed from the quasi-demeaned model estimated by Ordinary Least Squares. We show that the quasi-demeaned model cannot provide a reliable magnitude when implementing the Hausman test in a finite sample setting, although it is the most common approach used to produce the test statistic in econometric software. The difference between the Hausman statistics computed under the two methods can be substantial and even lead to opposite conclusions for the test of orthogonality between the regressors and the individual-specific effects. Furthermore, this difference remains important even with large cross-sectional dimensions as it mainly depends on the within-between structure of the regressors and on the presence of a significant correlation between the individual effects and the covariates in the data. We propose to supplement the test outcomes that are provided in the main econometric software packages with some metrics to address the issue at hand.

Suggested Citation

  • Julie Le Gallo & Marc-Alexandre Sénégas, 2023. "On the Proper Computation of the Hausman Test Statistic in Standard Linear Panel Data Models: Some Clarifications and New Results," Econometrics, MDPI, vol. 11(4), pages 1-28, November.
    • Handle: RePEc:gam:jecnmx:v:11:y:2023:i:4:p:25-:d:1276565
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    1. Arellano, Manuel, 1993. "On the testing of correlated effects with panel data," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 87-97, September.
    2. Álvarez, Inmaculada C. & Barbero, Javier & Zofío, José L., 2017. "A Panel Data Toolbox for MATLAB," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i06).
    3. 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.
    4. Swamy, P A V B & Arora, S S, 1972. "The Exact Finite Sample Properties of the Estimators of Coefficients in the Error Components Regression Models," Econometrica, Econometric Society, vol. 40(2), pages 261-275, March.
    5. Fuller, Wayne A. & Battese, George E., 1974. "Estimation of linear models with crossed-error structure," Journal of Econometrics, Elsevier, vol. 2(1), pages 67-78, May.
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