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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

    (CESAER - Centre d'Economie et de Sociologie Rurales Appliquées à l'Agriculture et aux Espaces Ruraux - UBFC - Université Bourgogne Franche-Comté [COMUE] - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Dijon - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

  • Marc-Alexandre Sénégas

    (UB - Université de Bordeaux, BSE - Bordeaux sciences économiques - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

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," Post-Print hal-04278648, HAL.
    • Handle: RePEc:hal:journl:hal-04278648
    DOI: 10.3390/econometrics11040025
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    References listed on IDEAS

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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. 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.
    3. 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.
    4. 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).
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