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On the consistency of the logistic quasi-MLE under conditional symmetry

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  • Wooldridge, Jeffrey M.

Abstract

For estimating the parameters of a linear conditional mean, I show that the quasi-maximum likelihood estimator (QMLE) obtained under the nominal assumption that the error term is independent of the explanatory variables with a logistic distribution is consistent provided the conditional distribution of the error term is symmetric. No other restrictions are required for Fisher consistency; in particular, the error and covariates need not be independent, and so general heteroskedasticity of unknown form is allowed. Importantly, the influence function of the logistic quasi-log likelihood is bounded, making it more resilient to outliers than ordinary least squares. Inference using the logistic QMLE is straightforward using a robust asymptotic variance–covariance matrix estimator.

Suggested Citation

  • Wooldridge, Jeffrey M., 2020. "On the consistency of the logistic quasi-MLE under conditional symmetry," Economics Letters, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:ecolet:v:194:y:2020:i:c:s0165176520302317
    DOI: 10.1016/j.econlet.2020.109363
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    References listed on IDEAS

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    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    3. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    4. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    More about this item

    Keywords

    Quasi-maximum likelihood estimation; Logistic distribution; Robust estimation; Influence function; Robust variance–covariance matrix; Outlier;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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