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Finite-Sample Properties of the Maximum Likelihood Estimator for the Binary Logit Model With Random Covariates

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Abstract

We examine the finite sample properties of the maximum likelihood estimator for the binary logit model with random covariates. Analytic expressions for the first-order bias and second-order mean squared error function for the maximum likelihood estimator in this model are derived, and we undertake some numerical evaluations to analyze and illustrate these analytic results for the single covariate case. For various data distributions, the bias of the estimator is signed the same as the covariate’s coefficient, and both the absolute bias and the mean squared errors increase symmetrically with the absolute value of that parameter. The behaviour of a bias-adjusted maximum likelihood estimator, constructed by subtracting the (maximum likelihood) estimator of the first-order bias from the original estimator, is examined in a Monte Carlo experiment. This bias-correction is effective in all of the cases considered, and is recommended when the logit model is estimated by maximum likelihood with small samples.

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  • Qian Chen & David E. Giles, 2009. "Finite-Sample Properties of the Maximum Likelihood Estimator for the Binary Logit Model With Random Covariates," Econometrics Working Papers 0906, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0906
    Note: ISSN 1485-6441
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    1. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    2. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    3. M. Menéndez & L. Pardo & M. Pardo, 2009. "Preliminary phi-divergence test estimators for linear restrictions in a logistic regression model," Statistical Papers, Springer, vol. 50(2), pages 277-300, March.
    4. Hughes, Gordon A. & Savin, N. E., 1994. "Is the minimum chi-square estimator the winner in logit regression?," Journal of Econometrics, Elsevier, vol. 61(2), pages 345-366, April.
    5. Joachim Wilde, 2008. "A note on GMM estimation of probit models with endogenous regressors," Statistical Papers, Springer, vol. 49(3), pages 471-484, July.
    6. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
    7. Qian Chen & David E. Giles, 2009. "Finite-Sample Properties of the Maximum Likelihood Estimator for the Poisson Regression Model With Random Covariates," Econometrics Working Papers 0907, Department of Economics, University of Victoria.
    8. Gourieroux, Christian & Monfort, Alain, 1981. "Asymptotic properties of the maximum likelihood estimator in dichotomous logit models," Journal of Econometrics, Elsevier, vol. 17(1), pages 83-97, September.
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    Cited by:

    1. David E. Giles & Hui Feng, 2009. "Almost Unbiased Estimation of the Poisson Regression Model," Econometrics Working Papers 0909, Department of Economics, University of Victoria.
    2. Paul Rilstone, 2021. "Higher-Order Stochastic Expansions and Approximate Moments for Non-linear Models with Heterogeneous Observations," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 99-120, December.
    3. Heckemeyer, Jost H. & Richter, Katharina & Spengel, Christoph, 2014. "Tax planning of R&D intensive multinationals," ZEW Discussion Papers 14-114, ZEW - Leibniz Centre for European Economic Research.
    4. Christopher Withers & Saralees Nadarajah, 2013. "Calibration with low bias," Statistical Papers, Springer, vol. 54(2), pages 371-379, May.
    5. Qian Chen & David E. Giles, 2009. "Finite-Sample Properties of the Maximum Likelihood Estimator for the Poisson Regression Model With Random Covariates," Econometrics Working Papers 0907, Department of Economics, University of Victoria.

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    More about this item

    Keywords

    Logit model; bias; mean squared error; bias correction; random covariates;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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