Finite-Sample Properties of the Maximum Likelihood Estimator for the Binary Logit Model With Random Covariates
AbstractWe 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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Bibliographic InfoPaper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0906.
Length: 22 pages
Date of creation: 05 Aug 2009
Date of revision:
Note: ISSN 1485-6441
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Logit model; bias; mean squared error; bias correction; random covariates;
Other versions of this item:
- Qian Chen & David Giles, 2012. "Finite-sample properties of the maximum likelihood estimator for the binary logit model with random covariates," Statistical Papers, Springer, vol. 53(2), pages 409-426, May.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-08-16 (All new papers)
- NEP-DCM-2009-08-16 (Discrete Choice Models)
- NEP-ECM-2009-08-16 (Econometrics)
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