Finite-sample Properties of the Maximum Likelihood Estimator for the Binary Logit Model with Random Covariates

Contact Author: David E. Giles, Dept. of Economics, University of Victoria, P.O. Box 1700, STN CSC, Victoria, B.C., Canada V8W 2Y2; e-mail: [email protected]; Voice: (250) 721-8540; FAX: (250) 721-6214 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 firstorder bias from the original estimator, is examined in a Monte Carlo experiment. This biascorrection is effective in all of the cases considered, and is recommended when the logit model is estimated by maximum likelihood with small samples.