Econometrica: May, 1983, Volume 51, Issue 3

Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model

https://doi.org/0012-9682(198305)51:3<765:DMLEOT>2.0.CO;2-8
p. 765-782

Stephen R. Cosslett

When the binary choice probability model is derived from a random utility maximization model, the choice probability for one alternative has the form F[V(z, @Q)]. Here V(z, @Q) is a given function of the exogenous variables z and unknown parameters @Q, representing the systematic component of the utility difference, and F is the distribution function of the random component of the utility difference. This paper describes a method of estimating the parameters @Q without assuming any functional form for the distribution function F, and proves that this estimator is consistent. F is also consistently estimated. The method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter @Q but also over a space which contains all distribution functions.