Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models.

The author shows that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term. This identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term. The estimator is shown to be strongly consistent and a two step procedure for its calculation is developed. The paper also includes examples of economic models that satisfy the conditions necessary to apply the results. Copyright 1992 by The Econometric Society.