COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 889

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

Rosa L. Matzkin

September 1988

This paper studies the problem of nonparametric identification and estimation of binary threshold-crossing and binary choice models. First, conditions are given that guarantee the nonparametric identification of both the function of exogenous observable variables and the distribution of the random terms. Second, the identification results are employed to develop strongly consistent estimation methods that are nonparametric in both the function of observable exogenous variables and the distribution of the unobservable random variables. The estimators are obtained by maximizing a likelihood function over nonparametric sets of functions. A two-step constrained optimization procedure is devised to compute these estimators.

JE Classification: 211

Keywords: Nonparametric models, identification, likelihood function, consistency