Semiparametric Estimation of Monotonic and Concave Utility Functions: The Discrete Choice Case

This paper develops a semiparametric method for estimating the nonrandom part V(.) of a random utility function U(v, omega) - V(v) + e(omega) from data on discrete choice behavior. Here v and omega are, respectively, vectors of observable and unobservable attributes of an alternative, and e(omega) is the random part of the utility for that alternative. The method is semiparametric because it assumes that the distribution of the random parts is know up to a finite-dimensional parameter theta, while not requiring specification of a parametric form for V( ). The nonstochastic part V( ) of the utility function U( ) is assumed to be Lipschitzian and to possess a set of properties, typically assumed for utility functions. The estimator of the pair (V,theta) is shown to be strongly consistent.