Efficiency Bounds for Distribution-free Estimators of the Binary.

Abstract

Lower bounds are derived for the asymptotic variances of regular distribution-free (or semiparametric) estimators of the parameters of the binary-choice model and the censored-regression (Tobit) model. A semiparametric estimator is one that does not require any assumption about the distribution of the stochastic error term in the model, apart from regularity conditions. Comparison of the bounds with the corresponding asymptotic Cramer-Rao bounds for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution. Copyright 1987 by The Econometric Society.