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Efficiency Bounds for Distribution-Free Estimation from Endogenously Stratified Samples Summary of Results

This paper considers estimation of the linear regression model and of the binary choice model from endogenously stratified samples (that is, the strata are defined in terms of the dependent variable), in the case where neither the independent variables nor the error term have a distribution function of known parametric form. This includes, as a special case, the truncated regression model with unknown error distribution. For these models, we derive lower bounds on the asymptotic variances for regular distribution-free (or semi-parametric) estimators, both with and without prior knowledge of the population shares of the strata. For comparison, we also give the corresponding results for the case of a known error distribution.