Efficiency bounds for some semiparametric selection models

In this paper, we calculate semiparametric efficiency bounds for the regression coefficients in an 'outcome' equation subject to censoring under weak conditions on the form of the selectivity bias. It is assumed that the regression function for the binary selection variable which governs the censoring mechanism is nonparametric, as is the form of the selection correction term in the outcome equation. Our results extend those of Chamberlain (1986), who considered models with an underlying linear structure for the selectivity effect. The results are useful for evaluation of some recently-proposed 'two-step' estimators for these models and for construction of improved estimators.