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This paper presents a new estimator of the intercept of a linear regressionmodel in cases where the outcome varaible is observed subject to a selectionrule. The intercept is often in this context of inherent interest; for example,in a program evaluation context, the difference between the intercepts inoutcome equations for participants and non-participants can be interpreted asthe difference in average outcomes of participants and their counterfactualaverage outcomes if they had chosen not to participate. The new estimator canunder mild conditions exhibit a rate of convergence in probability equal to$n^{-p/(2p+1)}$, where $p\ge 2$ is an integer that indexes the strength ofcertain smoothness assumptions. This rate of convergence is shown in thiscontext to be the optimal rate of convergence for estimation of the interceptparameter in terms of a minimax criterion. The new estimator, unlike otherproposals in the literature, is under mild conditions consistent andasymptotically normal with a rate of convergence that is the same regardless ofthe degree to which selection depends on unobservables in the outcome equation.Simulation evidence and an empirical example are included.

Rate-Optimal Estimation of the Intercept in a Semiparametric Sample-Selection Model