This paper provides a consistent and asymptotically normal estimator for the intercept of a semiparametrically estimated sample selection model. The estimator uses a decreasingly small fraction of all observations as the sample size goes to inﬁnity, as in Heckman (1990). In the semiparametrics literature, estimation of the intercept typically has been subsumed in the nonparametric sample selection bias correction term. The estimation of the intercept, however, is important from an economic perspective. For instance, it permits one to determine the “wage gap” between unionized and nonunionized workers, decompose the wage diﬀerential between diﬀerent socioeconomic groups (e.g., male-female and black-white), and evaluate the net beneﬁts of a social program.
Andrews, Donald W.K. and Schafgans, Marcia A., "Semiparametric Estimation of a Sample Selection Model" (1996). Cowles Foundation Discussion Papers. 1362.