Semiparametric estimation of a heteroskedastic sample selection model

Abstract

This paper considers estimation of a sample selection model subject to conditional heteroskedasticity in both the selection and outcome equations. The form of heteroskedasticity allowed for in each equation is multiplicative, and each of the two scale functions is left unspecified. A three-step estimator for the parameters of interest in the outcome equation is proposed. The first two stages involve nonparametric estimation of the "propensity score" and the conditional interquartile range of the outcome equation, respectively. The third stage reweights the data so that the conditional expectation of the reweighted dependent variable is of a partially linear form, and the parameters of interest are estimated by an approach analogous to that adopted in Ahn and Powell (1993, Journal of Econometrics 58, 3-29). Under standard regularity conditions the proposed estimator is shown to be √n-consistent and asymptotically normal, and the form of its limiting covariance matrix is derived.