Semiparametric estimation of censored selection models with a nonparametric selection mechanism

In this paper, estimation of the coefficients in a 'single-index selectivity bias' model is considered under the assumption that the selection correction function depends on the conditional mean of some observable 'selection' variable. The estimation method follows a familiar 'two-step' strategy: the first step uses a nonparametric regression estimator for the selection variable, while the second step uses a weighted instrumental variables estimator for the coefficients in the equation of interest. The paper gives conditions under which the proposed estimator is root-n-consistent and asymptotically normal. The proposed method is applied to data on labor supply.