A semi-parametric estimator for censored selection models with endogeneity

We propose a semi-parametric least-squares estimator for a censored-selection (type 3 tobit) model under the mean independence of the outcome equation error u from the regressors given the selection indicator and its error term ɛ . This assumption is relatively weak in comparison to alternative estimators for this model and allows certain unknown forms of heteroskedasticity, an asymmetric error distribution, and an arbitrary relationship between the u and ɛ . The estimator requires only one-dimensional smoothing on the estimate of ɛ . We generalize the estimator to allow for an endogenous regressor whose equation contains an error ω related to u and discuss how this latter procedure can be adapted to two-wave panel censored-selection models with double selection indicators. In general, each additional endogeneity problem can be controlled for with an extra dimensional smoothing on the residual for the “endogeneity-origin” error term. Our proposed estimators are N -consistent and asymptotically normal. An empirical example based on estimating a wage equation for Australian female youth is provided to illustrate our approach.