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.