Semiparametric estimation of a sample selection model with a binary endogenous regressor: the effect of chronicity in labour supply

The aim of this paper is to investigate the effect of chronicity in labour supply and the participation equation in a flexible framework. We analyse a semiparametric model for data including problems of sample selection and endogeneity, because a regressor is correlated with the disturbance term. One approach is to specify a simultaneous equation model where a dummy endogenous variable accounting for chronicity is included in the structural and selection equation. We propose a consistent estimator of the structural parameters robust to misspecification. The endogeneity and the selection are assumed to be nonparametric and the conditional distribution of the errors is left unspecified. Using a control function approach, the resulting estimator is obtained through a new pairwise differencing transformation. In addition to its empirical performance, the asymptotic properties are established. Our empirical findings confirm the idea that having a chronic illness has a negative effect on income, accounting for an approximately 32% decrease in expected income, which is close to the finding of Currie and Madrian (1999).