Estimation and interpretation of a Heckman selection model with endogenous covariates

In this paper, we develop a Heckman selection model with endogenous covariates. Estimation of this model is easy and can be done within any econometrics software which supports maximum likelihood estimation of the Heckman selection model. The most important benefit of our model is that it provides an easy-to-interpret measure of the composition of the fully observed sample with respect to unobservables. As an example, we apply our model to the study of the composition of the female full time full year workforce, as has been done by Mulligan and Rubinstein (Q J Econ 123:1061–1110, 2008). We find that their conclusion that the female workforce was negatively selected in the late 1970s is robust to accounting for the potential endogeneity of education in a Heckman selection model. However, we find that accounting for endogeneity leads to a huge increase in the estimated returns to education.