A Sample Selection Model for Fractional Response Variables

This paper develops a sample selection model for fractional response variables, i.e., variables taking values between zero and one. It is shown that the proposed model is consistent with the nature of the fractional response variable, i.e., it generates predictions between zero and one. A simulation study shows that the model performs well in finite samples and that competing models, the Heckman selection model and the fractional probit model (without selectivity), generate biased estimates. An empirical application to the impact of education on women's perceived probability of job loss illustrates that the choice of an appropriate model is important in practice. In particular, the Heckman selection model and the fractional probit model are found to underestimate (in absolute terms) the impact of education on the perceived probability of job loss.