A Sample Selection Model for Fractional Response Variables

This paper develops a sample selection model for fractional response variables, i.e., variables taking values in the [0, 1]-interval. It provides an extension of the Papke and Wooldridge (1996) fractional probit model to the case of non-random sample selectivity. The model differs from the Heckman sample selection model by specifying a main equation which is consistent with the bounded nature of the fractional outcome variable. The proposed model is parametric and does usually not require an exclusion restriction to hold, which makes is useful for empirical practice. A simulation study indicates that the gains of imposing a (valid) exclusion restriction are quite small, particularly with respect to the estimation of marginal effects, while imposing a wrong exclusion restriction leads to severely biased estimates. Finally, an empirical application to the impact of education on women’s perceived probability of job loss is provided, which 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.