Polychotomous choices and self-selection

The estimation of selection models has been one of the main topic in the analysis of macroeconomics data (Heckman, 1979, 1990). They have been widely used for the estimation of treatment effects, in particular the impacts of social programs. In the paper we discuss the issues related to the assessment of treatment effects for the case where the variable of interest is binary and the selectivity is induced by a polychotomouschoice model. The problem of the identification of the effects is addressed and a parametric model presented; tests to detect the selection bias are derived. We also show how the bounds on treatment effects (Manski, 1990) can be generalized to the case of more than two treatments. An empirical example, related to the estimation of faculty effects on the drop out of university studies, concludes the paper