The attractiveness of the Regression Discontinuity Design (RDD) rests on its similarity to an experimental design. On the other hand, it is of limited applicability since rarely assignment to the treatment is based on known pre-program measures. Besides, it only allows to identify the mean impact on a very specific sub-population. Here we show that the RDD generalizes to the instances in which eligibility is established on a pre-program measure and eligible individuals are allowed to self-select into the program. This set-up is also convenient to test the validity of conventional non-experimental estimators of the mean impact.