Ineligibles and eligible non-participants as a double comparison group in regression-discontinuity designs

In a sharp regression-discontinuity design (RDD) the participation status deterministically depends on whether a pre-programme characteristic is above or below a specified threshold. The attractiveness of such a design rests on close similarities with a formal experiment. Nevertheless, it is of limited applicability since participation into a programme is seldom determined according to this rule. Besides, in the presence of heterogeneous effects a sharp RDD only allows identification of mean effects for individuals around the threshold for participation. Two results are presented in this paper, and they both partially overcome the two limitations described above. We show that when individuals self-select into participation conditional on some eligibility criteria a sharp RDD provides a natural framework to define a specification test for the non-experimental estimation of programme effects for participants away from the threshold. We also show that, in this set-up, the regularity conditions required for the identification of the mean counterfactual outcome for participants marginally eligible for the programme are essentially the same as in a sharp RDD.