Robustness of the encouragement design in a two-treatment randomized control trial

In this paper we discuss how the " encouragement design "used in randomized controlled trials can be extended to a setting with two treatments and one control group. Conditions to interpret the Two-Stage Least Squares (TSLS) estimates causally are stronger than in the case with only one treatment and one control group. A rst case where a causal interpretation holds is when only those assigned to one of the two treatments can e ectively enter the corresponding program. A second case is when there are always takers. In that second case, entry rates into a given program should be the same among those assigned to the control group and those assigned to the other program; this restriction can be tested from the data. In cases where the restriction is rejected, we derive bounds to the Local Average Treatment E ect (LATE) based on weaker monotonicity conditions. We illustrate the results using data from a large randomized experiment where job seekers at risk of long term unemployment can receive a reinforced counseling scheme o ered either by the public or the private sector, or remain on a standard track.