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 first case where a causal interpretation holds is when only those assigned to one of the two treatments can effectively 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 Effect (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 offered either by the public or the private sector, or remain on a standard track.
randomized evaluation local average treatment effect bounds