Limited Monotonicity and the Combined Compliers LATE

Abstract We consider endogenous binary treatment with multiple binary instruments. We propose a novel limited monotonicity (LiM) assumption that is generally weaker than alternative monotonicity assumptions in the literature. We define and identify (under LiM) the combined compliers local average treatment effect (CC-LATE), which is arguably a more policy-relevant parameter than the weighted average of LATEs identified by two-stage least squares (TSLS), and is identified under more general conditions. Estimating the CC-LATE is trivial, equivalent to running TSLS with one constructed instrument on a subsample. We use our CC-LATE to empirically assess how knowledge of HIV status influences protective behaviors.