Defying the LATE? Identification of local treatment effects when the instrument violates monotonicity.

The instrumental variable method relies on a strong no-defiers condition, which requires that the instrument affect every subject's treatment decision in the same direction. This paper shows that no-defiers can be replaced by a weaker compliers-defiers condition, which requires that a subgroup of compliers have the same size and the same distribution of potential outcomes as defiers. This condition is necessary and sufficient for IV to capture causal effects for the remaining part of compliers. In many applications, compliers-defiers is a very weak condition. For instance, in Angrist & Evans (1998), 94 % of DGPs compatible with the data satisfy compliers-defiers, while 0 % satisfy no-defiers