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

The instrumental variable method relies on 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 reamining 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". JEL classification: C21 ; C26