Tolerating de ance ? Local average treatment e ects without monotonicity . ∗

Instrumental variable (IV) estimates a causal e ect if the instrument satis es a monotonicity condition. When this condition is not satis ed, we only know that IV estimates the di erence between the e ect of the treatment in two groups. This di erence could be a very misleading measure of the treatment e ect: it could be negative, even when the e ect is positive in both groups. There are a large number of studies in which monotonicity is implausible. One might then question whether we should trust their estimates. I show that IV estimates a causal e ect under a much weaker condition than monotonicity. I outline three criteria applied researchers can use to assess whether this condition is applicable in their studies. When this weaker condition is applicable, they can credibly interpret their estimates as causal e ects. When it is not, they should interpret their results with caution.