Tolerating defiance? Local average treatment effects without monotonicity

Instrumental variables (IVs) are commonly used to estimate the effects of some treatments. A valid IV should be as good as randomly assigned, it should not have a direct effect on the outcome, and it should not induce any unit to forgo treatment. This last condition, the so-called monotonicity condition, is often implausible. This paper starts by showing that actually, IVs are still valid under a weaker condition than monotonicity. It then derives conditions that are sufficient for this weaker condition to hold and whose plausibility can easily be assessed in applications. It finally reviews several applications where this weaker condition is applicable while monotonicity is not. Overall, this paper extends the applicability of the IV estimation method.