It's never too LATE: A new look at local average treatment effects with or without defiers

In heterogeneous treatment effect models with endogeneity, identification of the LATE typically relies on the availability of an exogenous instrument monotonically related to treatment participation. We demonstrate that a strictly weaker local monotonicity condition identifies the LATEs on compliers and on defiers. We propose simple estimators that are potentially more efficient than 2SLS, even under circumstances where 2SLS is consistent. Additionally, when easing local monotonicity to local stochastic monotonicity, our identification results still apply to subsets of compliers and defiers. Finally, we provide an empirical application, rejoining the endeavor of estimating returns to education using the quarter of birth instrument.