Relaxing conditions for local average treatment effect in fuzzy regression discontinuity

In fuzzy regression discontinuity with a running/forcing variable S and a cutoff c, the identified treatment effect is the 'effect on compliers at S=c'. This well-known 'local average treatment effect (LATE)' interpretation requires (i) a monotonicity condition and (ii) the independence of the potential treatment and potential response variables from S. These assumptions can be violated, however, particularly (ii) when S affects potential variables, which can easily happen in practice. In this paper, we weaken both assumptions so that LATE in fuzzy regression discontinuity has a better chance to hold in the real world, and practitioners can claim their findings in fuzzy regression discontinuity to be LATE.