Fuzzy regression discontinuity designs identify the local average treatment effect (LATE) for the subpopulation of compliers, and with forcing variable equal to the threshold. We develop methods that assess the external validity of LATE to other compliance groups at the threshold, and allow for identification away from the threshold. Specifically, we focus on the equality of outcome distributions between treated compliers and always-takers, and between untreated compliers and never-takers. These equalities imply continuity of expected outcomes conditional on both the forcing variable and the treatment status. We recommend that researchers plot these conditional expectations and test for discontinuities at the threshold to assess external validity. We provide new commands in STATA and MATLAB to implement our proposed procedures.
