Bias-aware inference in fuzzy regression discontinuity designs

Fuzzy regression discontinuity (FRD) designs are used frequently in many areas of applied economics. We argue that the confidence intervals based on nonparametric local linear regression that are commonly reported in empirical FRD studies can have poor finite sample coverage properties for reasons related to their general construction based on the delta method, and to how they account for smoothing bias. We therefore propose new confidence sets, which are based on an Anderson-Rubin-type construction. These confidence sets are bias-aware, in the sense that they explicitly take into account the exact smoothing bias of the local linear estimators on which they are based. They are simple to compute, highly efficient, and have excellent coverage properties in finite samples. They are also valid under weak identification (that is, if the jump in treatment probabilities at the threshold is small) and irrespective of whether the distribution of the running variable is continuous, discrete, or of some intermediate form