Bias-Aware Inference in Fuzzy Regression Discontinuity Designs

The confidence intervals (CIs) commonly reported in empirical fuzzy regression discontinuity studies are justified by theoretical arguments which assume that the running variable is continuously distributed with positive density around the cutoff, and that the jump in treatment probabilities at the cutoff is "large". In this paper, we provide new confidence sets (CSs) that do not rely on such assumptions. Their construction is analogous to that of Anderson-Rubin CSs in the literature on instrumental variable models. Our CSs are based on local linear regression, and are bias-aware, in the sense that they explicitly take the possible smoothing bias into account. They are valid under a wide range of empirically relevant conditions in which existing CIs generally fail. These conditions include discrete running variables, donut designs, and weak identification. But our CS also perform favorably relative to existing CIs in the canonical setting with a continuous running variable, and can thus be used in all fuzzy regression discontinuity applications.