Fuzzy regression discontinuity (FRD) designs occur 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, 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 variableis continuous, discrete, or of some intermediate form .
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 .
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Fuzzy regression discontinuity (FRD) designs occur frequently in many areas of applied economics. We argue that the confidence intervals based on nonparametric local linear regression that are
The confidence intervals (CIs)
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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
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
R
, which are based on an Anderson-Rubin-type construction . These confidence sets are
(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
R
into account the exact smoothing bias of the local linear estimators on which they are based
the possible smoothing bias into account
R
simple to compute, highly efficient, 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 variableis continuous, discrete, or of some intermediate form
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