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 .
We propose new confidence sets (CSs) for the regression discontinuity parameter in fuzzy designs . Our CSs are based on nonparametric local linear regression, and are bias-aware, in the sense that they take possible smoothing bias explicitly into account. Their construction shares similarities with that of Anderson-Rubin CSs in exactly identified instrumental variable models, and thereby avoids issues with "delta method" approximations that underlie most commonly used existing inference methods for fuzzy regression discontinuity analysis. Our CSs compare favorably in terms of both theoretical and practical performance to existing procedures in canonical settings with strong identification and a continuous running variable. However, due to their particular construction they are also valid under a wide range of empirically relevant conditions in which existing methods generally fail, such as setups with discrete running variables, donut designs, and weak identification .
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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
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that do not rely on such assumptions. Their construction is analogous to that of Anderson-Rubin CSs in the literature on instrumental variable models
for the regression discontinuity parameter in fuzzy designs
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explicitly take the
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Their construction shares similarities with that of Anderson-Rubin CSs in exactly identified instrumental variable models, and thereby avoids issues with "delta method" approximations that underlie most commonly used existing inference methods for fuzzy regression discontinuity analysis. Our CSs compare favorably in terms of both theoretical and practical performance to existing procedures in canonical settings with strong identification and a continuous running variable. However, due to their particular construction they are also
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CIs generally fail. These conditions include
methods generally fail, such as setups with
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. 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