In isotonic regression discontinuity designs, the average outcome and the treatment assignment probability are monotone in the running variable. We introduce novel nonparametric estimators for sharp and fuzzy designs based on the isotonic regression which is robust to the inference after the model selection problem . The large sample distributions of introduced estimators are driven by scaled Brownian motions originating from zero and moving in opposite directions. Since these distributions are not pivotal, we also introduce a novel trimmed wild bootstrap procedure, which does not require additional nonparametric smoothing, typically needed in such settings, and show its consistency. We illustrate our approach on the well-known dataset of Lee (2008), estimating the  incumbency effect in the U.S. House elections  .
In isotonic regression discontinuity designs, the average outcome and the treatment assignment probability are monotone in the running variable. We introduce novel nonparametric estimators for sharp and fuzzy designs based on the isotonic regression . The large sample distributions of introduced estimators are driven by scaled Brownian motions originating from zero and moving in opposite directions. Since these distributions are not pivotal, we also introduce a novel trimmed wild bootstrap procedure, which does not require additional nonparametric smoothing, typically needed in such settings, and show its consistency. We find in Monte Carlo experiments that shape restrictions can improve dramatically the finite-sample performance of unrestricted estimators. To illustrate the empirical applicability of our approach, we estimate the incumbency effect in the U.S. House elections following an influential study of (Lee, 2008) .
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which is robust to the inference after the model selection problem
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illustrate our approach on the well-known dataset of Lee (2008), estimating
find in Monte Carlo experiments that shape restrictions can improve dramatically the finite-sample performance of unrestricted estimators. To illustrate
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empirical applicability of our approach, we estimate the
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following an influential study of (Lee, 2008)