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 estimatorsare 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) .
This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the isotonic regression is inconsistent in this setting and derive the asymptotic distributions of boundary corrected estimators. Interestingly, the boundary corrected estimators can be bootstrapped without subsampling or additional nonparametric smoothing which is not the case for the interior point. The Monte Carlo experiments indicate that shape restrictions can improve dramatically the finite-sample performance of unrestricted estimators. Lastly, we apply the isotonic regression discontinuity designs to estimate the causal effect of incumbency in the U.S. House elections .
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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
This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that
R
. The large sample distributions of introduced estimatorsare 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
is inconsistent in this setting and derive the asymptotic distributions of boundary corrected estimators. Interestingly, the boundary corrected estimators can be bootstrapped without subsampling or
R
, typically needed in such settings, and show its consistency. We find in
which is not the case for the interior point. The
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indicate
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To illustrate the empirical applicability of our approach, we estimate the incumbency effect
Lastly, we apply the isotonic regression discontinuity designs to estimate the causal effect of incumbency
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following an influential study of (Lee, 2008)