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Title: Isotonic regression discontinuity designs Authors:  Andrii Babii - University of North Carolina (United States) [presenting]
Abstract: Estimation and inference for the isotonic regression at the boundary of its support are studied. This object is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the isotonic regression is inconsistent at the boundary and that consistency can be restored with a suitable boundary correction. The one-sided Brownian motion drives the large sample distribution at the boundary. Since the distribution is not pivotal, we also introduce the trimmed wild bootstrap and show its consistency without subsampling or additional nonparametric smoothing. The results are illustrated for sharp and fuzzy monotone regression discontinuity designs. We find in Monte Carlo experiments that shape restrictions can improve the finite-sample performance of unrestricted estimators dramatically. An empirical analysis of the incumbency effect in the U.S. House elections is provided.