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Regression discontinuity designs (RDDs) have become one of the mostwidely-used quasi-experimental tools for causal inference. A crucial assumptionon which they rely is that the running variable cannot be manipulated -- anassumption frequently violated in practice, jeopardizing point identification.In this paper, we introduce a novel method that provide partial identificationbounds on the causal parameter of interest in sharp and fuzzy RDDs. The methodfirst estimates the number of manipulators in the sample using a log-concavityassumption on the un-manipulated density of the running variable. It thenderives best- and worst-case bounds when we delete that number of points fromthe data, along with fast computational methods to obtain them. We apply thisprocedure to a dataset of blood donations from the Abu Dhabi blood bank toobtain the causal effect of donor deferral on future volunteering behavior. Wefind that, despite significant manipulation in the data, we are able to detectcausal effects where traditional methods, such as donut-hole RDDs, fail.

Optimized Partial Identification Bounds for Regression Discontinuity Designs with Manipulation