Optimized Partial Identification Bounds for Regression Discontinuity Designs with Manipulation

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