Manipulation-Robust Regression Discontinuity Designs

In regression discontinuity designs, manipulation threatens identification. A known channel of harmful manipulations is precise control over the observed assignment, but this channel is only an example. This study uncovers the only other channel: sample selection by deciding manipulation precisely based on the given assignment status. For example, in the assignment design of a qualification exam, self-selection by allowing test retakes precisely based on failing the exam is a precise decision. This precise decision harms identification without precisely controlling the final assignment. For instance, retaking the test never ensures passage, but it distorts the qualification assignment because some students that failed then pass. However, students that have already passed, never fail. This novel channel redefines the justification for identification. Furthermore, under a new auxiliary condition, McCrary (2008)'s test is able to confirm identification and the existing worst-case bounds are nested within our new bounds. In a replication study, another sample selection by analysts appears critical in the robustness of their original conclusion.