Manipulation-Robust Regression Discontinuity Designs

In regression discontinuity designs, manipulation, a threat to identification, had no formal characterization. This study is the first formalization of which manipulations harm identification and are detectable in the density test. Two channels characterize the harmful manipulation: the precise control of the manipulated assignment status, and the precise decision to manipulate by the given assignment status. The latter, a novel channel, redefines all the rationale for justifying point-identification, diagnostic tests, and worst-case bounds in more general forms than before. In the replication of the Romanian high-school admission study, the precise decision appears as selective attrition by admission results. Our replication demonstrates that the precise decision is critical for the robustness of the original conclusion of the study.