Manipulation-Robust Regression Discontinuity Design
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Regression discontinuity designs (RDDs) may not deliver reliable results if units manipulate their running variables. It is commonly believed that imprecise manipulations are harmless and, diagnostic tests detect precise manipulations. However, we demonstrate that RDDs may fail to point-identify in the presence of imprecise manipulation, and that not all harmful manipulations are detectable. To formalize these claims, we propose a class of RDDs with harmless or detectable manipulations over locally randomized running variables as manipulation-robust RDDs. The conditions for the manipulation-robust RDDs may be intuitively verified using the institutional background. We demonstrate its verification process in case studies of applications that use the McCrary (2008) density test. The restrictions of manipulation-robust RDDs generate partial identification results that are robust to possible manipulation. We apply the partial identification result to a controversy regarding the incumbency margin study of the U.S. House of Representatives elections. The results show the robustness of the original conclusion of Lee (2008).
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