Regression discontinuity designs (RDDs) may not deliver reliable results if unitsmanipulate 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).
Regression discontinuity (RD) design in a practical context is often contaminated by units' behavior to manipulate their treatment assignment. However, we have no formal justification for point identification in such a contaminated RD design. Diagnostic tests have been proposed to detect manipulations, but they do not guarantee identification without some auxiliary assumptions, and the auxiliary assumptions have not been proposed. This study proposes a set of restrictions for possibly manipulated RD designs to validate point identification and diagnostic tests. The same restrictions simultaneously validate worst-case bounds when the diagnostic tests are validated. Therefore, our designs are manipulation robust in testing and identification. The worst-case bounds have two shorter bounds as special cases, and we apply special-case bounds to a controversy regarding the incumbency margin study of the U.S. House of Representatives elections studied in Lee (2008).
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designs (RDDs) may not deliver reliable results if unitsmanipulate 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
(RD) design in a practical context is often contaminated by units' behavior to manipulate their treatment assignment. However, we have no formal justification for point identification in such a contaminated RD design. Diagnostic tests have been proposed to detect manipulations, but they do not guarantee identification without some auxiliary assumptions, and the auxiliary assumptions have not been proposed. This study proposes a set of restrictions for possibly manipulated RD designs to validate point identification and diagnostic tests. The same restrictions simultaneously validate worst-case bounds when the diagnostic tests are validated. Therefore, our designs are manipulation robust in testing and identification. The worst-case bounds have two shorter bounds as special cases, and we apply special-case bounds
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