Manipulation-Robust Regression Discontinuity Designs

We present simple low-level conditions for identification in regression discontinuity designs using a potential outcome framework for the manipulation of the running variable. Using this framework, we replace the existing identification statement with two restrictions on manipulation. Our framework highlights the critical role of the continuous density of the running variable in identification. In particular, we establish the low-level auxiliary assumption of the diagnostic density test under which the design may detect manipulation against identification and hence is manipulation-robust.