Score manipulation, density continuity and intent‐to‐treat effect for regression discontinuity

Regression discontinuity (RD) is widely used in many disciplines of science to find treatment effect when the treatment is determined by an underlying running variable (‘score') S crossing a cutoff c or not. The main attraction of RD is local randomization around c, which is, however, often ruined by manipulation on S. To detect manipulation, the continuity of score density function fSs at c is routinely tested in practice. In this paper, we examine how informative fS is for RD, and show the following. First, for incumbency effect in election to which RD has been heavily applied, fS may have no information content. Second, for RD in general, the fS continuity is neither necessary nor sufficient for RD validity. Third, if the treatment cannot be implemented without manipulation of S, then the manipulation had better be considered as part of the treatment effect, much as in ‘intent‐to‐treat effect’ for clinical trials. These findings call for relying less on fS continuity tests and, instead, thinking more about how subjects react to the treatment to modify their S, how to design the treatment to lessen manipulation, and what to take as the desired treatment effect.