Understanding Regression Discontinuity Designs As Observational Studies

Thistlethwaite and Campbell (1960) proposed to use a “regression-discontinuity analysis” in settings where exposure to a treatment or intervention is determined by an observable score and a fixed cutoff. The type of setting they described, now widely known as the regression discontinuity (RD) design, is one where units receive a score, and a binary treatment is assigned according to a very specific rule. In the simplest case, all units whose score is above a known cutoff are assigned to the treatment condition, and all units whose score is below the cutoff are assigned to the control (i.e., absence of treatment) condition. Thistlethwaite and Campbell insightfully noted that, under appropriate assumptions, the discontinuity in the probability of treatment status induced by such an assignment rule could be leveraged to learn about the effect of the treatment at the cutoff. Their seminal contribution led to what is now one of the most rigorous non-experimental research designs across the social and biomedical sciences. See Cook (2008), Imbens and Lemieux (2008) and Lee and Lemieux (2010) for reviews, and the recent volume edited by Cattaneo and Escanciano (2017) for recent specific applications and methodological developments.