Regression Discontinuity Designs as Local Randomized Experiments

In the seminal paper from 1960, Thistlethwaite and Campbell (1960) introduce the key ideas underlying regression discontinuity (RD) designs, which, even if initially almost completely ignored, have then acted as a fuse of a blowing number of studies applying and extending RD designs starting from the late nineties. Building on the original idea by Thistlethwaite and Campbell (1960), RD designs have been often described as designs that lead to locally randomized experiments for units with a realized value of a so-called forcing variable falling around a pre-fixed threshold. We embrace this perspective, and in this discussion we offer our view on how the original proposal by Thistlethwaite and Campbell (1960) should be formalized. We introduce an explicit local overlap assumption for a subpopulation around the threshold, for which we re-formulate the Stable Unit Treatment Value Assumption (SUTVA), and provide a formal definition of the hypothetical experiment underlying RD designs, by invoking a local randomization assumption. A distinguishing feature of this approach is that it embeds RD designs in a framework that is fully consistent with the potential outcome approach to causal inference. We discuss how to select suitable subpopulation(s) around the threshold with adjustment for multiple comparisons, and how to draw inference for the causal estimands of interest in this framework. We illustrate our approach in a study concerning the effects of University grants on students' dropout.