Effect Heterogeneity and the Challenges of Causal Attribution in Regression Discontinuity Designs

Research investigating subgroup differences in treatment effects recovered using regression discontinuity (RD) designs has become increasingly popular. For instance, scholars have investigated whether incumbency effects on candidate persistence or winning again vary by candidate characteristics or local context. Under what conditions can we interpret subgroup differences in treatment effects as a causal result of the moderating characteristic? In this study, we explore the difference between RD effect conditionality that is simply associated with versus causally driven by another variable. To make this distinction explicit and formal, we define two alternative estimands, and we lay out identification assumptions required for each estimand along with corresponding estimation procedures. In doing so, we demonstrate how investigating RD effect conditionality that is causally driven by another variable involves several serious challenges related to interpretation, identification, and estimation. Accordingly, we urge caution and offer practical advice for applied researchers considering these alternative quantities of interest. To illustrate, we include applications to several recent studies.