Effect Heterogeneity and Causal Attribution in Regression Discontinuity Designs

Research investigating subgroup differences in treatment effects recovered using regression discontinuity (RD) designs has become increasingly popular. For in- stance, scholars have investigated whether incumbency effects on candidate per- sistence or winning again vary by candidate characteristics (e.g., gender) or local context. Under what conditions can we interpret subgroup differences in treat- ment 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 lay out identification as- sumptions required for each, along with corresponding estimation procedures. In doing so, we highlight how investigating RD effect conditionality that is causally driven by another variable involves several additional challenges related to in- terpretation, identification, and estimation. We apply our framework to recent studies and offer practical advice for applied researchers considering these alter- native quantities of interest.