Analysis of Regression Discontinuity Designs with a Binary Moderating Variable

Regression discontinuity (RD) designs are increasingly used for causal evaluations. However, the literature contains little guidance for conducting a moderation analysis within an RDD context. The current article focuses on moderation with a single binary variable. A simulation study compares: (1) different bandwidth selectors and (2) local polynomial regressions with interactions to local regressions on subsets of the data defined by values of the moderating variable. We find that existing bandwidth selectors optimized for main effects will choose bandwidths that are too small for moderation analysis. Additionally, choosing an optimal bandwidth for the subset regression approach may not be feasible for small to moderate sample sizes unless the moderator prevalence is near 0.5 and correlation with the assignment variable is small. We conclude that when sample sizes are small a global regression approach is likely to be preferred to utilizing bandwidth selectors optimized for main effects.