Heterogeneous Groups and Covariate Adjustment in Regression Discontinuity Designs

Abstract: I study covariate adjustment in regression discontinuity designs with discrete covariates, such as education level, occupation, or gender, that partition the sample into subgroups with heterogeneous regression functions. The standard local-polynomial RD estimator pools observations across these heterogeneous groups, generating an additive pooling bias whenever group composition varies along the running variable. I show that covariate adjustment can eliminate this pooling bias from the leading term of the worst-case bias under a uniform asymptotic framework. Specifically, I propose the Stratified RD estimator, which avoids pooling through stratification: It first estimates group-specific treatment effects within each group and group weights at the cutoff and then forms a weighted average. I derive an explicit range of bandwidth choices under which the Stratified RD estimator achieves both weakly lower asymptotic variance and worst-case bias than the local-polynomial estimator, over a common smoothness class. These improvements yield shorter honest confidence intervals for the same target parameter. A placebo exercise using data from the Current Population Survey shows reductions in MSE of 8% to 33% and honest confidence intervals that are 6% to 16% shorter depending on sample sizes and bandwidths.

Recommended citation: Großbölting, Tobias. (2026). "Heterogeneous Groups and Covariate Adjustment in Regression Discontinuity Designs." Working Paper.