Donut Regression Discontinuity Designs

Donut regression discontinuity (RD) designs exclude observations in a neighborhood around the cutoff. They are widely used in empirical work to address concerns about manipulation, sorting, or measurement error in the running variable. Despite their popularity, donut RD estimators are typically implemented heuristically, with limited formal guidance and unclear implications for bias, variance, and statistical inference. This paper provides a theoretical analysis of donut RD designs within the local linear estimation framework. We derive new results for point estimation, inference, and specification testing in donut RD designs. We show that donut trimming affects the bias and variance of the estimator and thus introduces substantial additional uncertainty relative to conventional RD estimators. We further show that recently developed bias-aware confidence intervals accurately account for this additional uncertainty without requiring modifications. Finally, we formalize specification tests based on comparing conventional and donut RD estimators to allow for valid statistical inference. The results are illustrated with two empirical applications.