How Much Should We Trust Regression Discontinuity Design Estimates? Evidence from Experimental Benchmarks of the Incumbency Advantage

Regression discontinuity designs (RDD) are widely used in the social sciences to estimate causal effects from observational data. Following recent methodological advances, scholars can choose from various RDD estimators for point estimation and inference. This decision is mainly guided by theoretical results on optimality and Monte Carlo simulations because of a paucity of research on the performance of the different estimators in recovering real-world experimental benchmarks. Leveraging exact ties in personal votes in local elections in Colombia and Finland, which are resolved by a random lottery, we assess the performance of various estimators featuring different polynomial degrees, bias-correction methods, optimal bandwidths, and approaches to statistical inference. Using re-running and re-election as outcomes, we document only minor differences in the performance of the various implementation approaches when the conditional expectation function (CEF) of the outcomes in the vicinity of the discontinuity is close to linear. When approximating the curvature of the CEF is more challenging, bias-corrected and robust inference with coverage-error-rate-optimal bandwidths comes closer to the experimental benchmark than more widely used alternative implementations.