Overfitting in Regression Discontinuity Designs: A Reconsideration Of Global and Local Models

In regression discontinuity designs, global models using high-order polynomial functions of the running variable have a reputation for overfitting. Specifically in data sets with a weak relation between the outcome and running variable, such models can produce an unstable fit near the discontinuity. This leads to inflated estimates of the treatment effect and invalid confidence intervals. While the regression discontinuity literature suggests the local linear model as a solution, this paper demonstrates that the local linear model does not effectively prevent overfitting. By excluding observations further from the discontinuity, the local linear model relies more heavily on the remaining observations, which can result in implausibly steep fits. Through simulation evidence, experimental benchmark comparisons, and empirical applications, I show that local linear models are generally as likely to overfit as global fourth-order polynomial models. In contrast, global second- and third-order polynomial models reduce estimate variability compared to the local linear model. This paper therefore recommends complementing the local linear model with global second- and third-order polynomial models to demonstrate robustness against overfitting.