Comment on “Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs”

Gelman and Imbens (2019) argue against using global high-order polynomial models in regression discontinuity designs, recommending local linear or quadratic models instead. This comment revisits two of their arguments, showing they overstate the disadvantages of global models relative to local models. First, the extreme weights associated with global high-order polynomial models are of limited practical relevance. They only occur if the distribution of the running variable has parts with few observations and have a small impact on the estimated treatment effect. Second, local models can also yield excessive false positive findings, even when using best-practice modeling methods. Moreover, this problem worsens as the sample size increases. These results suggest that local models do not mitigate all the issues of global models and caution researchers against naively accepting their estimates.