Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs

A Comment on Gelman and Imbens (Journal of Business & Economic Statistics, 2019)

Abstract

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 are contingent on specific contexts and interpretations. First, the extreme weights associated with global high-order polynomial models only occur if the distribution of the running variable has parts with few observations. Moreover, a bootstrap aggregating procedure shows that their impact on the estimated treatment effect is relatively small, approximately 13% for the most affected models. Second, I establish that local models can also yield excessive false positive findings, even when using best-practice modeling methods, and that this problem worsens as the sample size grows. These results improve our understanding of the limitations of global high-order polynomial models and suggest that researchers should routinely investigate false positive rates in their study.