Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs. A Comment on Gelman and Imbens (Journal of Business & Economic Statistics, 2019)

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, global high-order polynomial models assign extreme weights when the running variable's distribution has regions with few observations. Because so few observations receive these weights, their contribution to the treatment estimate is usually small. 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.