Choosing Polynomial Order in Regression Discontinuity Design (RDD)

[Aisha Rahma]

Hi everyone, I’m running an RDD analysis using rdrobust to look at whether adolescent obesity affects life satisfaction. I’m using BMI-for-age z-score (zbmi) as the running variable with a cutoff at zBMI = 2. Here’s what confuses me: the results are not significant with p(1) and p(2), but become significant with p(3). The thing is, when I check the rdplot, I don’t really see a clear jump at the cutoff with p(3). In a case like this, would you treat the p(3) result as possible overfitting and stick with lower-order polynomials as the main specification? Any thoughts would be really appreciated!

[David Radwin]

I don't know much about the topic, but this article argues against high-order polynomials for RDD:
Gelman, A., & Imbens, G. (2019). Why high-order polynomials should not be used in regression discontinuity designs. Journal of Business & Economic Statistics, 37(3), 447-456. https://www.stat.columbia.edu/~gelma...elman_jbes.pdf