Local Polynomial Order in Regression Discontinuity Designs

Zhuan Pei, David S. Lee, David Card, Andrea Weber

Research output: Contribution to journalArticlepeer-review

Abstract

Treatment effect estimates in regression discontinuity (RD) designs are often sensitive to the choice of bandwidth and polynomial order, the two important ingredients of widely used local regression methods. While Imbens and Kalyanaraman and Calonico, Cattaneo, and Titiunik provided guidance on bandwidth, the sensitivity to polynomial order still poses a conundrum to RD practitioners. It is understood in the econometric literature that applying the argument of bias reduction does not help resolve this conundrum, since it would always lead to preferring higher orders. We therefore extend the frameworks of Imbens and Kalyanaraman and Calonico, Cattaneo, and Titiunik and use the asymptotic mean squared error of the local regression RD estimator as the criterion to guide polynomial order selection. We show in Monte Carlo simulations that the proposed order selection procedure performs well, particularly in large sample sizes typically found in empirical RD applications. This procedure extends easily to fuzzy regression discontinuity and regression kink designs.

Original languageEnglish (US)
JournalJournal of Business and Economic Statistics
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Keywords

  • Local polynomial estimation
  • Polynomial order
  • Regression discontinuity design
  • Regression kink design

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