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

By Andrew Gelman, Guido W. Imbens. 2014

1,608 citations recorded by the source corpus.

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In Statistics and Probability

Citations in the corpus

The State of Applied Econometrics - Causality and Policy Evaluation (2016, neutral): “Gelman and Imbens [2014] argue that in practice it is difficult to choose the order of the polynomials in a satisfactory way, and that confidence intervals based on such methods have poor properties.”
Do Women Give Up Competing More Easily? Evidence from the Lab and the Dutch Math Olympiad (2016, methodology): “In practice, this usually means using a quadratic control ( Gelman and Imbens ( 2014 ) advise against the use of higher order polynomials and show that confidence intervals based on them have poor properties .”
Rural Roads and Local Economic Development (2018, methodology): “Following the recommendations of Imbens and Lemieux (2008) and Gelman and Imbens (2017), our primary specification uses local linear regression within a given bandwidth of the treatment threshold, and controls for the running variable (village population) on ei- ther side of the threshold.”
Willingness to Pay for Clean Air: Evidence from Air Purifier Markets in China (2020, positive): “The recent literature suggests that a local linear regression based on data near the RD cutoff is likely to produce the most robust estimates (Imbens and Lemieux 2008; Gelman and Imbens 2014).”
Do tax incentives for research increase firm innovation? An RD design for R&D (2016, positive): “17 In the baseline results, being mindful of Gelman and Imbens’s (2014) warning against using higher order polynomials when higher order coefficients are not significant, we use a first order polynomial.”
Optimal Data-Driven Regression Discontinuity Plots (2015, methodology): “Employing results from the nonparametrics literature, it is possible to select kn using some data-driven approach such as (plug-in) IMSE minimization or cross-validation.”
Evidence on the deleterious impact of sustained use of polynomial regression on causal inference (2015, background): “In a companion paper (Gelman and Imbens, 2014) we present evidence that controlling for high-order polynomials in RD analysis results in noisy estimates with poor statistical properties and confidence intervals that are too narrow.”
Clicking on heaven's door: the effect of immigrant legalization on crime (2017, methodology): “Following Gelman and Imbens (2014), we focus on a quadratic polynomial in T in the main specification, although we explore the sensitivity of the results to using any polynomial degree between 0 and 6.”
A Survey of Learning Causality with Data: Problems and Methods (2018, background): “Athey and Imbens [11] described decision trees and ensemble machine learning models for learning causal effects.”
Use of Quasi-Experimental Research Designs in Education Research: Growth, Promise, and Challenges (2020, background): “Recently, however, statisticians have shown how those terms might introduce other biases to the estimates (Gelman & Imbens, 2019).”
External Validity in Fuzzy Regression Discontinuity Designs (2019, neutral): “…by HTV. Recent theoretical contributions include Porter (2003), McCrary (2008), Imbens and Kalyanaraman (2012), Calonico, Cattaneo, and Titiunik (2014, 2015), Dong and Lewbel (2015), Dong (2018), Bertanha (2017), Gelman and Imbens (2014), Armstrong and Kolesar (2018), and Imbens and Wager (2018).”