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

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  • Andrew Gelman
  • Guido Imbens

Abstract

It is common in regression discontinuity analysis to control for third, fourth, or higher-degree polynomials of the forcing variable. There appears to be a perception that such methods are theoretically justified, even though they can lead to evidently nonsensical results. We argue that controlling for global high-order polynomials in regression discontinuity analysis is a flawed approach with three major problems: it leads to noisy estimates, sensitivity to the degree of the polynomial, and poor coverage of confidence intervals. We recommend researchers instead use estimators based on local linear or quadratic polynomials or other smooth functions.

Suggested Citation

  • Andrew Gelman & Guido Imbens, 2019. "Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 447-456, July.
    • Handle: RePEc:taf:jnlbes:v:37:y:2019:i:3:p:447-456
    DOI: 10.1080/07350015.2017.1366909
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    References listed on IDEAS

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    1. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-620, September.
    2. David S. Lee & Thomas Lemieux, 2010. "Regression Discontinuity Designs in Economics," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 281-355, June.
    3. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
    4. Brian A. Jacob & Lars Lefgren, 2004. "Remedial Education and Student Achievement: A Regression-Discontinuity Analysis," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 226-244, February.
    5. Wilbert Van Der Klaauw, 2008. "Regression–Discontinuity Analysis: A Survey of Recent Developments in Economics," LABOUR, CEIS, vol. 22(2), pages 219-245, June.
    6. Guido Imbens & Karthik Kalyanaraman, 2012. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 933-959.
    7. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    8. Matsudaira, Jordan D., 2008. "Mandatory summer school and student achievement," Journal of Econometrics, Elsevier, vol. 142(2), pages 829-850, February.
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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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