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Local Polynomial Order in Regression Discontinuity Designs


  • Zhuan Pei

    (Cornell University and IZA)

  • David S. Lee

    (Princeton University and NBER)

  • David Card

    (UC Berkeley, NBER and IZA)

  • Andrea Weber

    (Central European University and IZA)


It has become standard practice to use local linear regressions in regression discontinuity designs. This paper highlights that the same theoretical arguments used to justify local linear regression suggest that alternative local polynomials could be preferred. We show in simulations that the local linear estimator is often dominated by alternative polynomial specifications. Additionally, we provide guidance on the selection of the polynomial order. The Monte Carlo evidence shows that the order-selection procedure (which is also readily adapted to fuzzy regression discontinuity and regression kink designs) performs well, particularly with large sample sizes typically found in empirical applications.

Suggested Citation

  • Zhuan Pei & David S. Lee & David Card & Andrea Weber, 2018. "Local Polynomial Order in Regression Discontinuity Designs," Working Papers 622, Princeton University, Department of Economics, Industrial Relations Section..
  • Handle: RePEc:pri:indrel:622

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    References listed on IDEAS

    1. David Card & David S. Lee & Zhuan Pei & Andrea Weber, 2015. "Inference on Causal Effects in a Generalized Regression Kink Design," Econometrica, Econometric Society, vol. 83, pages 2453-2483, November.
    2. David E. Card & David S. Lee & Zhuan Pei & Andrea Weber, 2012. "Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design," NRN working papers 2012-14, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria.
    3. Jens Ludwig & Douglas L. Miller, 2007. "Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design," The Quarterly Journal of Economics, Oxford University Press, vol. 122(1), pages 159-208.
    4. Hall, Peter G. & Racine, Jeffrey S., 2015. "Infinite order cross-validated local polynomial regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 510-525.
    5. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
    6. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-209, January.
    7. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, January.
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    Cited by:

    1. Kyyrä, Tomi & Pesola, Hanna, 2016. "The effects of UI benefits on unemployment and subsequent outcomes: Evidence from a kinked benefit rule," Working Papers 82, VATT Institute for Economic Research.
    2. David Card & David S. Lee & Zhuan Pei & Andrea Weber, 2015. "Inference on Causal Effects in a Generalized Regression Kink Design," Econometrica, Econometric Society, vol. 83, pages 2453-2483, November.
    3. Ari Hyytinen & Jaakko Meriläinen & Tuukka Saarimaa & Otto Toivanen & Janne Tukiainen, 2018. "When does regression discontinuity design work? Evidence from random election outcomes," Quantitative Economics, Econometric Society, vol. 9(2), pages 1019-1051, July.
    4. Kettlewell, Nathan & Siminski, Peter, 2020. "Optimal Model Selection in RDD and Related Settings Using Placebo Zones," IZA Discussion Papers 13639, Institute of Labor Economics (IZA).

    More about this item


    Regression Discontinuity Design; Regression Kink Design; Local Polynomial Estimation; Polynomial Order;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models


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