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Adaptive Estimation of the Regression Discontinuity Model

Author

Listed:
  • Yixiao Sun

    (University of California, San Diego)

Abstract
In order to reduce the finite sample bias and improve the rate of convergence, local polynomial estimators have been introduced into the econometric literature to estimate the regression discontinuity model. In this paper, we show that, when the degree of smoothness is known, the local polynomial estimator achieves the optimal rate of convergence within the Hölder smoothness class. However, when the degree of smoothness is not known, the local polynomial estimator may actually inflate the finite sample bias and reduce the rate of convergence. We propose an adaptive version of the local polynomial estimator which selects both the bandwidth and the polynomial order adaptively and show that the adaptive estimator achieves the optimal rate of convergence up to a logarithm factor without knowing the degree of smoothness. Simulation results show that the finite sample performance of the locally cross-validated adaptive estimator is robust to the parameter combinations and data generating processes, reflecting the adaptive nature of the estimator. The root mean squared error of the adaptive estimator compares favorably to local polynomial estimators in the Monte Carlo experiments.

Suggested Citation

  • Yixiao Sun, 2005. "Adaptive Estimation of the Regression Discontinuity Model," Econometrics 0506003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0506003
    Note: Type of Document - pdf; pages: 41
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0506/0506003.pdf
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    References listed on IDEAS

    as
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    8. 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.
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    Cited by:

    1. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    2. Ping Yu & Qin Liao & Peter C.B. Phillips, 2019. "Inference and Specification Testing in Threshold Regression with Endogeneity," Cowles Foundation Discussion Papers 2209, Cowles Foundation for Research in Economics, Yale University.
    3. Jaeger, Simon C & Ganong, Peter Nathan, 2014. "A Permutation Test and Estimation Alternatives for the Regression Kink Design," Scholarly Articles 34222894, Harvard University Department of Economics.
    4. Wilbert Van Der Klaauw, 2008. "Regression–Discontinuity Analysis: A Survey of Recent Developments in Economics," LABOUR, CEIS, vol. 22(2), pages 219-245, June.
    5. Tuvaandorj, Purevdorj, 2020. "Regression discontinuity designs, white noise models, and minimax," Journal of Econometrics, Elsevier, vol. 218(2), pages 587-608.
    6. Agyei-Holmes,Andrew & Buehren,Niklas & Goldstein,Markus P. & Osei,Robert Darko & Osei-Akoto,Isaac & Udry,Christopher Robert, 2020. "The Effects of Land Title Registration on Tenure Security, Investment and the Allocation of Productive Resources : Evidence from Ghana," Policy Research Working Paper Series 9376, The World Bank.
    7. Torres, Santiago, 2023. "The Oracle Local Polynomial Estimator," Documentos CEDE 20937, Universidad de los Andes, Facultad de Economía, CEDE.
    8. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    9. Xie, Haitian, 2024. "Nonlinear and nonseparable structural functions in regression discontinuity designs with a continuous treatment," Journal of Econometrics, Elsevier, vol. 242(1).
    10. Porter, Jack & Yu, Ping, 2015. "Regression discontinuity designs with unknown discontinuity points: Testing and estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 132-147.
    11. Bertanha, Marinho, 2020. "Regression discontinuity design with many thresholds," Journal of Econometrics, Elsevier, vol. 218(1), pages 216-241.
    12. Ganong, Peter & Jäger, Simon, 2014. "A Permutation Test and Estimation Alternatives for the Regression Kink Design," IZA Discussion Papers 8282, Institute of Labor Economics (IZA).

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    More about this item

    Keywords

    Adaptive estimator; local cross validation; local polynomial; minimax rate; optimal bandwidth; optimal smoothness parameter;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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