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Empirical likelihood for regression discontinuity design

Author

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  • Otsu, Taisuke
  • Xu, Ke-Li
  • Matsushita, Yukitoshi
Abstract
This paper proposes empirical likelihood based inference methods for causal effects identified from regression discontinuity designs. We consider both the sharp and fuzzy regression discontinuity designs and treat the regression functions as nonparametric. The proposed inference procedures do not require asymptotic variance estimation and the confidence sets have natural shapes, unlike the conventional Wald-type method. These features are illustrated by simulations and an empirical example which evaluates the effect of class size on pupils’ scholastic achievements. Furthermore, for the sharp regression discontinuity design, we show that the empirical likelihood statistic admits a higher-order refinement, so-called the Bartlett correction. Bandwidth selection methods are also discussed.

Suggested Citation

  • Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    • Handle: RePEc:eee:econom:v:186:y:2015:i:1:p:94-112
    DOI: 10.1016/j.jeconom.2014.04.023
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    Cited by:

    1. Lee Myoung-Jae, 2017. "Regression Discontinuity with Errors in the Running Variable: Effect on Truthful Margin," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-8, January.
    2. Donna Feir & Thomas Lemieux & Vadim Marmer, 2016. "Weak Identification in Fuzzy Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 185-196, April.
    3. Chiang, Harold D. & Hsu, Yu-Chin & Sasaki, Yuya, 2019. "Robust uniform inference for quantile treatment effects in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 211(2), pages 589-618.
    4. Hector Galindo Silva; Nibene Habib Somé; Guy Tchuente & Nibene Habib Somé & Guy Tchuente, 2019. "Does Obamacare Care? A Fuzzy Difference-in-discontinuities Approach," Vniversitas Económica 17211, Universidad Javeriana - Bogotá.
    5. Xu, Ke-Li, 2020. "Inference of local regression in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 218(2), pages 532-560.
    6. Xu, Ke-Li, 2017. "Regression discontinuity with categorical outcomes," Journal of Econometrics, Elsevier, vol. 201(1), pages 1-18.
    7. Xu, Ke-Li, 2018. "A semi-nonparametric estimator of regression discontinuity design with discrete duration outcomes," Journal of Econometrics, Elsevier, vol. 206(1), pages 258-278.
    8. Tuvaandorj, Purevdorj, 2020. "Regression discontinuity designs, white noise models, and minimax," Journal of Econometrics, Elsevier, vol. 218(2), pages 587-608.
    9. Yingying DONG & Ying-Ying LEE & Michael GOU, 2019. "Regression Discontinuity Designs with a Continuous Treatment," Discussion papers 19058, Research Institute of Economy, Trade and Industry (RIETI).
    10. Philip Gleason & Alexandra Resch & Jillian Berk, 2018. "RD or Not RD: Using Experimental Studies to Assess the Performance of the Regression Discontinuity Approach," Evaluation Review, , vol. 42(1), pages 3-33, February.
    11. Hector Galindo-Silva & Nibene Habib Some & Guy Tchuente, 2018. "Fuzzy Difference-in-Discontinuities: Identification Theory and Application to the Affordable Care Act," Papers 1812.06537, arXiv.org, revised Apr 2021.
    12. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    13. Jun Ma & Zhengfei Yu, 2020. "Empirical Likelihood Covariate Adjustment for Regression Discontinuity Designs," Papers 2008.09263, arXiv.org, revised May 2024.

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    More about this item

    Keywords

    Empirical likelihood; Nonparametric methods; Regression discontinuity design; Treatment effect; Bartlett correction;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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