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A new estimator of a jump discontinuity in regression

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  • Martins-Filho, Carlos
  • Xie, Sihong
  • Yao, Feng

Abstract

We propose a new class of estimators for a jump discontinuity on nonparametric regression. While there is a vast literature in econometrics that addresses this issue (e.g., Hahn et al., 2001; Porter, 2003; Imbens and Lemieux, 2008; Cattaneo and Escanciano, 2017), the main approach in these studies is to use local polynomial (linear) estimators on both sides of the discontinuity to produce an estimator for the jump that has desirable boundary properties. Our approach extends the regression from both sides of the discontinuity using a theorem of Hestenes (1941). The extended regressions are then estimated and used to construct an estimator for the jump discontinuity that solves the boundary problems normally associated with classical Nadaraya–Watson estimators. We provide asymptotic characterizations for the jump estimators, including bias and variance orders, and asymptotic distributions after suitable centering and normalization. Monte Carlo simulations show that our jump estimators can outperform those based on local polynomial (linear) regression.

Suggested Citation

  • Martins-Filho, Carlos & Xie, Sihong & Yao, Feng, 2022. "A new estimator of a jump discontinuity in regression," Economics Letters, Elsevier, vol. 218(C).
    • Handle: RePEc:eee:ecolet:v:218:y:2022:i:c:s0165176522002440
    DOI: 10.1016/j.econlet.2022.110711
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    References listed on IDEAS

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    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. 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. Kairat Mynbaev & Carlos Martins-Filho, 2019. "Unified estimation of densities on bounded and unbounded domains," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 853-887, August.
    4. 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.
    5. Hardle, W. & Marron, J.S. & Wand, Mp., 1990. "Bandwith choice for density derivatives," LIDAM Reprints CORE 945, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Guido Imbens & Karthik Kalyanaraman, 2012. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 933-959.
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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