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Local Composite Quantile Regression for Regression Discontinuity

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  • Xiao Huang
  • Zhaoguo Zhan

Abstract

We introduce the local composite quantile regression (LCQR) to causal inference in regression discontinuity (RD) designs. Kai et al. (2010) study the efficiency property of LCQR, while we show that its nice boundary performance translates to accurate estimation of treatment effects in RD under a variety of data generating processes. Moreover, we propose a bias-corrected and standard error-adjusted t-test for inference, which leads to confidence intervals with good coverage probabilities. A bandwidth selector is also discussed. For illustration, we conduct a simulation study and revisit a classic example from Lee (2008). A companion R package rdcqr is developed.

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  • Xiao Huang & Zhaoguo Zhan, 2020. "Local Composite Quantile Regression for Regression Discontinuity," Papers 2009.03716, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2009.03716
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    1. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    2. Frandsen, Brigham R. & Frölich, Markus & Melly, Blaise, 2012. "Quantile treatment effects in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 168(2), pages 382-395.
    3. Timothy B. Armstrong & Michal Kolesár, 2018. "Optimal Inference in a Class of Regression Models," Econometrica, Econometric Society, vol. 86(2), pages 655-683, March.
    4. 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.
    5. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    6. 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.
    7. 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.
    8. 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, President and Fellows of Harvard College, vol. 122(1), pages 159-208.
    9. 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.
    10. 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.
    11. Li, Degui & Li, Runze, 2016. "Local composite quantile regression smoothing for Harris recurrent Markov processes," Journal of Econometrics, Elsevier, vol. 194(1), pages 44-56.
    12. Zhao, Zhibiao & Xiao, Zhijie, 2014. "Efficient Regressions Via Optimally Combining Quantile Information," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1272-1314, December.
    13. 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.
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    Cited by:

    1. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    2. Zhen Yu & Keming Yu & Wolfgang K. Härdle & Xueliang Zhang & Kai Wang & Maozai Tian, 2022. "Bayesian spatio‐temporal modeling for the inpatient hospital costs of alcohol‐related disorders," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 644-667, December.
    3. Guy Tchuente & Johnson Kakeu & John Nana Francois, 2021. "The Forest Behind the Tree: Heterogeneity in How US Governor's Party Affects Black Workers," Papers 2110.00582, arXiv.org.

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