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Inference in Regression Discontinuity Designs with High-Dimensional Covariates

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  • Alexander Krei{ss}
  • Christoph Rothe

Abstract

We study regression discontinuity designs in which many predetermined covariates, possibly much more than the number of observations, can be used to increase the precision of treatment effect estimates. We consider a two-step estimator which first selects a small number of "important" covariates through a localized Lasso-type procedure, and then, in a second step, estimates the treatment effect by including the selected covariates linearly into the usual local linear estimator. We provide an in-depth analysis of the algorithm's theoretical properties, showing that, under an approximate sparsity condition, the resulting estimator is asymptotically normal, with asymptotic bias and variance that are conceptually similar to those obtained in low-dimensional settings. Bandwidth selection and inference can be carried out using standard methods. We also provide simulations and an empirical application.

Suggested Citation

  • Alexander Krei{ss} & Christoph Rothe, 2021. "Inference in Regression Discontinuity Designs with High-Dimensional Covariates," Papers 2110.13725, arXiv.org, revised May 2022.
    • Handle: RePEc:arx:papers:2110.13725
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    References listed on IDEAS

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    1. Markus Frölich & Martin Huber, 2019. "Including Covariates in the Regression Discontinuity Design," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 736-748, October.
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    3. Claudia Noack & Tomasz Olma & Christoph Rothe, 2021. "Flexible Covariate Adjustments in Regression Discontinuity Designs," Papers 2107.07942, arXiv.org, revised May 2023.
    4. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    5. David Card & Raj Chetty & Andrea Weber, 2007. "Cash-on-Hand and Competing Models of Intertemporal Behavior: New Evidence from the Labor Market," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(4), pages 1511-1560.
    6. Yingying Dong, 2018. "Alternative Assumptions to Identify LATE in Fuzzy Regression Discontinuity Designs," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 80(5), pages 1020-1027, October.
    7. Myung Hwan Seo & Yoichi Arai & Taisuke Otsu, 2021. "Regression Discontinuity Design with Potentially Many Covariates," Working Paper Series no142, Institute of Economic Research, Seoul National University.
    8. 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.
    9. 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. Myung Hwan Seo & Yoichi Arai & Taisuke Otsu, 2021. "Regression Discontinuity Design with Potentially Many Covariates," Working Paper Series no142, Institute of Economic Research, Seoul National University.

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