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Regression discontinuity design with covariates

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  • Markus Frölich

Abstract

In this paper, the regression discontinuity design (RDD) is generalized to account for differences in observed covariates X in a fully nonparametric way. It is shown that the treatment effect can be estimated at the rate for one-dimensional nonparametric regression irrespective of the dimension of X. It thus extends the analysis of Hahn, Todd and van der Klaauw (2001) and Porter (2003), who examined identification and estimation without covariates, requiring assumptions that may often be too strong in applications. In many applications, individuals to the left and right of the threshold differ in observed characteristics. Houses may be constructed in different ways across school attendance district boundaries. Firms may differ around a threshold that implies certain legal changes, etc. Accounting for these differences in covariates is important to reduce bias. In addition, accounting for covariates may also reduces variance. Finally, estimation of quantile treatment effects (QTE) is also considered.

Suggested Citation

  • Markus Frölich, 2007. "Regression discontinuity design with covariates," University of St. Gallen Department of Economics working paper series 2007 2007-32, Department of Economics, University of St. Gallen.
    • Handle: RePEc:usg:dp2007:2007-32
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    References listed on IDEAS

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    Cited by:

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    2. Reto Foellmi & Stefan Legge & Lukas Schmid, 2016. "Do Professionals Get It Right? Limited Attention and Risk‐taking Behaviour," Economic Journal, Royal Economic Society, vol. 0(592), pages 724-755, May.
    3. 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.
    4. Bartalotti, Otávio C. & Calhoun, Gray & He, Yang, 2016. "Bootstrap Confidence Intervals for Sharp Regression Discontinuity Designs with the Uniform Kernel," ISU General Staff Papers 201605010700001003, Iowa State University, Department of Economics.
    5. Tohari, Achmad & Parsons, Christopher & Rammohan, Anu, 2017. "Does Information Empower the Poor? Evidence from Indonesia's Social Security Card," IZA Discussion Papers 11137, Institute of Labor Economics (IZA).
    6. Ciani, Emanuele, 2016. "Retirement, pension eligibility and home production," Labour Economics, Elsevier, vol. 38(C), pages 106-120.
    7. Bergolo, Marcelo & Galván, Estefanía, 2018. "Intra-household Behavioral Responses to Cash Transfer Programs. Evidence from a Regression Discontinuity Design," World Development, Elsevier, vol. 103(C), pages 100-118.
    8. Legge, Stefan & Schmid, Lukas, 2016. "Media attention and betting markets," European Economic Review, Elsevier, vol. 87(C), pages 304-333.
    9. Nadiia Matsiuk, 2022. "Thrive, survive, or perish: The impact of regional autonomy on the demographic dynamics of Italian Alpine territories," Journal of Regional Science, Wiley Blackwell, vol. 62(5), pages 1512-1558, November.
    10. Yusuke Narita & Kohei Yata, 2021. "Algorithm is Experiment: Machine Learning, Market Design, and Policy Eligibility Rules," Working Papers 2021-022, Human Capital and Economic Opportunity Working Group.
    11. Tohari, Achmad & Parsons, Christopher & Rammohan, Anu, 2021. "Literacy and Information," IZA Discussion Papers 14358, Institute of Labor Economics (IZA).
    12. Achmad Tohari & Christopher Parsons & Anu Rammohan, 2017. "Does Information Empower the Poor? Evidence from Indonesia’s Social Security Card," Working Papers id:12241, eSocialSciences.
    13. Hidano, Noboru & Hoshino, Tadao & Sugiura, Ayako, 2015. "The effect of seismic hazard risk information on property prices: Evidence from a spatial regression discontinuity design," Regional Science and Urban Economics, Elsevier, vol. 53(C), pages 113-122.

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    More about this item

    Keywords

    Treatment effect; causal effect; complier; LATE; nonparametric regression; endogeneity;
    All these keywords.

    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
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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