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Understanding Estimators of Treatment Effects in Regression Discontinuity Designs

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  • Ping Yu

Abstract

In this paper, we propose two new estimators of treatment effects in regression discontinuity designs. These estimators can aid understanding of the existing estimators such as the local polynomial estimator and the partially linear estimator. The first estimator is the partially polynomial estimator which extends the partially linear estimator by further incorporating derivative differences of the conditional mean of the outcome on the two sides of the discontinuity point. This estimator is related to the local polynomial estimator by a relocalization effect. Unlike the partially linear estimator, this estimator can achieve the optimal rate of convergence even under broader regularity conditions. The second estimator is an instrumental variable estimator in the fuzzy design. This estimator will reduce to the local polynomial estimator if higher order endogeneities are neglected. We study the asymptotic properties of these two estimators and conduct simulation studies to confirm the theoretical analysis.

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  • Ping Yu, 2016. "Understanding Estimators of Treatment Effects in Regression Discontinuity Designs," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 586-637, April.
    • Handle: RePEc:taf:emetrv:v:35:y:2016:i:4:p:586-637
    DOI: 10.1080/07474938.2013.833831
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    1. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
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    Cited by:

    1. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    2. Zhong, Xiaohan & Zhu, Lin, 2021. "The medium-run efficiency consequences of unfair school matching: Evidence from Chinese college admissions," Journal of Econometrics, Elsevier, vol. 224(2), pages 271-285.

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