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When Can We Ignore Measurement Error in the Running Variable?

Author

Listed:
  • Yingying Dong

    (University of California Irvine)

  • Michal Kolesár

    (Princeton University)

Abstract

In many empirical applications of regression discontinuity designs, the running variable used by the administrator to assign treatment is only observed with error. We show that, provided the observed running variable (i) correctly classifies the treatment assignment, and (ii) affects the conditional means of the potential outcomes smoothly, ignoring the measurement error nonetheless yields an estimate with a causal interpretation: the average treatment effect for units with the value of the observed running variable equal to the cutoff. To accommodate various types of measurement error, we propose to conduct inference using recently developed bias-aware methods, which remain valid even when discreteness or irregular support in the observed running variable may lead to partial identification. We illustrate the results for both sharp and fuzzy designs in an empirical application.

Suggested Citation

  • Yingying Dong & Michal Kolesár, 2023. "When Can We Ignore Measurement Error in the Running Variable?," Working Papers 2022-13, Princeton University. Economics Department..
    • Handle: RePEc:pri:econom:2022-13
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    File URL: https://www.princeton.edu/~mkolesar/papers/rd_rounded.pdf
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    References listed on IDEAS

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    1. Douglas Almond & Joseph J. Doyle & Amanda E. Kowalski & Heidi Williams, 2010. "Estimating Marginal Returns to Medical Care: Evidence from At-risk Newborns," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(2), pages 591-634.
    2. Pei, Zhuan & Shen, Yi, 2016. "The Devil is in the Tails: Regression Discontinuity Design with Measurement Error in the Assignment Variable," IZA Discussion Papers 10320, Institute of Labor Economics (IZA).
    3. Douglas Almond & Joseph J. Doyle & Amanda E. Kowalski & Heidi Williams, 2011. "The Role of Hospital Heterogeneity in Measuring Marginal Returns to Medical Care: A Reply to Barreca, Guldi, Lindo, and Waddell," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 2125-2131.
    4. Zhuan Pei & Yi Shen, 2017. "The Devil is in the Tails: Regression Discontinuity Design with Measurement Error in the Assignment Variable," Advances in Econometrics, in: Regression Discontinuity Designs, volume 38, pages 455-502, Emerald Group Publishing Limited.
    5. Whitney K. Newey, 2013. "Nonparametric Instrumental Variables Estimation," American Economic Review, American Economic Association, vol. 103(3), pages 550-556, May.
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    Cited by:

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    2. João R. Ferreira & Wayne Aaron Sandholtz & Wayne Sandholtz, 2024. "Sibling Spillovers and Free Schooling," CESifo Working Paper Series 11436, CESifo.
    3. Pastore, Chiara & Jones, Andrew M., 2023. "Human capital consequences of missing out on a grammar school education," Economic Modelling, Elsevier, vol. 126(C).
    4. Xie, Haitian, 2024. "Nonlinear and nonseparable structural functions in regression discontinuity designs with a continuous treatment," Journal of Econometrics, Elsevier, vol. 242(1).

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    More about this item

    Keywords

    Running Variable; Measurement Error; Regression Discontinuity Designs; Bias-aware Methods;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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