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The Devil is in the Tails: Regression Discontinuity Design with Measurement Error in the Assignment Variable

In: Regression Discontinuity Designs

Author

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  • Zhuan Pei
  • Yi Shen

Abstract

Identification in a regression discontinuity (RD) design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known threshold. If the assignment variable is measured with error, however, the discontinuity in the relationship between the probability of treatment and the observed mismeasured assignment variable may disappear. Therefore, the presence of measurement error in the assignment variable poses a challenge to treatment effect identification. This chapter provides sufficient conditions to identify the RD treatment effect using the mismeasured assignment variable, the treatment status and the outcome variable. We prove identification separately for discrete and continuous assignment variables and study the properties of various estimation procedures. We illustrate the proposed methods in an empirical application, where we estimate Medicaid takeup and its crowdout effect on private health insurance coverage.

Suggested Citation

  • 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.
    • Handle: RePEc:eme:aecozz:s0731-905320170000038019
    DOI: 10.1108/S0731-905320170000038019
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    Cited by:

    1. Christina Korting & Carl Lieberman & Jordan Matsudaira & Zhuan Pei & Yi Shen, 2023. "Visual Inference and Graphical Representation in Regression Discontinuity Designs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(3), pages 1977-2019.
    2. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    3. Gallagher, Emily A. & Gopalan, Radhakrishnan & Grinstein-Weiss, Michal, 2019. "The effect of health insurance on home payment delinquency: Evidence from ACA Marketplace subsidies," Journal of Public Economics, Elsevier, vol. 172(C), pages 67-83.
    4. Rodrigo Carril & Andres Gonzalez-Lira & Michael S. Walker, 2026. "Competition under Incomplete Contracts and the Design of Procurement Policies," American Economic Review, American Economic Association, vol. 116(2), pages 535-581, February.
    5. Andres Gonzalez-Lira & Michael S. Walker & Rodrigo Carril, 2022. "Competition under Incomplete Contracts and the Design of Procurement Policies," Working Papers 1327, Barcelona School of Economics.
    6. Deng, Taotao & Hu, Yukun & Ma, Mulan, 2019. "Regional policy and tourism: A quasi-natural experiment," Annals of Tourism Research, Elsevier, vol. 74(C), pages 1-16.
    7. Matias D. Cattaneo & Luke Keele & Rocio Titiunik, 2021. "Covariate Adjustment in Regression Discontinuity Designs," Papers 2110.08410, arXiv.org, revised Aug 2022.
    8. Gastón Illanes & Sarah Moshary, 2020. "Market Structure and Product Assortment: Evidence from a Natural Experiment in Liquor Licensure," NBER Working Papers 27016, National Bureau of Economic Research, Inc.
    9. Mauricio Villamizar‐Villegas & Freddy A. Pinzon‐Puerto & Maria Alejandra Ruiz‐Sanchez, 2022. "A comprehensive history of regression discontinuity designs: An empirical survey of the last 60 years," Journal of Economic Surveys, Wiley Blackwell, vol. 36(4), pages 1130-1178, September.
    10. Yingying Dong & Michal Kolesár, 2023. "When Can We Ignore Measurement Error in the Running Variable?," Working Papers 2022-13, Princeton University. Economics Department..
    11. Dean Eckles & Nikolaos Ignatiadis & Stefan Wager & Han Wu, 2020. "Noise-Induced Randomization in Regression Discontinuity Designs," Papers 2004.09458, arXiv.org, revised Mar 2025.
    12. Strazzeri, Maurizio, 2021. "Assessing the Role of Asylum Policies in Refugees' Labor Market Integration: The Case of Protection Statuses in the German Asylum System," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242395, Verein für Socialpolitik / German Economic Association.
    13. Wei, Wei & Young, Alex, 2025. "Beyond Russell reconstitution: A re-examination of methodologies for natural experiments," Journal of Corporate Finance, Elsevier, vol. 91(C).

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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