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

Author

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  • Zhuan Pei

    (Cornell University and IZA)

  • Yi Shen

    (University of Waterloo)

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 first stage 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 paper provides sufficient conditions for identification when only the mismeasured assignment variable, the treatment status and the outcome variable are observed. 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, 2016. "The Devil is in the Tails: Regression Discontinuity Design with Measurement Error in the Assignment Variable," Working Papers 606, Princeton University, Department of Economics, Industrial Relations Section..
    • Handle: RePEc:pri:indrel:606
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    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. 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.
    5. Rodrigo Carril & Andres Gonzalez-Lira & Michael S. Walker, 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. Yingying Dong & Michal Kolesár, 2023. "When Can We Ignore Measurement Error in the Running Variable?," Working Papers 2022-13, Princeton University. Economics Department..
    10. Dean Eckles & Nikolaos Ignatiadis & Stefan Wager & Han Wu, 2020. "Noise-Induced Randomization in Regression Discontinuity Designs," Papers 2004.09458, arXiv.org, revised Nov 2023.
    11. 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.

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    More about this item

    Keywords

    Regression Discontinuity Design; Measurement Error;

    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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