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A Correction for Regression Discontinuity Designs with Group-Specific Mismeasurement of the Running Variable

Author

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  • Bartalotti, Otávio

    (Monash University)

  • Brummet, Quentin

    (NORC at the University of Chicago)

  • Dieterle, Steven G.

    (University of Edinburgh)

Abstract

When the running variable in a regression discontinuity (RD) design is measured with error, identification of the local average treatment effect of interest will typically fail. While the form of this measurement error varies across applications, in many cases the measurement error structure is heterogeneous across different groups of observations. We develop a novel measurement error correction procedure capable of addressing heterogeneous mismeasurement structures by leveraging auxiliary information. We also provide adjusted asymptotic variance and standard errors that take into consideration the variability introduced by the estimation of nuisance parameters, and honest confidence intervals that account for potential misspecification. Simulations provide evidence that the proposed procedure corrects the bias introduced by heterogeneous measurement error and achieves empirical coverage closer to nominal test size than "naïve" alternatives. Two empirical illustrations demonstrate that correcting for measurement error can either reinforce the results of a study or provide a new empirical perspective on the data.

Suggested Citation

  • Bartalotti, Otávio & Brummet, Quentin & Dieterle, Steven G., 2019. "A Correction for Regression Discontinuity Designs with Group-Specific Mismeasurement of the Running Variable," IZA Discussion Papers 12366, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp12366
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    References listed on IDEAS

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    1. Davezies, Laurent & Le Barbanchon, Thomas, 2017. "Regression discontinuity design with continuous measurement error in the running variable," Journal of Econometrics, Elsevier, vol. 200(2), pages 260-281.
    2. Sandra E. Black, 1999. "Do Better Schools Matter? Parental Valuation of Elementary Education," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 577-599.
    3. Dieterle, Steven & Bartalotti, Otávio C. & Brummet, Quentin O., 2016. "Revisiting the Effects of Unemployment Insurance Extensions on Unemployment: A Measurement Error-Corrected RD Approach," Staff General Research Papers Archive 3392, Iowa State University, Department of Economics.
    4. Patrick Bayer & Fernando Ferreira & Robert McMillan, 2007. "A Unified Framework for Measuring Preferences for Schools and Neighborhoods," Journal of Political Economy, University of Chicago Press, vol. 115(4), pages 588-638, August.
    5. Beatrix Eugster & Rafael Lalive & Andreas Steinhauer & Josef Zweimüller, 2011. "The Demand for Social Insurance: Does Culture Matter?," Economic Journal, Royal Economic Society, vol. 121(556), pages 413-448, November.
    6. Victor Lavy, 2006. "From Forced Busing to Free Choice in Public Schools: Quasi-Experimental Evidence of Individual and General Effects," NBER Working Papers 11969, National Bureau of Economic Research, Inc.
    7. Lalive, Rafael, 2008. "How do extended benefits affect unemployment duration A regression discontinuity approach," Journal of Econometrics, Elsevier, vol. 142(2), pages 785-806, February.
    8. Alan I. Barreca & Melanie Guldi & Jason M. Lindo & Glen R. Waddell, 2011. "Saving Babies? Revisiting the effect of very low birth weight classification," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 2117-2123.
    9. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
    10. 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.
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    Citations

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    Cited by:

    1. Bartalotti Otávio, 2019. "Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-26, January.
    2. Yang He & Otávio Bartalotti, 2020. "Wild bootstrap for fuzzy regression discontinuity designs: obtaining robust bias-corrected confidence intervals [Using Maimonides’ rule to estimate the effect of class size on scholastic achievemen," The Econometrics Journal, Royal Economic Society, vol. 23(2), pages 211-231.
    3. Conny Wunsch & Véra Zabrodina, 2023. "Unemployment Insurance with Response Heterogeneity," CESifo Working Paper Series 10704, CESifo.
    4. David Slichter, 2023. "The employment effects of the minimum wage: A selection ratio approach to measuring treatment effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 334-357, April.
    5. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    6. Hao Dong & Taisuke Otsu & Luke Taylor, 2023. "Bandwidth selection for nonparametric regression with errors-in-variables," Econometric Reviews, Taylor & Francis Journals, vol. 42(4), pages 393-419, April.
    7. Matias D. Cattaneo & Luke Keele & Rocio Titiunik, 2021. "Covariate Adjustment in Regression Discontinuity Designs," Papers 2110.08410, arXiv.org, revised Aug 2022.
    8. Matias D. Cattaneo & Luke Keele & Rocio Titiunik, 2023. "A Guide to Regression Discontinuity Designs in Medical Applications," Papers 2302.07413, arXiv.org, revised May 2023.
    9. Myoung-Jae Lee & Hyae-Chong Shim & Sang Soo Park, 2023. "Regression Discontinuity with Integer Score and Non-Integer Cutoff," Korean Economic Review, Korean Economic Association, vol. 39, pages 73-101.
    10. 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.
    11. Steven Dieterle & Otávio Bartalotti & Quentin Brummet, 2020. "Revisiting the Effects of Unemployment Insurance Extensions on Unemployment: A Measurement-Error-Corrected Regression Discontinuity Approach," American Economic Journal: Economic Policy, American Economic Association, vol. 12(2), pages 84-114, May.
    12. Carolina Caetano & Gregorio Caetano & Juan Carlos Escanciano, 2023. "Regression discontinuity design with multivalued treatments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(6), pages 840-856, September.
    13. Yingying Dong & Michal Koles'ar, 2021. "When Can We Ignore Measurement Error in the Running Variable?," Papers 2111.07388, arXiv.org, revised Feb 2023.
    14. Yingying Dong & Michal Kolesár, 2023. "When can we ignore measurement error in the running variable?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 735-750, August.

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    More about this item

    Keywords

    nonclassical measurement error; regression discontinuity; heterogeneous measurement error;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior
    • J65 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment Insurance; Severance Pay; Plant Closings

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