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Inference in Regression Discontinuity Designs with a Discrete Running Variable

Author

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  • Kolesár, Michal

    () (Princeton University)

  • Rothe, Christoph

    () (University of Mannheim)

Abstract

We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable. We derive theoretical results and present simulation and empirical evidence showing that these CIs have poor coverage properties and therefore recommend that they not be used in practice. We also suggest alternative CIs with guaranteed coverage properties under easily interpretable restrictions on the conditional expectation function.

Suggested Citation

  • Kolesár, Michal & Rothe, Christoph, 2016. "Inference in Regression Discontinuity Designs with a Discrete Running Variable," IZA Discussion Papers 9990, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp9990
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    References listed on IDEAS

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    1. Paul J. Devereux & Robert A. Hart, 2010. "Forced to be Rich? Returns to Compulsory Schooling in Britain," Economic Journal, Royal Economic Society, vol. 120(549), pages 1345-1364, December.
    2. Yingying Dong, 2012. "Regression Discontinuity Applications with Rounding Errors in the Running Variable," Working Papers 111206, University of California-Irvine, Department of Economics.
    3. Andrew Gelman & Guido Imbens, 2014. "Why High-order Polynomials Should not be Used in Regression Discontinuity Designs," NBER Working Papers 20405, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Dan Anderberg & Jesper Bagger & V. Bhaskar & Tanya Wilson, 2019. "Marriage market equilibrium, qualifications, and ability," CESifo Working Paper Series 7570, CESifo Group Munich.
    2. Lochmann, Alexia & Rapoport, Hillel & Speciale, Biagio, 2019. "The effect of language training on immigrants’ economic integration: Empirical evidence from France," European Economic Review, Elsevier, vol. 113(C), pages 265-296.
    3. Martin Huber, 2019. "An introduction to flexible methods for policy evaluation," Papers 1910.00641, arXiv.org.
    4. Alessandro Tondini & Cally Ardington & Ingrid Woolard, 2017. "Public pensions and elderly informal employment: Evidence from a change in retirement age in South Africa," SALDRU Working Papers 206, Southern Africa Labour and Development Research Unit, University of Cape Town.
    5. Eric J. Brunner & Shaun Dougherty & Stephen L. Ross, 2019. "The Effects of Career and Technical Education: Evidence from the Connecticut Technical High School System," Working papers 2019-13, University of Connecticut, Department of Economics.
    6. Lee, M-j.; & Park, S-s.; & Shim, H-c.;, 2019. "Regression Discontinuity with Integer Running Variable and Non-Integer Cutoff: Dental Care Program Effect on Expenditure," Health, Econometrics and Data Group (HEDG) Working Papers 19/16, HEDG, c/o Department of Economics, University of York.
    7. Eren, Ozkan & Depew, Briggs & Barnes, Stephen, 2017. "Test-based promotion policies, dropping out, and juvenile crime," Journal of Public Economics, Elsevier, vol. 153(C), pages 9-31.
    8. Heinesen, Eskil, 2018. "Admission to higher education programmes and student educational outcomes and earnings–Evidence from Denmark," Economics of Education Review, Elsevier, vol. 63(C), pages 1-19.
    9. Gaggero, Alessio & Haile, Getinet Astatike, 2019. "Does Class Size Matter in Postgraduate Education?," IZA Discussion Papers 12628, Institute of Labor Economics (IZA).
    10. Zhao, Meng & Konishi, Yoshifumi & Noguchi, Haruko, 2017. "Retiring for better health? Evidence from health investment behaviors in Japan," Japan and the World Economy, Elsevier, vol. 42(C), pages 56-63.
    11. Agata MAIDA & Daniela SONEDDA, 2019. "Getting Out of the Starting Gate on the Right Foot: Employment Effects of Investment in Human Capital," Departmental Working Papers 2019-03, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    12. Navarro-Palau, Patricia, 2017. "Effects of differentiated school vouchers: Evidence from a policy change and date of birth cutoffs," Economics of Education Review, Elsevier, vol. 58(C), pages 86-107.
    13. Guido Imbens & Stefan Wager, 2019. "Optimized Regression Discontinuity Designs," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 264-278, May.
    14. Amy Ellen Schwartz & Douglas Almond & Ajin Lee, 2016. "Retention Heterogeneity in New York City Schools," Center for Policy Research Working Papers 198, Center for Policy Research, Maxwell School, Syracuse University.
    15. Rebecca Mary Myerson & Reginald Tucker-Seeley & Dana Goldman & Darius N. Lakdawalla, 2019. "Does Medicare Coverage Improve Cancer Detection and Mortality Outcomes?," NBER Working Papers 26292, National Bureau of Economic Research, Inc.
    16. He, Yang & Bartalotti, Otávio, 2019. "Wild Bootstrap for Fuzzy Regression Discontinuity Designs: Obtaining Robust Bias-Corrected Confidence Intervals," IZA Discussion Papers 12801, Institute of Labor Economics (IZA).
    17. Ozkan Eren & Michael F. Lovenheim & Naci H. Mocan, 2018. "The Effect of Grade Retention on Adult Crime: Evidence from a Test-Based Promotion Policy," NBER Working Papers 25384, National Bureau of Economic Research, Inc.

    More about this item

    Keywords

    regression discontinuity design; discrete running variable; clustered standard errors;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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