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External Validity in Fuzzy Regression Discontinuity Designs


  • Marinho Bertanha
  • Guido W. Imbens


Many empirical studies use Fuzzy Regression Discontinuity (FRD) designs to identify treatment effects when the receipt of treatment is potentially correlated to outcomes. Existing FRD methods identify the local average treatment effect (LATE) on the subpopulation of compliers with values of the forcing variable that are equal to the threshold. We develop methods that assess the plausibility of generalizing LATE to subpopulations other than compliers, and to subpopulations other than those with forcing variable equal to the threshold. Specifically, we focus on testing the equality of the distributions of potential outcomes for treated compliers and always-takers, and for non-treated compliers and never-takers. We show that equality of these pairs of distributions implies that the expected outcome conditional on the forcing variable and the treatment status is continuous in the forcing variable at the threshold, for each of the two treatment regimes. As a matter of routine, we recommend that researchers present graphs with estimates of these two conditional expectations in addition to graphs with estimates of the expected outcome conditional on the forcing variable alone. We illustrate our methods using data on the academic performance of students attending the summer school program in two large school districts in the US.

Suggested Citation

  • Marinho Bertanha & Guido W. Imbens, 2014. "External Validity in Fuzzy Regression Discontinuity Designs," NBER Working Papers 20773, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:20773

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    References listed on IDEAS

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    Cited by:

    1. Thomas Dee & Emily Penner, 2016. "The Causal Effects of Cultural Relevance: Evidence from an Ethnic Studies Curriculum," NBER Working Papers 21865, National Bureau of Economic Research, Inc.
    2. Dan A. Black & Joonhwi Joo & Robert LaLonde & Jeffrey Andrew Smith & Evan J. Taylor, 2017. "Simple Tests for Selection: Learning More from Instrumental Variables," CESifo Working Paper Series 6392, CESifo Group Munich.
    3. Patrick Kline & Christopher R. Walters, 2017. "On Heckits, LATE, and Numerical Equivalence," Papers 1706.05982,, revised Oct 2018.
    4. Christopher Jepsen & Peter Mueser & Kenneth Troske, 2017. "Second Chance for High School Dropouts? A Regression Discontinuity Analysis of Postsecondary Educational Returns to the GED," Journal of Labor Economics, University of Chicago Press, vol. 35(S1), pages 273-304.
    5. Yoichi Arai & Yu-Chin Hsu & Toru Kitagawa & Ismael Mourifie & Yuanyuan Wan, 2018. "Testing Identifying Assumptions In Fuzzy Regression Discontinuity Designs," Working Papers tecipa-623, University of Toronto, Department of Economics.
    6. Amanda E. Kowalski, 2018. "Extrapolation using Selection and Moral Hazard Heterogeneity from within the Oregon Health Insurance Experiment," Cowles Foundation Discussion Papers 2135, Cowles Foundation for Research in Economics, Yale University.
    7. Bertanha, Marinho Angelo & Moreira, Marcelo J., 2017. "Impossible inference in econometrics: theory and applications to regression discontinuity, bunching, and exogeneity tests," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 787, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    8. Thomas S. Dee & Hans Henrik Sievertsen, 2018. "The gift of time? School starting age and mental health," Health Economics, John Wiley & Sons, Ltd., vol. 27(5), pages 781-802, May.
    9. Karthik Muralidharan & Abhijeet Singh & Alejandro J. Ganimian, 2016. "Disrupting Education? Experimental Evidence on Technology-Aided Instruction in India," NBER Working Papers 22923, National Bureau of Economic Research, Inc.
    10. Amanda Kowalski, 2016. "Doing more when you're running LATE: Applying marginal treatment effect methods to examine treatment effect heterogeneity in experiments," Artefactual Field Experiments 00560, The Field Experiments Website.
    11. Gabriel Ehrlich & Jeffrey Perry, 2015. "Do Large-Scale Refinancing Programs Reduce Mortgage Defaults? Evidence From a Regression Discontinuity Design: Working Paper 2015-06," Working Papers 50871, Congressional Budget Office.
    12. Denni Tommasi & Arthur Lewbel & Rossella Calvi, 2017. "LATE with Mismeasured or Misspecified Treatment: An application to Women's Empowerment in India," Working Papers ECARES ECARES 2017-27, ULB -- Universite Libre de Bruxelles.
    13. Gerard, Francois & Rokkanen, Miikka & Rothe, Christoph, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs under Manipulation of the Running Variable, with an Application to Unemployment Insurance in Brazil," CEPR Discussion Papers 11668, C.E.P.R. Discussion Papers.
    14. Amanda E. Kowalski, 2018. "Behavior within a Clinical Trial and Implications for Mammography Guidelines," NBER Working Papers 25049, National Bureau of Economic Research, Inc.
    15. Amanda E. Kowalski, 2016. "Doing More When You're Running LATE: Applying Marginal Treatment Effect Methods to Examine Treatment Effect Heterogeneity in Experiments for the Young and Privately Insured?," Cowles Foundation Discussion Papers 2045, Cowles Foundation for Research in Economics, Yale University.
    16. Marinho Bertanha & Marcelo J. Moreira, 2016. "Impossible Inference in Econometrics: Theory and Applications," Papers 1612.02024,, revised Nov 2018.
    17. Susan Athey & Guido Imbens, 2016. "The Econometrics of Randomized Experiments," Papers 1607.00698,
    18. Isaiah Andrews & Emily Oster, 2017. "Weighting for External Validity," NBER Working Papers 23826, National Bureau of Economic Research, Inc.
    19. Schleicher, Michael & Klonner, Stefan & Sauerborn, Rainer & Sié, Alie & Souares, Aurélia, 2018. "The Demand for Health Insurance in a Poor Economy: Evidence from Burkina Faso," Working Papers 0648, University of Heidelberg, Department of Economics.
    20. Black, Dan A. & Joo, Joonhwi & LaLonde, Robert J. & Smith, Jeffrey A. & Taylor, Evan J., 2015. "Simple Tests for Selection Bias: Learning More from Instrumental Variables," IZA Discussion Papers 9346, Institute for the Study of Labor (IZA).
    21. repec:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-016-0745-z is not listed on IDEAS
    22. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    23. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    24. Matias D. Cattaneo & Luke Keele & Rocio Titiunik & Gonzalo Vazquez-Bare, 2018. "Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs," Papers 1808.04416,
    25. François Gerard & Miikka Rokkanen & Christoph Rothe, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs with a Manipulated Running Variable," NBER Working Papers 22892, National Bureau of Economic Research, Inc.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General


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