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Regression Discontinuity Design with Many Thresholds


  • BERTANHA, Marinho


Numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments. A common practice is to normalize all the cutoffs to zero and estimate one effect. This procedure identifies the average treatment effect (ATE) on the observed distribution of individuals local to existing cutoffs. However, researchers often want to make inferences on more meaningful ATEs computed over general counterfactual distributions of individuals rather than simply the observed distribution of individuals local to existing cutoffs. This paper proposes a root-n consistent and asymptotically normal estimator for such ATEs when heterogeneity follows a non-parametric function of cutoff characteristics in the sharp case. It shows that identification in the fuzzy case with multiple cutoffs is impossible unless heterogeneity follows a finite dimensional function of cutoff characteristics. Under parametric heterogeneity, this paper proposes an ATE estimator for the fuzzy case that optimally combines observations to minimize its mean squared error.

Suggested Citation

  • BERTANHA, Marinho, 2016. "Regression Discontinuity Design with Many Thresholds," CORE Discussion Papers 2016026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2016026

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    Cited by:

    1. Marinho Bertanha & Marcelo J. Moreira, 2016. "Impossible Inference in Econometrics: Theory and Applications," Papers 1612.02024,, revised Feb 2020.
    2. Marinho Bertanha & Guido W. Imbens, 2014. "External Validity in Fuzzy Regression Discontinuity Designs," NBER Working Papers 20773, National Bureau of Economic Research, Inc.
    3. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    4. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    5. Benjamin Faber & Rosa Sanchis-Guarner & Felix Weinhardt, 2015. "ICT and Education: Evidence from Student Home Addresses," SERC Discussion Papers 0186, Spatial Economics Research Centre, LSE.
    6. Yingying DONG & Ying-Ying LEE & Michael GOU, 2019. "Regression Discontinuity Designs with a Continuous Treatment," Discussion papers 19058, Research Institute of Economy, Trade and Industry (RIETI).
    7. von Buxhoeveden, Mathias, 2019. "Unemployment insurance and youth labor market entry," Working Paper Series 2019:12, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    8. 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, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    9. Booij, Adam S. & Haan, Ferry & Plug, Erik, 2017. "Can Gifted and Talented Education Raise the Academic Achievement of All High-Achieving Students?," IZA Discussion Papers 10836, Institute of Labor Economics (IZA).
    10. Miguel Ángel Borrella Mas & Mariano Bosch Mossi & Marcello Sartarelli, 2016. "Non-Contributory Pensions Number-Gender Effects on Poverty and Household Decisions," Working Papers. Serie AD 2016-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    11. David, Guy & Smith-McLallen, Aaron & Ukert, Benjamin, 2019. "The effect of predictive analytics-driven interventions on healthcare utilization," Journal of Health Economics, Elsevier, vol. 64(C), pages 68-79.

    More about this item


    Regression Discontinuity Designs; Multiple Cutoffs; Average Treat- ment Effect; Alternative Asymptotics; Peer-effects;

    JEL classification:

    • 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education


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