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Regression discontinuity design with many thresholds

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  • Bertanha, Marinho

Abstract

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 consistent and asymptotically normal estimator for such ATEs when heterogeneity follows a non-parametric function of cutoff characteristics in the sharp case. The proposed estimator converges at the minimax optimal rate of root-n for a specific choice of tuning parameters. 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 maximize its precision.

Suggested Citation

  • Bertanha, Marinho, 2020. "Regression discontinuity design with many thresholds," Journal of Econometrics, Elsevier, vol. 218(1), pages 216-241.
  • Handle: RePEc:eee:econom:v:218:y:2020:i:1:p:216-241
    DOI: 10.1016/j.jeconom.2019.09.010
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    4. Marinho Bertanha & Guido W. Imbens, 2020. "External Validity in Fuzzy Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 593-612, July.
    5. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
    6. Tchuente, Guy & Kakeu, Johnson & Francois, John Nana, 2021. "The Forest Behind the Tree: Heterogeneity in How US Governor's Party Affects Black Workers," GLO Discussion Paper Series 947, Global Labor Organization (GLO).
    7. Valentin Verdier, 2020. "Average treatment effects for stayers with correlated random coefficient models of panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(7), pages 917-939, November.
    8. 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).
    9. Yu‐Chin Hsu & Shu Shen, 2021. "Testing monotonicity of conditional treatment effects under regression discontinuity designs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(3), pages 346-366, April.
    10. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    11. 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).
    12. Porter, Jack & Yu, Ping, 2015. "Regression discontinuity designs with unknown discontinuity points: Testing and estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 132-147.
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    15. 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).

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    More about this item

    Keywords

    Regression discontinuity; Multiple cutoffs; Average treatment effect; Peer-effects;
    All these keywords.

    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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