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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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    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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