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Regression discontinuity designs, white noise models, and minimax

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  • Tuvaandorj, Purevdorj
Abstract
This paper studies an approximation of sharp regression discontinuity (RD) designs with normal homoskedastic errors by ideal Gaussian white noise models with discontinuous drifts. After establishing an asymptotic equivalence of the two models, we first provide a simple derivation of a lower bound on the minimax optimal convergence rate for estimating the discontinuity size in a derivative (of an arbitrary order) of the regression function. We show that the optimal convergence rate is attained by the local polynomial estimator. We also establish an analogous correspondence between the RD designs with an unknown threshold and a convolution white noise model, and derive the minimax optimal rate for estimating the discontinuity location in a derivative of the regression function.

Suggested Citation

  • Tuvaandorj, Purevdorj, 2020. "Regression discontinuity designs, white noise models, and minimax," Journal of Econometrics, Elsevier, vol. 218(2), pages 587-608.
    • Handle: RePEc:eee:econom:v:218:y:2020:i:2:p:587-608
    DOI: 10.1016/j.jeconom.2020.04.030
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    3. Wanying Rao & Pingfeng Liu, 2024. "Can Digital Innovation Improve Green Total Factor Productivity: Evidence from Digital Patents of China," Sustainability, MDPI, vol. 16(10), pages 1-21, May.

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    More about this item

    Keywords

    Asymptotic equivalence; Minimax estimation; Regression discontinuity design; White noise model;
    All these keywords.

    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
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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