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Testing identifying assumptions in fuzzy regression discontinuity designs

Author

Listed:
  • Yoichi Arai

    (Institute for Fiscal Studies)

  • Yu-Chin Hsu

    (Institute for Fiscal Studies)

  • Toru Kitagawa

    (Institute for Fiscal Studies and cemmap and University College London)

  • Ismael Mourifié

    (Institute for Fiscal Studies)

  • Yuanyuan Wan

    (Institute for Fiscal Studies)

Abstract

We propose a new specification test for assessing the validity of fuzzy regression discontinuity designs (FRD-validity). We derive a new set of testable implications, characterized by a set of inequality restrictions on the joint distribution of observed outcomes and treatment status at the cut-off. We show that this new characterization exploits all the information in the data useful for detecting violations of FRD-validity. Our approach differs from, and complements existing approaches that test continuity of the distributions of running variables and baseline covariates at the cut-off since ours focuses on the distribution of the observed outcome and treatment status. We show that the proposed test has appealing statistical properties. It controls size in large sample uniformly over a large class of distributions, is consistent against all fixed alternatives, and has non-trivial power against some local alternatives. We apply our test to evaluate the validity of two FRD designs. The test does not reject the FRD-validity in the class size design studied by Angrist and Lavy (1999) and rejects in the insurance subsidy design for poor households in Colombia studied by Miller, Pinto, and Vera-Hernández (2013) for some outcome variables, while existing density tests suggest the opposite in each of the cases.

Suggested Citation

  • Yoichi Arai & Yu-Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2019. "Testing identifying assumptions in fuzzy regression discontinuity designs," CeMMAP working papers CWP10/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:10/19
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    References listed on IDEAS

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    Cited by:

    1. Takuya Ishihara & Masayuki Sawada, 2020. "Manipulation-Robust Regression Discontinuity Designs," Papers 2009.07551, arXiv.org, revised Jun 2021.
    2. 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).
    3. Acerenza, Santiago & Bartalotti, Otávio & Kedagni, Desire, 2021. "Testing Identifying Assumptions in Bivariate Probit Models," ISU General Staff Papers 202103290700001124, Iowa State University, Department of Economics.
    4. Atila Abdulkadiroglu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak, 2019. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Cowles Foundation Discussion Papers 2170R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2020.
    5. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.

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    More about this item

    Keywords

    Fuzzy regression discontinuity design; nonparametric test; inequality restriction; multiplier bootstrap;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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