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Testing Identifying Assumptions In Fuzzy Regression Discontinuity Designs

Author

Listed:
  • Yoichi Arai
  • Yu-Chin Hsu
  • Toru Kitagawa
  • Ismael Mourifie
  • Yuanyuan Wan

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 Mourifie & Yuanyuan Wan, 2018. "Testing Identifying Assumptions In Fuzzy Regression Discontinuity Designs," Working Papers tecipa-623, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-623
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    References listed on IDEAS

    as
    1. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    2. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    3. François Gerard & Miikka Rokkanen & Christoph Rothe, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs with a Manipulated Running Variable," NBER Working Papers 22892, National Bureau of Economic Research, Inc.
    4. Marinho Bertanha & Guido W. Imbens, 2014. "External Validity in Fuzzy Regression Discontinuity Designs," NBER Working Papers 20773, National Bureau of Economic Research, Inc.
    5. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    6. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    7. Arai, Yoichi & Ichimura, Hidehiko, 2016. "Optimal bandwidth selection for the fuzzy regression discontinuity estimator," Economics Letters, Elsevier, vol. 141(C), pages 103-106.
    8. Yingying Dong & Arthur Lewbel, 2015. "Identifying the Effect of Changing the Policy Threshold in Regression Discontinuity Models," The Review of Economics and Statistics, MIT Press, vol. 97(5), pages 1081-1092, December.
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    More about this item

    Keywords

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

    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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