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Testing identifying assumptions in fuzzy regression discontinuity designs

Author

Listed:
  • Yoichi Arai
  • Yu‐Chin Hsu
  • Toru Kitagawa
  • Ismael Mourifié
  • 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 of the information in the data that is 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 in that we focus on the distribution of the observed outcome and treatment status. We show that the proposed test has appealing statistical properties. It controls size in a large sample setting uniformly over a large class of data generating processes, 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 FRD‐validity in the class size design studied by Angrist and Lavy (1999) but rejects it in the insurance subsidy design for poor households in Colombia studied by Miller, Pinto, and Vera‐Hernández (2013) for some outcome variables. Existing density continuity tests suggest the opposite in each of the two cases.

Suggested Citation

  • Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    • Handle: RePEc:wly:quante:v:13:y:2022:i:1:p:1-28
    DOI: 10.3982/QE1367
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    2. Takuya Ishihara & Masayuki Sawada, 2020. "Manipulation-Robust Regression Discontinuity Designs," Papers 2009.07551, arXiv.org, revised Sep 2024.
    3. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    4. Santiago Acerenza & Ot'avio Bartalotti & Federico Veneri, 2024. "Testing identifying assumptions in Tobit Models," Papers 2408.02573, arXiv.org.
    5. Shenglong Liu & Yuanyuan Wan & Xiaoming Zhang, 2024. "Retirement Spillover Effects on Spousal Health in Urban China," Journal of Family and Economic Issues, Springer, vol. 45(3), pages 756-783, September.
    6. Santiago Acerenza & Otávio Bartalotti & Désiré Kédagni, 2023. "Testing identifying assumptions in bivariate probit models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 407-422, April.
    7. 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).
    8. Hsu, Yu-Chin & Shiu, Ji-Liang & Wan, Yuanyuan, 2024. "Testing identification conditions of LATE in fuzzy regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 241(1).
    9. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    10. Mario Fiorini & Katrien Stevens, 2021. "Scrutinizing the Monotonicity Assumption in IV and fuzzy RD designs," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(6), pages 1475-1526, December.
    11. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    12. Joshua D. Angrist, 2022. "Empirical Strategies in Economics: Illuminating the Path From Cause to Effect," Econometrica, Econometric Society, vol. 90(6), pages 2509-2539, November.
    13. Matias D. Cattaneo & Luke Keele & Rocio Titiunik, 2023. "A Guide to Regression Discontinuity Designs in Medical Applications," Papers 2302.07413, arXiv.org, revised May 2023.

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    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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