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On Interpreting the Regression Discontinuity Design as a Local Experiment

In: Regression Discontinuity Designs

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  • Jasjeet S. Sekhon
  • Rocío Titiunik

Abstract

We discuss the two most popular frameworks for identification, estimation and inference in regression discontinuity (RD) designs: the continuity-based framework, where the conditional expectations of the potential outcomes are assumed to be continuous functions of the score at the cutoff, and the local randomization framework, where the treatment assignment is assumed to be as good as randomized in a neighborhood around the cutoff. Using various examples, we show that (i) assuming random assignment of the RD running variable in a neighborhood of the cutoff implies neither that the potential outcomes and the treatment are statistically independent, nor that the potential outcomes are unrelated to the running variable in this neighborhood; and (ii) assuming local independence between the potential outcomes and the treatment does not imply the exclusion restriction that the score affects the outcomes only through the treatment indicator. Our discussion highlights key distinctions between “locally randomized” RD designs and real experiments, including that statistical independence and random assignment are conceptually different in RD contexts, and that the RD treatment assignment rule places no restrictions on how the score and potential outcomes are related. Our findings imply that the methods for RD estimation, inference, and falsification used in practice will necessarily be different (both in formal properties and in interpretation) according to which of the two frameworks is invoked.

Suggested Citation

  • Jasjeet S. Sekhon & Rocío Titiunik, 2017. "On Interpreting the Regression Discontinuity Design as a Local Experiment," Advances in Econometrics, in: Regression Discontinuity Designs, volume 38, pages 1-28, Emerald Group Publishing Limited.
  • Handle: RePEc:eme:aecozz:s0731-905320170000038001
    DOI: 10.1108/S0731-905320170000038001
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    Citations

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    Cited by:

    1. Yusuke Narita & Kohei Yata, 2021. "Algorithm is Experiment: Machine Learning, Market Design, and Policy Eligibility Rules," Working Papers 2021-022, Human Capital and Economic Opportunity Working Group.
    2. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell & Rocío Titiunik, 2019. "Regression Discontinuity Designs Using Covariates," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 442-451, July.
    3. Matakos, Konstantinos & Savolainen, Riikka & Troumpounis, Orestis & Tukiainen, Janne & Xefteris, Dimitrios, 2018. "Electoral Institutions and Intraparty Cohesion," Working Papers 109, VATT Institute for Economic Research.
    4. Atı̇la Abdulkadı̇roğlu & Joshua D. Angrist & Yusuke Narita & Parag Pathak, 2022. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Econometrica, Econometric Society, vol. 90(1), pages 117-151, January.
    5. Sebastian Calonico & Matias D Cattaneo & Max H Farrell, 2020. "Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs [Econometric methods for program evaluation]," The Econometrics Journal, Royal Economic Society, vol. 23(2), pages 192-210.
    6. Nicholas A. Bowman & Nayoung Jang, 2022. "What is the Purpose of Academic Probation? Its Substantial Negative Effects on Four-Year Graduation," Research in Higher Education, Springer;Association for Institutional Research, vol. 63(8), pages 1285-1311, December.
    7. Crespo Cristian, 2020. "Beyond Manipulation: Administrative Sorting in Regression Discontinuity Designs," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 164-181, January.
    8. Narita, Yusuke & Yata, Kohei, 2022. "Algorithm is Experiment: Machine Learning, Market Design, and Policy Eligibility Rules," CEI Working Paper Series 2021-05, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
    9. Narita, Yusuke & Yata, Kohei, 2022. "Algorithm is Experiment: Machine Learning, Market Design, and Policy Eligibility Rules," Discussion Paper Series 730, Institute of Economic Research, Hitotsubashi University.
    10. Berg, Heléne, 2020. "On the returns to holding political office (Is it worth it?)," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 840-865.
    11. Crespo Cristian, 2020. "Beyond Manipulation: Administrative Sorting in Regression Discontinuity Designs," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 164-181, January.

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