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Manipulation Tests in Regression Discontinuity Design: The Need for Equivalence Testing

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  • Fitzgerald, Jack

Abstract

Researchers utilizing regression discontinuity design (RDD) commonly test for running variable (RV) manipulation around a cutoff, but incorrectly assert that insignificant manipulation test statistics are evidence of negligible manipulation. I introduce simple frequentist equivalence testing procedures that can provide statistically significant evidence that RV manipulation around a cutoff is practically equal to zero. I then demonstrate the necessity of these procedures, leveraging replication data from 36 RDD publications to conduct 45 equivalence-based RV manipulation tests. Over 44% of RV density discontinuities at the cutoff cannot be significantly bounded beneath a 50% upward jump. Bounding equivalence-based manipulation test failure rates beneath 5% requires arguing that a 350% upward density jump is practically equal to zero. Meta-analytic estimates reveal that average RV manipulation around the cutoff is equivalent to a 26% upward density jump. These results imply that many published RDD estimates may be confounded by discontinuities in potential outcomes due to RV manipulation that remains undetectable by existing tests. I provide research guidelines and commands in Stata and R to help researchers conduct more credible equivalencebased manipulation testing in future RDD research.

Suggested Citation

  • Fitzgerald, Jack, 2024. "Manipulation Tests in Regression Discontinuity Design: The Need for Equivalence Testing," I4R Discussion Paper Series 136, The Institute for Replication (I4R).
    • Handle: RePEc:zbw:i4rdps:136
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    References listed on IDEAS

    as
    1. Stommes, Drew & Aronow, P. M. & Sävje, Fredrik, 2023. "On the Reliability of Published Findings Using the Regression Discontinuity Design in Political Science," I4R Discussion Paper Series 22, The Institute for Replication (I4R).
    2. Gaku Igarashi, 2023. "A nonparametric discontinuity test of density using a beta kernel," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 35(2), pages 323-354, April.
    3. François Gerard & Miikka Rokkanen & Christoph Rothe, 2020. "Bounds on treatment effects in regression discontinuity designs with a manipulated running variable," Quantitative Economics, Econometric Society, vol. 11(3), pages 839-870, July.
    4. Andrew C. Eggers & Anthony Fowler & Jens Hainmueller & Andrew B. Hall & James M. Snyder, 2015. "On the Validity of the Regression Discontinuity Design for Estimating Electoral Effects: New Evidence from Over 40,000 Close Races," American Journal of Political Science, John Wiley & Sons, vol. 59(1), pages 259-274, January.
    5. Erin Hartman & F. Daniel Hidalgo, 2018. "An Equivalence Approach to Balance and Placebo Tests," American Journal of Political Science, John Wiley & Sons, vol. 62(4), pages 1000-1013, October.
    6. Jun Ma & Hugo Jales & Zhengfei Yu, 2020. "Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 934-950, October.
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    More about this item

    Keywords

    McCrary density test; rddensity; DCdensity; Hartman test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • P00 - Political Economy and Comparative Economic Systems - - General - - - General

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