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

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  • Fitzgerald, Jack

    (Vrije Universiteit Amsterdam)

Abstract

Researchers applying regression discontinuity design (RDD) often test for endogenous running variable (RV) manipulation around treatment cutoffs, but misinterpret statistically insignificant RV manipulation as evidence of negligible RV manipulation. I introduce novel procedures that can provide statistically significant evidence that RV manipulation around a cutoff is bounded beneath practically negligible levels. The procedures augment classic RV density tests with an equivalence testing framework, along with bootstrap methods for (cluster-)robust inference. I apply these procedures to replication data from 36 RDD publications, conducting 45 equivalence-based RV manipulation tests. Over 44% of RV density discontinuities at the cutoff cannot be significantly bounded beneath a 50% upward jump. Obtaining equivalence testing failure rates beneath 5% requires arguing that a 350% upward RV density jump at the cutoff is practically equal to zero. My results imply that meaningful RV manipulation around treatment cutoffs cannot be ruled out in many published RDD papers, and that standard tests frequently misclassify the practical significance of RV manipulation. I provide research guidelines and help researchers conduct more credible equivalence-based manipulation testing in future RDD research. The lddtest estimation routine is available in R, Stata, and Python.

Suggested Citation

  • Fitzgerald, Jack, 2025. "Manipulation Tests in Regression Discontinuity Design: The Need for Equivalence Testing," MetaArXiv 2dgrp_v1, Center for Open Science.
    • Handle: RePEc:osf:metaar:2dgrp_v1
    DOI: 10.31219/osf.io/2dgrp_v1
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    1. Bugni, Federico A. & Canay, Ivan A., 2021. "Testing continuity of a density via g-order statistics in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 221(1), pages 138-159.
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    More about this item

    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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