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Testing Partial Instrument Monotonicity

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  • Hongyi Jiang
  • Zhenting Sun

Abstract

When multi-dimensional instruments are used to identify and estimate causal effects, the monotonicity condition may not hold due to heterogeneity in the population. Under a partial monotonicity condition, which only requires the monotonicity to hold for each instrument separately holding all the other instruments fixed, the 2SLS estimand can still be a positively weighted average of LATEs. In this paper, we provide a simple nonparametric test for partial instrument monotonicity. We demonstrate the good finite sample properties of the test through Monte Carlo simulations. We then apply the test to monetary incentives and distance from results centers as instruments for the knowledge of HIV status.

Suggested Citation

  • Hongyi Jiang & Zhenting Sun, 2023. "Testing Partial Instrument Monotonicity," Papers 2308.08390, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2308.08390
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    References listed on IDEAS

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    1. Zhenting Sun, 2020. "Instrument Validity for Heterogeneous Causal Effects," Papers 2009.01995, arXiv.org, revised Oct 2023.
    2. Magne Mogstad & Alexander Torgovitsky & Christopher R. Walters, 2021. "The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables," American Economic Review, American Economic Association, vol. 111(11), pages 3663-3698, November.
    3. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    4. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    5. 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.
    6. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    7. Ismael Mourifié & Yuanyuan Wan, 2017. "Testing Local Average Treatment Effect Assumptions," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 305-313, May.
    8. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    9. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2013. "Testing functional inequalities," Journal of Econometrics, Elsevier, vol. 172(1), pages 14-32.
    10. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    11. Rebecca L. Thornton, 2008. "The Demand for, and Impact of, Learning HIV Status," American Economic Review, American Economic Association, vol. 98(5), pages 1829-1863, December.
    12. Zhenting Sun & Brendan K. Beare, 2021. "Improved Nonparametric Bootstrap Tests of Lorenz Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 189-199, January.
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    Cited by:

    1. Leonard Goff, 2024. "When does IV identification not restrict outcomes?," Papers 2406.02835, arXiv.org, revised Feb 2025.
    2. Sun, Zhenting & Wüthrich, Kaspar, 2025. "Pairwise valid instruments," Journal of Econometrics, Elsevier, vol. 250(C).

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