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Bounding Causes of Effects With Mediators

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  • Dawid, Philip
  • Humphreys, Macartan
  • Musio, Monica

Abstract

Suppose X and Y are binary exposure and outcome variables, and we have full knowledge of the distribution of Y, given application of X. We are interested in assessing whether an outcome in some case is due to the exposure. This “probability of causation” is of interest in comparative historical analysis where scholars use process tracing approaches to learn about causes of outcomes for single units by observing events along a causal path. The probability of causation is typically not identified, but bounds can be placed on it. Here, we provide a full characterization of the bounds that can be achieved in the ideal case that X and Y are connected by a causal chain of complete mediators, and we know the probabilistic structure of the full chain. Our results are largely negative. We show that, even in these very favorable conditions, the gains from positive evidence on mediators is modest.

Suggested Citation

  • Dawid, Philip & Humphreys, Macartan & Musio, Monica, 2024. "Bounding Causes of Effects With Mediators," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 53(1), pages 28-56.
    • Handle: RePEc:zbw:espost:251185
    DOI: 10.1177/00491241211036161
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    References listed on IDEAS

    as
    1. Deborah Ghate, 2018. "Developing theories of change for social programmes: co-producing evidence-supported quality improvement," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 4(1), pages 1-13, December.
    2. Andrew Gelman & Guido Imbens, 2013. "Why ask Why? Forward Causal Inference and Reverse Causal Questions," NBER Working Papers 19614, National Bureau of Economic Research, Inc.
    3. Humphreys, Macartan & Scacco, Alexandra, 2020. "The aggregation challenge," World Development, Elsevier, vol. 127(C).
    4. Humphreys, Macartan & Scacco, Alexandra, 2020. "The aggregation challenge," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 127, pages 1-3.
    5. Blair, Graeme & Cooper, Jasper & Coppock, Alexander & Humphreys, Macartan, 2019. "Declaring and Diagnosing Research Designs," American Political Science Review, Cambridge University Press, vol. 113(3), pages 838-859, August.
    6. Howard White, 2009. "Theory-Based Impact Evaluation," 3ie Publications 2009-3, International Initiative for Impact Evaluation (3ie).
    7. Grossman, Guy & Humphreys, Macartan & Sacramone-Lutz, Gabriella, 2020. "Information Technology and Political Engagement: Mixed Evidence from Uganda," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 82(4), pages 1321-1336.
    8. repec:cup:apsrev:v:113:y:2019:i:03:p:838-859_00 is not listed on IDEAS
    9. Blair, Graeme & Cooper, Jasper & Coppock, Alexander & Humphreys, Macartan, 2019. "Declaring and Diagnosing Research Designs," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 113(3), pages 838-859.
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    Cited by:

    1. Neil Christy & Amanda Ellen Kowalski, 2024. "Counting Defiers: A Design-Based Model of an Experiment Can Reveal Evidence Beyond the Average Effect," Papers 2412.16352, arXiv.org, revised Dec 2025.
    2. Monica Musio & Philip Dawid, 2025. "Individual causation with biased data," METRON, Springer;Sapienza Università di Roma, vol. 83(1), pages 141-150, April.

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