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Average Direct and Indirect Causal Effects under Interference

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  • Yuchen Hu
  • Shuangning Li
  • Stefan Wager

Abstract

We propose a definition for the average indirect effect of a binary treatment in the potential outcomes model for causal inference under cross-unit interference. Our definition is analogous to the standard definition of the average direct effect, and can be expressed without needing to compare outcomes across multiple randomized experiments. We show that the proposed indirect effect satisfies a decomposition theorem whereby, in a Bernoulli trial, the sum of the average direct and indirect effects always corresponds to the effect of a policy intervention that infinitesimally increases treatment probabilities. We also consider a number of parametric models for interference, and find that our non-parametric indirect effect remains a natural estimand when re-expressed in the context of these models.

Suggested Citation

  • Yuchen Hu & Shuangning Li & Stefan Wager, 2021. "Average Direct and Indirect Causal Effects under Interference," Papers 2104.03802, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2104.03802
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    References listed on IDEAS

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    Cited by:

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    2. Christopher Harshaw & Fredrik Savje & Yitan Wang, 2022. "A Design-Based Riesz Representation Framework for Randomized Experiments," Papers 2210.08698, arXiv.org, revised Oct 2022.
    3. Yi Zhang & Kosuke Imai, 2023. "Individualized Policy Evaluation and Learning under Clustered Network Interference," Papers 2311.02467, arXiv.org, revised Feb 2024.
    4. Tadao Hoshino & Takahide Yanagi, 2021. "Causal Inference with Noncompliance and Unknown Interference," Papers 2108.07455, arXiv.org, revised Oct 2023.
    5. Victoria Stack & Lana L. Narine, 2022. "Sustainability at Auburn University: Assessing Rooftop Solar Energy Potential for Electricity Generation with Remote Sensing and GIS in a Southern US Campus," Sustainability, MDPI, vol. 14(2), pages 1-14, January.
    6. Cyrus Samii & Ye Wang & Jonathan Sullivan & P. M. Aronow, 2023. "Inference in Spatial Experiments with Interference using the SpatialEffect Package," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 138-156, March.
    7. Zhaonan Qu & Ruoxuan Xiong & Jizhou Liu & Guido Imbens, 2021. "Efficient Treatment Effect Estimation in Observational Studies under Heterogeneous Partial Interference," Papers 2107.12420, arXiv.org, revised Jun 2022.
    8. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.
    9. Luofeng Liao & Yuan Gao & Christian Kroer, 2022. "Statistical Inference for Fisher Market Equilibrium," Papers 2209.15422, arXiv.org.
    10. Eric Auerbach & Yong Cai & Ahnaf Rafi, 2024. "Regression Discontinuity Design with Spillovers," Papers 2404.06471, arXiv.org.

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