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Rate-optimal cluster-randomized designs for spatial interference

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  • Leung, Michael P

Abstract

We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares outcomes under the counterfactuals that all or no units are treated. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz-Thompson estimator that compares the average outcomes of units with all or no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator's rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms.
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  • Leung, Michael P, 2022. "Rate-optimal cluster-randomized designs for spatial interference," Santa Cruz Department of Economics, Working Paper Series qt8t44s021, Department of Economics, UC Santa Cruz.
    • Handle: RePEc:cdl:ucscec:qt8t44s021
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    1. Eckles Dean & Karrer Brian & Ugander Johan, 2017. "Design and Analysis of Experiments in Networks: Reducing Bias from Interference," Journal of Causal Inference, De Gruyter, vol. 5(1), pages 1-23, March.
    2. Charles F. Manski, 2013. "Identification of treatment response with social interactions," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-23, February.
    3. Michael Pollmann, 2020. "Causal Inference for Spatial Treatments," Papers 2011.00373, arXiv.org, revised Jan 2023.
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    6. Mihai Valcu & Bart Kempenaers, 2010. "Spatial autocorrelation: an overlooked concept in behavioral ecology," Behavioral Ecology, International Society for Behavioral Ecology, vol. 21(5), pages 902-905.
    7. Sarah Baird & J. Aislinn Bohren & Craig McIntosh & Berk Özler, 2018. "Optimal Design of Experiments in the Presence of Interference," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 844-860, December.
    8. Davide Viviano, 2020. "Experimental Design under Network Interference," Papers 2003.08421, arXiv.org, revised Jul 2022.
    9. Michael P. Leung, 2022. "Causal Inference Under Approximate Neighborhood Interference," Econometrica, Econometric Society, vol. 90(1), pages 267-293, January.
    10. Sobel, Michael E., 2006. "What Do Randomized Studies of Housing Mobility Demonstrate?: Causal Inference in the Face of Interference," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1398-1407, December.
    11. Laura Forastiere & Edoardo M. Airoldi & Fabrizia Mealli, 2021. "Identification and Estimation of Treatment and Interference Effects in Observational Studies on Networks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 901-918, April.
    12. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
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    Cited by:

    1. Michael P. Leung, 2023. "Design of Cluster-Randomized Trials with Cross-Cluster Interference," Papers 2310.18836, arXiv.org, revised Nov 2023.
    2. Evan Munro & David Jones & Jennifer Brennan & Roland Nelet & Vahab Mirrokni & Jean Pouget-Abadie, 2023. "Causal Estimation of User Learning in Personalized Systems," Papers 2306.00485, arXiv.org.
    3. Christopher Harshaw & Fredrik Savje & Yitan Wang, 2022. "A Design-Based Riesz Representation Framework for Randomized Experiments," Papers 2210.08698, arXiv.org, revised Oct 2022.

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    Keywords

    Economics; Statistics; Econometrics; Mathematical Sciences; Causal inference; interference; experimental design; spatial dependence; Applied Mathematics; Statistics & Probability;
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