IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2111.04219.html
   My bibliography  Save this paper

Rate-Optimal Cluster-Randomized Designs for Spatial Interference

Author

Listed:
  • Michael P. Leung

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.

Suggested Citation

  • Michael P. Leung, 2021. "Rate-Optimal Cluster-Randomized Designs for Spatial Interference," Papers 2111.04219, arXiv.org, revised Sep 2022.
    • Handle: RePEc:arx:papers:2111.04219
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2111.04219
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Davide Viviano, 2020. "Experimental Design under Network Interference," Papers 2003.08421, arXiv.org, revised Jul 2022.
    4. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    5. David Choi, 2017. "Estimation of Monotone Treatment Effects in Network Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1147-1155, July.
    6. Michael P. Leung, 2022. "Causal Inference Under Approximate Neighborhood Interference," Econometrica, Econometric Society, vol. 90(1), pages 267-293, January.
    7. 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.
    8. 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.
    9. 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.
    10. Michael Pollmann, 2020. "Causal Inference for Spatial Treatments," Papers 2011.00373, arXiv.org, revised Jan 2023.
    11. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michael P. Leung, 2023. "Cluster-Randomized Trials with Cross-Cluster Interference," Papers 2310.18836, arXiv.org, revised Nov 2024.
    2. Dario Tortarolo & Guillermo Cruces & Gonzalo Vazquez-Bare, 2023. "Design of partial population experiments with an application to spillovers in tax compliance," IFS Working Papers W23/17, Institute for Fiscal Studies.
    3. 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.
    4. Christopher Harshaw & Fredrik Savje & Yitan Wang, 2022. "A Design-Based Riesz Representation Framework for Randomized Experiments," Papers 2210.08698, arXiv.org, revised Oct 2022.
    5. Ke Sun & Linglong Kong & Hongtu Zhu & Chengchun Shi, 2024. "Optimal Treatment Allocation Strategies for A/B Testing in Partially Observable Time Series Experiments," Papers 2408.05342, arXiv.org, revised Oct 2024.
    6. Jinglong Zhao, 2024. "Experimental Design For Causal Inference Through An Optimization Lens," Papers 2408.09607, arXiv.org, revised Aug 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael P. Leung, 2022. "Causal Inference Under Approximate Neighborhood Interference," Econometrica, Econometric Society, vol. 90(1), pages 267-293, January.
    2. Denis Fougère & Nicolas Jacquemet, 2020. "Policy Evaluation Using Causal Inference Methods," SciencePo Working papers Main hal-03455978, HAL.
    3. Davide Viviano & Jess Rudder, 2020. "Policy design in experiments with unknown interference," Papers 2011.08174, arXiv.org, revised May 2024.
    4. Davide Viviano, 2020. "Experimental Design under Network Interference," Papers 2003.08421, arXiv.org, revised Jul 2022.
    5. Tadao Hoshino & Takahide Yanagi, 2021. "Causal Inference with Noncompliance and Unknown Interference," Papers 2108.07455, arXiv.org, revised Oct 2023.
    6. Jinglong Zhao, 2024. "Experimental Design For Causal Inference Through An Optimization Lens," Papers 2408.09607, arXiv.org, revised Aug 2024.
    7. Vazquez-Bare, Gonzalo, 2023. "Identification and estimation of spillover effects in randomized experiments," Journal of Econometrics, Elsevier, vol. 237(1).
    8. Stefan Wager & Kuang Xu, 2021. "Experimenting in Equilibrium," Management Science, INFORMS, vol. 67(11), pages 6694-6715, November.
    9. Davide Viviano & Lihua Lei & Guido Imbens & Brian Karrer & Okke Schrijvers & Liang Shi, 2023. "Causal clustering: design of cluster experiments under network interference," Papers 2310.14983, arXiv.org, revised Jan 2024.
    10. Ruonan Xu, 2023. "Difference-in-Differences with Interference," Papers 2306.12003, arXiv.org, revised May 2024.
    11. Yuehao Bai & Azeem M. Shaikh & Max Tabord-Meehan, 2024. "A Primer on the Analysis of Randomized Experiments and a Survey of some Recent Advances," Papers 2405.03910, arXiv.org.
    12. C. Tort`u & I. Crimaldi & F. Mealli & L. Forastiere, 2020. "Modelling Network Interference with Multi-valued Treatments: the Causal Effect of Immigration Policy on Crime Rates," Papers 2003.10525, arXiv.org, revised Jun 2020.
    13. Stefan Wager & Kuang Xu, 2019. "Experimenting in Equilibrium," Papers 1903.02124, arXiv.org, revised Jun 2020.
    14. Fredrik Savje, 2021. "Causal inference with misspecified exposure mappings: separating definitions and assumptions," Papers 2103.06471, arXiv.org, revised Mar 2023.
    15. Gonzalo Vazquez-Bare, 2017. "Identification and Estimation of Spillover Effects in Randomized Experiments," Papers 1711.02745, arXiv.org, revised Jan 2022.
    16. Tadao Hoshino, 2021. "Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach," Papers 2112.15114, arXiv.org, revised Jan 2023.
    17. Supriya Tiwari & Pallavi Basu, 2024. "Quasi-randomization tests for network interference," Papers 2403.16673, arXiv.org, revised Oct 2024.
    18. Julius Owusu, 2023. "Randomization Inference of Heterogeneous Treatment Effects under Network Interference," Papers 2308.00202, arXiv.org, revised Jan 2024.
    19. Hao, Shiming, 2021. "True structure change, spurious treatment effect? A novel approach to disentangle treatment effects from structure changes," MPRA Paper 108679, University Library of Munich, Germany.
    20. Han, Kevin & Basse, Guillaume & Bojinov, Iavor, 2024. "Population interference in panel experiments," Journal of Econometrics, Elsevier, vol. 238(1).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2111.04219. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.