IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2211.14354.html
   My bibliography  Save this paper

A Design-Based Approach to Spatial Correlation

Author

Listed:
  • Ruonan Xu
  • Jeffrey M. Wooldridge

Abstract

When observing spatial data, what standard errors should we report? With the finite population framework, we identify three channels of spatial correlation: sampling scheme, assignment design, and model specification. The Eicker-Huber-White standard error, the cluster-robust standard error, and the spatial heteroskedasticity and autocorrelation consistent standard error are compared under different combinations of the three channels. Then, we provide guidelines for whether standard errors should be adjusted for spatial correlation for both linear and nonlinear estimators. As it turns out, the answer to this question also depends on the magnitude of the sampling probability.

Suggested Citation

  • Ruonan Xu & Jeffrey M. Wooldridge, 2022. "A Design-Based Approach to Spatial Correlation," Papers 2211.14354, arXiv.org.
    • Handle: RePEc:arx:papers:2211.14354
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2211.14354
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Charles F. Manski, 2013. "Identification of treatment response with social interactions," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-23, February.
    2. 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.
    3. Aliprantis, Dionissi & Hartley, Daniel, 2015. "Blowing it up and knocking it down: The local and city-wide effects of demolishing high concentration public housing on crime," Journal of Urban Economics, Elsevier, vol. 88(C), pages 67-81.
    4. Michael P. Leung, 2022. "Causal Inference Under Approximate Neighborhood Interference," Econometrica, Econometric Society, vol. 90(1), pages 267-293, January.
    5. Ashesh Rambachan & Jonathan Roth, 2020. "Design-Based Uncertainty for Quasi-Experiments," Papers 2008.00602, arXiv.org, revised Feb 2024.
    6. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    7. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2020. "Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis," Econometrica, Econometric Society, vol. 88(1), pages 265-296, January.
    8. Alberto Abadie & Susan Athey & Guido W Imbens & Jeffrey M Wooldridge, 2023. "When Should You Adjust Standard Errors for Clustering?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(1), pages 1-35.
    9. Pinkse, Joris & Shen, Lihong & Slade, Margaret, 2007. "A central limit theorem for endogenous locations and complex spatial interactions," Journal of Econometrics, Elsevier, vol. 140(1), pages 215-225, September.
    10. Xu, Xingbai & Lee, Lung-fei, 2019. "Theoretical foundations for spatial econometric research," Regional Science and Urban Economics, Elsevier, vol. 76(C), pages 2-12.
    11. Iavor Bojinov & Ashesh Rambachan & Neil Shephard, 2021. "Panel experiments and dynamic causal effects: A finite population perspective," Quantitative Economics, Econometric Society, vol. 12(4), pages 1171-1196, November.
    12. Hudgens, Michael G. & Halloran, M. Elizabeth, 2008. "Toward Causal Inference With Interference," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 832-842, June.
    13. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    14. Jean-Francois Houde, 2012. "Spatial Differentiation and Vertical Mergers in Retail Markets for Gasoline," American Economic Review, American Economic Association, vol. 102(5), pages 2147-2182, August.
    15. Richard C. Bradley & Cristina Tone, 2017. "A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields," Journal of Theoretical Probability, Springer, vol. 30(2), pages 655-674, June.
    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. Ruonan Xu, 2023. "Difference-in-Differences with Interference," Papers 2306.12003, arXiv.org, revised Feb 2024.
    2. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.

    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. Ruonan Xu, 2023. "Difference-in-Differences with Interference," Papers 2306.12003, arXiv.org, revised Feb 2024.
    2. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Mar 2024.
    3. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.
    4. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.
    5. Tadao Hoshino & Takahide Yanagi, 2021. "Causal Inference with Noncompliance and Unknown Interference," Papers 2108.07455, arXiv.org, revised Oct 2023.
    6. 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.
    7. Michael P. Leung, 2021. "Rate-Optimal Cluster-Randomized Designs for Spatial Interference," Papers 2111.04219, arXiv.org, revised Sep 2022.
    8. 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.
    9. Xu, Xingbai & Lee, Lung-fei, 2015. "A spatial autoregressive model with a nonlinear transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 186(1), pages 1-18.
    10. Alejandro Sanchez-Becerra, 2022. "The Network Propensity Score: Spillovers, Homophily, and Selection into Treatment," Papers 2209.14391, arXiv.org.
    11. Fredrik Savje, 2021. "Causal inference with misspecified exposure mappings: separating definitions and assumptions," Papers 2103.06471, arXiv.org, revised Mar 2023.
    12. Michael Pollmann, 2020. "Causal Inference for Spatial Treatments," Papers 2011.00373, arXiv.org, revised Jan 2023.
    13. Tadao Hoshino, 2021. "Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach," Papers 2112.15114, arXiv.org, revised Jan 2023.
    14. Luis Alvarez & Bruno Ferman, 2020. "Inference in Difference-in-Differences with Few Treated Units and Spatial Correlation," Papers 2006.16997, arXiv.org, revised Apr 2023.
    15. Yann Bramoullé & Habiba Djebbari & Bernard Fortin, 2020. "Peer Effects in Networks: A Survey," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 603-629, August.
    16. Giovanni Cerulli, 2014. "ntreatreg: a Stata module for estimation of treatment effects in the presence of neighborhood interactions," United Kingdom Stata Users' Group Meetings 2014 15, Stata Users Group.
    17. Lee, Jungyoon & Robinson, Peter M., 2016. "Series estimation under cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 190(1), pages 1-17.
    18. Ashesh Rambachan & Jonathan Roth, 2020. "Design-Based Uncertainty for Quasi-Experiments," Papers 2008.00602, arXiv.org, revised Feb 2024.
    19. Derksen, Laura & Kerwin, Jason Theodore & Reynoso, Natalia Ordaz & Sterck, Olivier, 2021. "Appointments: A More Effective Commitment Device for Health Behaviors," SocArXiv y8gh7, Center for Open Science.
    20. Jungyoon Lee & Peter Robinson, 2016. "Series estimation under cross-sectional dependence," LSE Research Online Documents on Economics 63380, London School of Economics and Political Science, LSE Library.

    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:2211.14354. 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.