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Measuring the Graph Concordance of Locally Dependent Observations

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  • Kyungchul Song

    (Vancouver School of Economics, University of British Columbia)

Abstract

This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, that is, the pattern in which adjacent outcomes tend to be more strongly correlated than nonadjacent outcomes. The graph concordance measure can be generally used to quantify the empirical relevance of a network in explaining cross-sectional dependence of the outcomes, and as shown in the paper, it can also be used to quantify the extent of homophily under certain conditions. When one observes a single large network, it is nontrivial to make inferences about the concordance pattern. Assuming a dependency graph, this paper develops a permutation-based confidence interval for the graph concordance measure. The confidence interval is valid in finite samples when the outcomes are exchangeable, and under the dependency graph, an assumption together with other regularity conditions, is shown to exhibit asymptotic validity. Monte Carlo simulation results show that the validity of the permutation method is more robust than the asymptotic method to various graph configurations.

Suggested Citation

  • Kyungchul Song, 2018. "Measuring the Graph Concordance of Locally Dependent Observations," The Review of Economics and Statistics, MIT Press, vol. 100(3), pages 535-549, July.
    • Handle: RePEc:tpr:restat:v:100:y:2018:i:3:p:535-549
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    File URL: http://www.mitpressjournals.org/doi/pdf/10.1162/rest_a_00714
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    Cited by:

    1. Kojevnikov, Denis & Song, Kyungchul, 2023. "Some impossibility results for inference with cluster dependence with large clusters," Other publications TiSEM 80b8e4ed-54bc-4a34-883f-f, Tilburg University, School of Economics and Management.
    2. Jozef Barunik & Mattia Bevilacqua & Radu Tunaru, 2022. "Asymmetric Network Connectedness of Fears," The Review of Economics and Statistics, MIT Press, vol. 104(6), pages 1304-1316, November.
    3. Kojevnikov, Denis & Marmer, Vadim & Song, Kyungchul, 2021. "Limit theorems for network dependent random variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 882-908.
    4. Kojevnikov, Denis & Song, Kyungchul, 2023. "Some impossibility results for inference with cluster dependence with large clusters," Journal of Econometrics, Elsevier, vol. 237(2).
    5. Lina Zhang, 2020. "Spillovers of Program Benefits with Missing Network Links," Papers 2009.09614, arXiv.org, revised Aug 2024.

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