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An econometric model of link formation with degree heterogeneity

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  • Bryan S. Graham

Abstract

I introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics (homophily) as well as unrestricted agent level heterogeneity in link surplus (degree heterogeneity). Like in fixed effects panel data analyses, the joint distribution of observed and unobserved agent-level characteristics is left unrestricted. Two estimators for the (common) homophily parameter, `beta_0`, are developed and their properties studied under an asymptotic sequence involving a single network growing large. The first, tetrad logit (TL), estimator conditions on a sufficient statistic for the degree heterogeneity. The second, joint maximum likelihood (JML), estimator treats the degree heterogeneity ` {A_(i0)}_(i=1)^N` as additional (incidental) parameters to be estimated. The TL estimate is consistent under both sparse and dense graph sequences, whereas consistency of the JML estimate is shown only under dense graph sequences.

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  • Bryan S. Graham, 2014. "An econometric model of link formation with degree heterogeneity," NBER Working Papers 20341, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:20341
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    Cited by:

    1. Koen Jochmans, 2017. "Two-Way Models for Gravity," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 478-485, July.
    2. Koen Jochmans, 2018. "Semiparametric Analysis of Network Formation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 705-713, October.
    3. González-Díaz, Julio & Palacios-Huerta, Ignacio, 2016. "Cognitive performance in competitive environments: Evidence from a natural experiment," Journal of Public Economics, Elsevier, vol. 139(C), pages 40-52.
    4. Matthew O. Jackson, 2014. "Networks in the Understanding of Economic Behaviors," Journal of Economic Perspectives, American Economic Association, vol. 28(4), pages 3-22, Fall.
    5. Koen Jochmans & Martin Weidner, 2019. "Fixed‐Effect Regressions on Network Data," Econometrica, Econometric Society, vol. 87(5), pages 1543-1560, September.
    6. Bryan S. Graham, 2015. "Methods of Identification in Social Networks," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 465-485, August.
    7. Yann Algan & Quoc-Anh Do & Nicolò Dalvit & Alexis Le Chapelain & Yves Zenou, 2015. "How Social Networks Shape Our Beliefs: A Natural Experiment among Future French Politicians," Sciences Po publications info:hdl:2441/78vacv4udu9, Sciences Po.
    8. Marco Battaglini & Valerio Leone Sciabolazza & Eleonora Patacchini, 2020. "Effectiveness of Connected Legislators," American Journal of Political Science, John Wiley & Sons, vol. 64(4), pages 739-756, October.
    9. Chih‐Sheng Hsieh & Lung‐Fei Lee & Vincent Boucher, 2020. "Specification and estimation of network formation and network interaction models with the exponential probability distribution," Quantitative Economics, Econometric Society, vol. 11(4), pages 1349-1390, November.
    10. Boucher, Vincent, 2016. "Conformism and self-selection in social networks," Journal of Public Economics, Elsevier, vol. 136(C), pages 30-44.
    11. Bryan S. Graham, 2016. "Homophily and transitivity in dynamic network formation," CeMMAP working papers 16/16, Institute for Fiscal Studies.
    12. repec:hal:wpspec:info:hdl:2441/75dbbb2hc596np6q8flqf6i79k is not listed on IDEAS
    13. repec:hal:wpspec:info:hdl:2441/dpido2upv86tqc7td18fd2mna is not listed on IDEAS
    14. repec:hal:spmain:info:hdl:2441/75dbbb2hc596np6q8flqf6i79k is not listed on IDEAS
    15. Bryan S. Graham, 2016. "Homophily and transitivity in dynamic network formation," CeMMAP working papers CWP16/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    17. Zenou, Yves & picard, pierre & Patacchini, Eleonora, 2015. "Urban Social Structure, Social Capital and Spatial Proximity," CEPR Discussion Papers 10501, C.E.P.R. Discussion Papers.
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    20. Harsh Gupta & Mason A. Porter, 2020. "Mixed Logit Models and Network Formation," Papers 2006.16516, arXiv.org, revised Aug 2022.
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    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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