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An econometric model of network 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, β0 , 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 {Ai0}Ni=1 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 shownonly under dense graph sequences.Supplement for CWP 08/17

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  • Bryan S. Graham, 2017. "An econometric model of network formation with degree heterogeneity," CeMMAP working papers 08/17, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:08/17
    DOI: 10.1920/wp.cem.2017.0817
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    References listed on IDEAS

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    Cited by:

    1. Bryan S. Graham & Andrin Pelican, 2023. "Scenario Sampling for Large Supermodular Games," Papers 2307.11857, arXiv.org.
    2. Brice Romuald Gueyap Kounga, 2023. "Nonparametric Regression with Dyadic Data," Papers 2310.12825, arXiv.org.
    3. St'ephane Bonhomme & Kevin Dano, 2023. "Functional Differencing in Networks," Papers 2307.11484, arXiv.org.
    4. Braun, Martin & Verdier, Valentin, 2023. "Estimation of spillover effects with matched data or longitudinal network data," Journal of Econometrics, Elsevier, vol. 233(2), pages 689-714.
    5. Luis E. Candelaria & Yichong Zhang, 2024. "Robust Inference in Locally Misspecified Bipartite Networks," Papers 2403.13725, arXiv.org.
    6. Alan Griffith, 2022. "A continuous model of strong and weak ties," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(6), pages 1519-1563, December.
    7. Qiuping Wang & Yuan Zhang & Ting Yan, 2023. "Asymptotic theory in network models with covariates and a growing number of node parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 369-392, April.
    8. Mathieu Lambotte & Sandrine Mathy & Anna Risch & Carole Treibich, 2022. "Spreading active transportation: peer effects and key players in the workplace," Post-Print hal-03702684, HAL.
    9. Valeria Costantini & Valerio Leone Sciabolazza & Elena Paglialunga, 2023. "Network-driven positive externalities in clean energy technology production: the case of energy efficiency in the EU residential sector," The Journal of Technology Transfer, Springer, vol. 48(2), pages 716-748, April.
    10. Bryan S. Graham & Andrin Pelican, 2023. "Scenario sampling for large supermodular games," CeMMAP working papers 15/23, Institute for Fiscal Studies.
    11. Gao, Wayne Yuan & Li, Ming & Xu, Sheng, 2023. "Logical differencing in dyadic network formation models with nontransferable utilities," Journal of Econometrics, Elsevier, vol. 235(1), pages 302-324.
    12. Mathieu Lambotte & Sandrine Mathy & Anna Risch & Carole Treibich, 2022. "Spreading active transportation: peer effects and key players in the workplace," Working Papers 2022-02, Grenoble Applied Economics Laboratory (GAEL).
    13. Francesco Bartolucci & Francesco Valentini & Claudia Pigini, 2023. "Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 529-557, February.
    14. Candelaria, Luis E. & Ura, Takuya, 2023. "Identification and inference of network formation games with misclassified links," Journal of Econometrics, Elsevier, vol. 235(2), pages 862-891.

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