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My friend far, far away: a random field approach to exponential random graph models


  • Vincent Boucher
  • Ismael Mourifié


We explore the asymptotic properties of strategic models of network formation in very large populations. Specifically, we focus on (undirected) exponential random graph models. We want to recover a set of parameters from the individuals' utility functions using the observation of a single, but large, social network. We show that, under some conditions, a simple logit‐based estimator is coherent, consistent and asymptotically normally distributed under a weak version of homophily. The approach is compelling as the computing time is minimal and the estimator can be easily implemented using pre‐programmed estimators available in most statistical packages. We provide an application of our method using the Add Health database.

Suggested Citation

  • Vincent Boucher & Ismael Mourifié, 2017. "My friend far, far away: a random field approach to exponential random graph models," Econometrics Journal, Royal Economic Society, vol. 20(3), pages 14-46, October.
  • Handle: RePEc:wly:emjrnl:v:20:y:2017:i:3:p:s14-s46

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    Cited by:

    1. Luis E. Candelaria, 2020. "A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity," Papers 2007.05403,, revised Aug 2020.
    2. Candelaria, Luis E., 2020. "A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity," The Warwick Economics Research Paper Series (TWERPS) 1279, University of Warwick, Department of Economics.
    3. Carrillo, Juan D. & Gaduh, Arya, 2021. "Dynamics and stability of social and economic networks: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 1144-1176.
    4. Michael P. Leung, 2019. "Inference in Models of Discrete Choice with Social Interactions Using Network Data," Papers 1911.07106,
    5. Alex Centeno, 2022. "A Structural Model for Detecting Communities in Networks," Papers 2209.08380,, revised Oct 2022.
    6. Kojevnikov, Denis & Marmer, Vadim & Song, Kyungchul, 2021. "Limit theorems for network dependent random variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 882-908.
    7. 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.
    8. Philip Solimine & Luke Boosey, 2021. "Resource sharing on endogenous networks," Papers 2109.14204,, revised Jan 2022.
    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. Juan Nelson Mart'inez Dahbura & Shota Komatsu & Takanori Nishida & Angelo Mele, 2021. "A Structural Model of Business Card Exchange Networks," Papers 2105.12704,, revised Aug 2021.
    11. Michail Tsagris, 2021. "A New Scalable Bayesian Network Learning Algorithm with Applications to Economics," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 341-367, January.
    12. Shuyang Sheng, 2020. "A Structural Econometric Analysis of Network Formation Games Through Subnetworks," Econometrica, Econometric Society, vol. 88(5), pages 1829-1858, September.
    13. 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.
    14. Vincent Boucher, 2017. "The Estimation of Network Formation Games with Positive Spillovers," Cahiers de recherche 1710, Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques.
    15. Boucher, Vincent, 2020. "Equilibrium homophily in networks," European Economic Review, Elsevier, vol. 123(C).
    16. Michael P. Leung & Hyungsik Roger Moon, 2019. "Normal Approximation in Large Network Models," Papers 1904.11060,, revised Feb 2023.

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