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Two-Step Estimation of a Strategic Network Formation Model with Clustering

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  • Geert Ridder
  • Shuyang Sheng

Abstract

This paper explores strategic network formation under incomplete information using data from a single large network. We allow the utility function to be nonseparable in an individual's link choices to capture the spillover effects from friends in common. In a network with n individuals, the nonseparable utility drives an individual to choose between 2^{n-1} overlapping portfolios of links. We develop a novel approach that applies the Legendre transform to the utility function so that the optimal decision of an individual can be represented as a sequence of correlated binary choices. The link dependence that results from the preference for friends in common is captured by an auxiliary variable introduced by the Legendre transform. We propose a two-step estimator that is consistent and asymptotically normal. We also derive a limiting approximation of the game as n grows large that can help simplify the computation in very large networks. We apply these methods to favor exchange networks in rural India and find that the direction of support from a mutual link matters in facilitating favor provision.

Suggested Citation

  • Geert Ridder & Shuyang Sheng, 2020. "Two-Step Estimation of a Strategic Network Formation Model with Clustering," Papers 2001.03838, arXiv.org, revised Nov 2022.
  • Handle: RePEc:arx:papers:2001.03838
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    File URL: http://arxiv.org/pdf/2001.03838
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    References listed on IDEAS

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    1. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    2. Miyauchi, Yuhei, 2016. "Structural estimation of pairwise stable networks with nonnegative externality," Journal of Econometrics, Elsevier, vol. 195(2), pages 224-235.
    3. à ureo de Paula & Seth Richards†Shubik & Elie Tamer, 2018. "Identifying Preferences in Networks With Bounded Degree," Econometrica, Econometric Society, vol. 86(1), pages 263-288, January.
    4. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    5. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    6. Konrad Menzel, 2016. "Inference for Games with Many Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(1), pages 306-337.
    7. Leung, Michael P., 2015. "Two-step estimation of network-formation models with incomplete information," Journal of Econometrics, Elsevier, vol. 188(1), pages 182-195.
    8. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
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    Cited by:

    1. Shuyang Sheng, 2020. "A Structural Econometric Analysis of Network Formation Games Through Subnetworks," Econometrica, Econometric Society, vol. 88(5), pages 1829-1858, September.
    2. Luis E. Candelaria, 2020. "A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity," Papers 2007.05403, arXiv.org, revised Aug 2020.
    3. 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.
    4. Bora Kim, 2020. "Analysis of Randomized Experiments with Network Interference and Noncompliance," Papers 2012.13710, arXiv.org.
    5. Shuyang Sheng & Xiaoting Sun, 2023. "Social Interactions with Endogenous Group Formation," Papers 2306.01544, arXiv.org.

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