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Single-Network Finite-Sample Inference in Strategic Network Formation Models

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  • Wayne Yuan Gao
  • Ming Li

Abstract

We develop a finite-sample valid inference procedure for strategic network formation models with endogenous network statistics, using only a single observed network. We impose no restrictions on network density, equilibrium selection, or the dependence structure induced by strategic interaction. Using a "bounding-by-c" technique, we obtain realization-wise sandwich inequalities whose middle term depends only on exogenous covariates and i.i.d. pairwise shocks. These inequalities deliver pathwise identifying restrictions and simulable finite-sample critical values in both parametric and semiparametric settings. Our proposed procedure is also computationally tractable: it does not involve solving, simulating, or enumerating equilibrium (sub)networks, and easily scales to networks with 10000 agents in simulations. In two empirical applications, we find statistical evidence for positive link interdependence at the 95% confidence level.

Suggested Citation

  • Wayne Yuan Gao & Ming Li, 2026. "Single-Network Finite-Sample Inference in Strategic Network Formation Models," Papers 2607.27505, arXiv.org, revised Sep 2026.
    • Handle: RePEc:arx:papers:2607.27505
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    References listed on IDEAS

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    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. Gualdani, Cristina, 2021. "An econometric model of network formation with an application to board interlocks between firms," Journal of Econometrics, Elsevier, vol. 224(2), pages 345-370.
    3. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    4. Arun G Chandrasekhar & Matthew O Jackson, 2025. "A Network Formation Model Based on Subgraphs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 92(6), pages 3741-3787.
    5. Bryan S. Graham, 2017. "An econometric model of network formation with degree heterogeneity," CeMMAP working papers 08/17, Institute for Fiscal Studies.
    6. Andreas Dzemski, 2019. "An Empirical Model of Dyadic Link Formation in a Network with Unobserved Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 101(5), pages 763-776, December.
    7. Cristina Gualdani, 2021. "An Econometric Model of Network Formation with an Application to Board Interlocks between Firms," Post-Print hal-03548907, HAL.
    8. David Puelz & Guillaume Basse & Avi Feller & Panos Toulis, 2022. "A graph‐theoretic approach to randomization tests of causal effects under general interference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 174-204, February.
    9. Michael P. Leung & Hyungsik Roger Moon, 2019. "Normal Approximation in Large Network Models," Papers 1904.11060, arXiv.org, revised Mar 2026.
    10. 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.
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