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Identification and Estimation of a Partially Linear Regression Model Using Network Data

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  • Eric Auerbach

Abstract

I study a regression model in which one covariate is an unknown function of a latent driver of link formation in a network. Rather than specify and fit a parametric network formation model, I introduce a new method based on matching pairs of agents with similar columns of the squared adjacency matrix, the ijth entry of which contains the number of other agents linked to both agents i and j. The intuition behind this approach is that for a large class of network formation models the columns of the squared adjacency matrix characterize all of the identifiable information about individual linking behavior. In this paper, I describe the model, formalize this intuition, and provide consistent estimators for the parameters of the regression model.

Suggested Citation

  • Eric Auerbach, 2022. "Identification and Estimation of a Partially Linear Regression Model Using Network Data," Econometrica, Econometric Society, vol. 90(1), pages 347-365, January.
    • Handle: RePEc:wly:emetrp:v:90:y:2022:i:1:p:347-365
    DOI: 10.3982/ECTA19794
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    References listed on IDEAS

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    Cited by:

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    11. Jin, Jiashun & Ke, Zheng Tracy & Luo, Shengming, 2024. "Mixed membership estimation for social networks," Journal of Econometrics, Elsevier, vol. 239(2).
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    13. Guo, Shujian & Xu, Zhiduan & Ruanzhou, Yilong, 2025. "Are strong neighbors good neighbors? “Doing business” spatial spillover effects and policy learning," Journal of International Money and Finance, Elsevier, vol. 158(C).
    14. Wu, Zhibin & Li, Yueyuan & Pedrycz, Witold, 2026. "Peer influence in social network: a review of identification, modeling and application," Journal of Business Research, Elsevier, vol. 203(C).
    15. Alejandro Sanchez-Becerra, 2022. "The Network Propensity Score: Spillovers, Homophily, and Selection into Treatment," Papers 2209.14391, arXiv.org.
    16. Raúl Duarte & Frederico Finan & Horacio Larreguy & Laura Schechter, 2019. "Brokering Votes With Information Spread Via Social Networks," NBER Working Papers 26241, National Bureau of Economic Research, Inc.
    17. Kensuke Sakamoto, 2024. "Dyadic Regression with Sample Selection," Papers 2405.17787, arXiv.org, revised Sep 2025.
    18. Aifen Feng & Xiaogai Chang & Jingya Fan & Zhengfen Jin, 2023. "Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model," Mathematics, MDPI, vol. 11(19), pages 1-14, October.
    19. Mugnier, Martin, 2025. "A simple and computationally trivial estimator for grouped fixed effects models," Journal of Econometrics, Elsevier, vol. 250(C).
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    21. Aifen Feng & Xiaogai Chang & Youlin Shang & Jingya Fan, 2022. "Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model," Mathematics, MDPI, vol. 10(24), pages 1-13, December.
    22. Xie, Jianhui & Pan, Zhewen, 2025. "Structure identification for partially linear partially concave models," European Journal of Operational Research, Elsevier, vol. 324(1), pages 142-154.
    23. Shanjukta Nath & Jiwon Hong & Jae Ho Chang & Keith Warren & Subhadeep Paul, 2025. "Recidivism and Peer Influence with LLM Text Embeddings in Low Security Correctional Facilities," Papers 2509.20634, arXiv.org, revised Jan 2026.
    24. Michael P. Leung & Pantelis Loupos, 2022. "Graph Neural Networks for Causal Inference Under Network Confounding," Papers 2211.07823, arXiv.org, revised Dec 2025.
    25. Arthur Lewbel & Xi Qu & Xun Tang, 2024. "Estimating Social Network Models with Link Misclassification," Boston College Working Papers in Economics 1079, Boston College Department of Economics.

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