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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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    1. Sacerdote, Bruce, 2011. "Peer Effects in Education: How Might They Work, How Big Are They and How Much Do We Know Thus Far?," Handbook of the Economics of Education, in: Erik Hanushek & Stephen Machin & Ludger Woessmann (ed.), Handbook of the Economics of Education, edition 1, volume 3, chapter 4, pages 249-277, Elsevier.
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    4. Eric Auerbach, 2019. "Identification and Estimation of a Partially Linear Regression Model using Network Data," Papers 1903.09679, arXiv.org, revised Jun 2021.
    5. Charles F. Manski, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 531-542.
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    7. Ida Johnsson & Hyungsik Roger Moon, 2021. "Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach," The Review of Economics and Statistics, MIT Press, vol. 103(2), pages 328-345, May.
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    10. Eric Auerbach, 2021. "Identification and Estimation of a Partially Linear Regression Model using Network Data: Inference and an Application to Network Peer Effects," Papers 2105.10002, arXiv.org.
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    Cited by:

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    3. Shuyang Sheng & Xiaoting Sun, 2023. "Social Interactions with Endogenous Group Formation," Papers 2306.01544, arXiv.org.
    4. Jochmans, Koen, 2023. "Peer effects and endogenous social interactions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1203-1214.
    5. Brice Romuald Gueyap Kounga, 2023. "Identification and Estimation of a Semiparametric Logit Model using Network Data," Papers 2310.07151, arXiv.org, revised Jun 2024.
    6. 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.
    7. Sukjin Han & Hiroaki Kaido, 2024. "Set-Valued Control Functions," Papers 2403.00347, arXiv.org, revised Feb 2025.
    8. Tiziano Arduini & Edoardo Rainone, 2024. "Partial identification of treatment response under complementarity and substitutability," Temi di discussione (Economic working papers) 1473, Bank of Italy, Economic Research and International Relations Area.
    9. Jin, Jiashun & Ke, Zheng Tracy & Luo, Shengming, 2024. "Mixed membership estimation for social networks," Journal of Econometrics, Elsevier, vol. 239(2).
    10. 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.
    11. Alejandro Sanchez-Becerra, 2022. "The Network Propensity Score: Spillovers, Homophily, and Selection into Treatment," Papers 2209.14391, arXiv.org.
    12. Kensuke Sakamoto, 2024. "Dyadic Regression with Sample Selection," Papers 2405.17787, arXiv.org, revised Jul 2024.
    13. 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.
    14. Steven Wilkins Reeves & Shane Lubold & Arun G. Chandrasekhar & Tyler H. McCormick, 2024. "Model-Based Inference and Experimental Design for Interference Using Partial Network Data," Papers 2406.11940, arXiv.org.
    15. 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.
    16. Michael P. Leung & Pantelis Loupos, 2022. "Graph Neural Networks for Causal Inference Under Network Confounding," Papers 2211.07823, arXiv.org, revised Mar 2024.

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