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Estimating Social Network Models with Missing Links

Author

Listed:
  • Arthur Lewbel

    (Boston College)

  • Xi Qu

    (Shanghai Jiao Tong University)

  • Xun Tang

    (Rice University)

Abstract

We propose an adjusted 2SLS estimator for social network models when some existing network links are missing from the sample (due, e.g., to recall errors by survey respondents, or lapses in data input). In the feasible structural form, missing links make all covariates endogenous and add a new source of correlation between the structural errors and endogenous peer outcomes (in addition to simultaneity), thus invalidating conventional estimators used in the literature. We resolve these issues by rescaling peer outcomes with estimates of missing rates and constructing instruments that exploit properties of the noisy network measures. We apply our method to study peer effects in household decisions to participate in a microfinance program in Indian villages. We find that ignoring missing links and applying conventional instruments would result in a sizeable upward bias in peer effect estimates.

Suggested Citation

  • Arthur Lewbel & Xi Qu & Xun Tang, 2022. "Estimating Social Network Models with Missing Links," Boston College Working Papers in Economics 1056, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:1056
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    References listed on IDEAS

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    1. Liu, Xiaodong, 2013. "Estimation of a local-aggregate network model with sampled networks," Economics Letters, Elsevier, vol. 118(1), pages 243-246.
    2. Bramoullé, Yann & Djebbari, Habiba & Fortin, Bernard, 2009. "Identification of peer effects through social networks," Journal of Econometrics, Elsevier, vol. 150(1), pages 41-55, May.
    3. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    4. Paul Goldsmith-Pinkham & Guido W. Imbens, 2013. "Social Networks and the Identification of Peer Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 253-264, July.
    5. Lee, Lung-fei, 2007. "Identification and estimation of econometric models with group interactions, contextual factors and fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 333-374, October.
    6. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    7. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    8. Xu Lin, 2010. "Identifying Peer Effects in Student Academic Achievement by Spatial Autoregressive Models with Group Unobservables," Journal of Labor Economics, University of Chicago Press, vol. 28(4), pages 825-860, October.
    9. Hu, Yingyao, 2008. "Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 27-61, May.
    10. Arun Advani & Bansi Malde, 2018. "Credibly Identifying Social Effects: Accounting For Network Formation And Measurement Error," Journal of Economic Surveys, Wiley Blackwell, vol. 32(4), pages 1016-1044, September.
    11. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
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    Cited by:

    1. Pu, Dan & Fang, Kuangnan & Lan, Wei & Yu, Jihai & Zhang, Qingzhao, 2024. "Multivariate spatiotemporal models with low rank coefficient matrix," Journal of Econometrics, Elsevier, vol. 246(1).
    2. Kieran Marray, 2024. "Estimating Spillovers from Sampled Connections," Papers 2410.17154, arXiv.org, revised Apr 2025.

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    Keywords

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    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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