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Network-Adjusted GMM Estimation under Network Uncertainty

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  • Tadao Hoshino

Abstract

This paper proposes a network-adjusted generalized method of moments (NA-GMM) estimator for social interaction models when the observed network may differ from the true interaction network. NA-GMM is a novel penalized GMM approach that allows the elements of the observed interaction matrix to be modified to improve the fit of the moment conditions. To avoid unrestricted network adjustments, the NA-GMM criterion introduces a penalty on the amount of adjustment. Since NA-GMM does not aim to estimate the true interaction network itself, the estimator generally converges to a pseudo-true parameter. For a linear spatial autoregressive model, we prove that the NA-GMM estimator is consistent for the pseudo-true parameter and is asymptotically normally distributed under general moment misspecification. We also prove that a fixed-weight version of the NA-GMM estimator has a desirable bias reduction property relative to conventional GMM without network adjustment. An empirical application to U.S. county-level COVID-19 infection data demonstrates the usefulness of the proposed method.

Suggested Citation

  • Tadao Hoshino, 2026. "Network-Adjusted GMM Estimation under Network Uncertainty," Papers 2607.10613, arXiv.org, revised Aug 2026.
    • Handle: RePEc:arx:papers:2607.10613
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    References listed on IDEAS

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    1. 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.
    2. Frank Kleibergen & Zhaoguo Zhan, 2025. "Double robust inference for continuous updating GMM," Quantitative Economics, Econometric Society, vol. 16(1), pages 295-327, January.
    3. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    4. Arthur Lewbel & Xi Qu & Xun Tang, 2023. "Social Networks with Unobserved Links," Journal of Political Economy, University of Chicago Press, vol. 131(4), pages 898-946.
    5. Hall, Alastair R. & Inoue, Atsushi, 2007. "Corrigendum to: "The large sample behaviour of the generalized method of moments estimator in misspecified models": [Journal of Econometrics 114 (2003) 361-394]," Journal of Econometrics, Elsevier, vol. 141(2), pages 1417-1418, December.
    6. Denis Kojevnikov, 2021. "The Bootstrap for Network Dependent Processes," Papers 2101.12312, arXiv.org.
    7. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    8. Áureo de Paula & Imran Rasul & Pedro C L Souza, 2025. "Identifying Network Ties from Panel Data: Theory and an Application to Tax Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 92(4), pages 2691-2729.
    9. Susanne Schennach & Vincent Starck, 2026. "Optimally‐Transported Generalized Method of Moments," Econometrica, Econometric Society, vol. 94(2), pages 619-640, March.
    10. Arthur Lewbel & Xi Qu & Xun Tang, 2024. "Ignoring measurement errors in social networks," The Econometrics Journal, Royal Economic Society, vol. 27(2), pages 171-187.
    11. Isaiah Andrews & Harvey Barnhard & Jacob Carlson, 2026. "True and Pseudo-True Parameters," Papers 2604.15563, arXiv.org.
    12. Bruce E. Hansen & Seojeong Lee, 2021. "Inference for Iterated GMM Under Misspecification," Econometrica, Econometric Society, vol. 89(3), pages 1419-1447, May.
    13. Timothy G. Conley & Sílvia Gonçalves & Min Seong Kim & Benoit Perron, 2023. "Bootstrap inference under cross‐sectional dependence," Quantitative Economics, Econometric Society, vol. 14(2), pages 511-569, May.
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