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Identification and Efficient Estimation of Simultaneous Equations Network Models

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  • Xiaodong Liu

Abstract

This article considers identification and estimation of social network models in a system of simultaneous equations. We show that, with or without row-normalization of the social adjacency matrix, the network model has different equilibrium implications, needs different identification conditions, and requires different estimation strategies. When the adjacency matrix is not row-normalized, the variation in the Bonacich centrality across nodes in a network can be used as an IV to identify social interaction effects and improve estimation efficiency. The number of such IVs depends on the number of networks. When there are many networks in the data, the proposed estimators may have an asymptotic bias due to the presence of many IVs. We propose a bias-correction procedure for the many-instrument bias. Simulation experiments show that the bias-corrected estimators perform well in finite samples. We also provide an empirical example to illustrate the proposed estimation procedure.

Suggested Citation

  • Xiaodong Liu, 2014. "Identification and Efficient Estimation of Simultaneous Equations Network Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 516-536, October.
  • Handle: RePEc:taf:jnlbes:v:32:y:2014:i:4:p:516-536
    DOI: 10.1080/07350015.2014.907093
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    Cited by:

    1. AMBA OYON, Claude Marius & Mbratana, Taoufiki, 2017. "Simultaneous equation models with spatially autocorrelated error components," MPRA Paper 82395, University Library of Munich, Germany.
    2. Tiziano Arduini & Eleonora Patacchini & Edoardo Rainone, 2020. "Treatment Effects With Heterogeneous Externalities," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 826-838, October.
    3. Hsieh, Chih-Sheng & König, Michael D. & Liu, Xiaodong & Zimmermann, Christian, 2018. "Superstar Economists: Coauthorship Networks and Research Output," IZA Discussion Papers 11916, Institute of Labor Economics (IZA).
    4. Elhorst, J. Paul & Emili, Silvia, 2022. "A spatial econometric multivariate model of Okun's law," Regional Science and Urban Economics, Elsevier, vol. 93(C).
    5. Xiaodong Liu, 2020. "GMM identification and estimation of peer effects in a system of simultaneous equations," Journal of Spatial Econometrics, Springer, vol. 1(1), pages 1-27, December.
    6. Koenig, Michael & Hsieh, Chih-Sheng & Liu, Xiaodong & Zimmermann, Christian, 2020. "Collaboration in Bipartite Networks, with an Application to Coauthorship Networks," CEPR Discussion Papers 15195, C.E.P.R. Discussion Papers.
    7. Zhu, Xuening & Huang, Danyang & Pan, Rui & Wang, Hansheng, 2020. "Multivariate spatial autoregressive model for large scale social networks," Journal of Econometrics, Elsevier, vol. 215(2), pages 591-606.
    8. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2022. "Bayesian estimation of multivariate panel probits with higher‐order network interdependence and an application to firms' global market participation in Guangdong," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1356-1378, November.
    9. Yang, Kai & Lee, Lung-fei, 2021. "Estimation of dynamic panel spatial vector autoregression: Stability and spatial multivariate cointegration," Journal of Econometrics, Elsevier, vol. 221(2), pages 337-367.
    10. Huang, Danyang & Wang, Feifei & Zhu, Xuening & Wang, Hansheng, 2020. "Two-mode network autoregressive model for large-scale networks," Journal of Econometrics, Elsevier, vol. 216(1), pages 203-219.
    11. Yang, Kai & Lee, Lung-fei, 2017. "Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 196(1), pages 196-214.
    12. William C. Horrace & Hyunseok Jung & Shane Sanders, 2022. "Network Competition and Team Chemistry in the NBA," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 35-49, January.
    13. Giovanni Abbiati & Jonathan Pratschke, 2021. "‘Like with Like’ or ‘Do Like’? Modelling Peer Effects in The Classroom," CSEF Working Papers 603, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    14. Wang, Wei & Lee, Lung-Fei & Bao, Yan, 2018. "GMM estimation of the spatial autoregressive model in a system of interrelated networks," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 167-198.
    15. Tatsi, Eirini, 2015. "Endogenous Social Interactions: Which Peers Matter?," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113168, Verein für Socialpolitik / German Economic Association.
    16. Zhou, Meihua & Angelopoulos, Spyros & Ou, Carol & Liu, Hongwei & Liang, Zhouyang, 2023. "Optimization of dynamic product offerings on online marketplaces: A network theory perspective," Other publications TiSEM 75d71155-88bf-4ff7-aba1-9, Tilburg University, School of Economics and Management.
    17. AMBA OYON, Claude Marius & Mbratana, Taoufiki, 2018. "Simultaneous Generalized Method of Moments Estimator for Panel Data Models with Spatially Correlated Error Components," MPRA Paper 84746, University Library of Munich, Germany.
    18. Alex Centeno, 2022. "A Structural Model for Detecting Communities in Networks," Papers 2209.08380, arXiv.org, revised Oct 2022.
    19. Liangjun Su & Xi Qu, 2017. "Specification Test for Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 572-584, October.
    20. Ando, Tomohiro & Li, Kunpeng & Lu, Lina, 2023. "A spatial panel quantile model with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 232(1), pages 191-213.
    21. Marius C. O. Amba & Taoufiki Mbratana & Julie Gallo, 2023. "Spatial panel simultaneous equations models with error components," Empirical Economics, Springer, vol. 65(3), pages 1149-1196, September.
    22. Lina Lu, 2017. "Simultaneous Spatial Panel Data Models with Common Shocks," Supervisory Research and Analysis Working Papers RPA 17-3, Federal Reserve Bank of Boston.
    23. Kwok, Hon Ho, 2019. "Identification and estimation of linear social interaction models," Journal of Econometrics, Elsevier, vol. 210(2), pages 434-458.

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