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Fixed-effect regressions on network data

Author

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  • Koen Jochmans

    (Institute for Fiscal Studies and University of Cambridge)

  • Martin Weidner

    (Institute for Fiscal Studies and University College London)

Abstract

This paper studies inference on fixed eff ects in a linear regression model estimated from network data. We derive bounds on the variance of the fixed-e ffect estimator that uncover the importance of the smallest non-zero eigenvalue of the (normalized) Laplacian of the network and of the degree structure of the network. The eigenvalue is a measure of connectivity, with smaller values indicating less-connected networks. These bounds yield conditions for consistent estimation and convergence rates, and allow to evaluate the accuracy of first-order approximations to the variance of the fixed-eff ect estimator. Supplement for CWP32/16

Suggested Citation

  • Koen Jochmans & Martin Weidner, 2016. "Fixed-effect regressions on network data," CeMMAP working papers CWP32/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:32/16
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    Cited by:

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    3. Weidner, Martin & Zylkin, Thomas, 2021. "Bias and consistency in three-way gravity models," Journal of International Economics, Elsevier, vol. 132(C).
    4. Vanessa Alviarez & Keith Head & Thierry Mayer, 2020. "Global giants and local stars: How changes in brand ownership affect competition," Working Papers 2020-13, CEPII research center.
    5. Kramarz, Francis & Martin, Julien & Mejean, Isabelle, 2020. "Volatility in the small and in the large: The lack of diversification in international trade," Journal of International Economics, Elsevier, vol. 122(C).
    6. Stephane Bonhomme & Angela Denis, 2024. "Estimating Heterogeneous Effects: Applications to Labor Economics," Papers 2404.01495, arXiv.org.
    7. Thibaut Lamadon & Elena Manresa & Stephane Bonhomme, 2016. "Discretizing Unobserved Heterogeneity," 2016 Meeting Papers 1536, Society for Economic Dynamics.
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    9. Junhui Cai & Dan Yang & Wu Zhu & Haipeng Shen & Linda Zhao, 2021. "Network regression and supervised centrality estimation," Papers 2111.12921, arXiv.org.
    10. Faia, Ester & Ottaviano, Gianmarco & Spinella, Saverio, 2022. "Robot Adoption, Worker-Firm Sorting and Wage Inequality: Evidence from Administrative Panel Data," CEPR Discussion Papers 17451, C.E.P.R. Discussion Papers.
    11. Ajay Bhaskarabhatla & Luis Cabral & Deepak Hegde & Thomas Peeters, 2021. "Are Inventors or Firms the Engines of Innovation?," Management Science, INFORMS, vol. 67(6), pages 3899-3920, June.
    12. Patrick Kline & Raffaele Saggio & Mikkel Sølvsten, 2020. "Leave‐Out Estimation of Variance Components," Econometrica, Econometric Society, vol. 88(5), pages 1859-1898, September.
    13. repec:hal:spmain:info:hdl:2441/6q707l4svn8k3bt630nhgdqgdu is not listed on IDEAS
    14. Stéphane Bonhomme & Kerstin Holzheu & Thibaut Lamadon & Elena Manresa & Magne Mogstad & Bradley Setzler, 2023. "How Much Should We Trust Estimates of Firm Effects and Worker Sorting?," Journal of Labor Economics, University of Chicago Press, vol. 41(2), pages 291-322.
    15. Peeters, Thomas & van Ours, Jan C., 2022. "International Assortative Matching in the European Labor Market," IZA Discussion Papers 15521, Institute of Labor Economics (IZA).
    16. repec:spo:wpmain:info:hdl:2441/6q707l4svn8k3bt630nhgdqgdu is not listed on IDEAS
    17. Arthur Lewbel & Samuel Norris & Krishna Pendakur & Xi Qu, 2022. "Consumption peer effects and utility needs in India," Quantitative Economics, Econometric Society, vol. 13(3), pages 1257-1295, July.
    18. Jochmans, K., 2019. "Heteroskedasticity-Robust Inference in Linear Regression Models," Cambridge Working Papers in Economics 1957, Faculty of Economics, University of Cambridge.
    19. Michael P. Leung, 2023. "Network Cluster‐Robust Inference," Econometrica, Econometric Society, vol. 91(2), pages 641-667, March.
    20. repec:spo:wpecon:info:hdl:2441/6q707l4svn8k3bt630nhgdqgdu is not listed on IDEAS
    21. Bartanen, Brendan & Husain, Aliza N., 2022. "Connected networks in principal value-added models," Economics of Education Review, Elsevier, vol. 90(C).
    22. Halvarsson, Daniel & Lark, Olga & Gustavsson Tingvall, Patrik, 2022. "Foreign Ownership and Transferring of Gender Norms," Working Paper Series 1433, Research Institute of Industrial Economics.
    23. Halvarsson, Daniel & Lark, Olga & Gustavsson Tingvall, Patrik, 2022. "Foreign Ownership and Transferring of Gender Norms," Working Papers 2022:6, Lund University, Department of Economics.
    24. Esteves, Rui & Geisler Mesevage, Gabriel, 2019. "Social Networks in Economic History: Opportunities and Challenges," Explorations in Economic History, Elsevier, vol. 74(C).
    25. Philippe CHONÉ & Lionel WILNER, 2019. "Competition on Unobserved Attributes: The Case of the Hospital Industry," Working Papers 2019-21, Center for Research in Economics and Statistics.

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    More about this item

    Keywords

    fixed effects; graph; Laplacian; network data; variance bound;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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