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Linear Social Interactions Models

Author

Listed:
  • Lawrence E. Blume
  • William A. Brock
  • Steven N. Durlauf
  • Rajshri Jayaraman

Abstract

This paper provides a systematic analysis of identification in linear social interactions models. This is both a theoretical and an econometric exercise as the analysis is linked to a rigorously delineated model of interdependent decisions. We develop an incomplete information game that describes individual choices in the presence of social interactions. The equilibrium strategy profiles are linear. Standard models in the empirical social interactions literature are shown to be exact or approximate special cases of our general framework, which in turn provides a basis for understanding the microeconomic foundations of those models. We consider identification of both endogenous (peer) and contextual social effects under alternative assumptions on a priori information about network structure available to an analyst, and contrast the informational content of individual-level and aggregated data. Finally, we discuss potential ramifications for identification of endogenous group selection and differences between the information sets of analysts and agents.

Suggested Citation

  • Lawrence E. Blume & William A. Brock & Steven N. Durlauf & Rajshri Jayaraman, 2013. "Linear Social Interactions Models," NBER Working Papers 19212, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:19212
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    References listed on IDEAS

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    1. Edward L. Glaeser & Bruce Sacerdote & José A. Scheinkman, 1996. "Crime and Social Interactions," The Quarterly Journal of Economics, Oxford University Press, vol. 111(2), pages 507-548.
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    7. Henderson, Vernon & Mieszkowski, Peter & Sauvageau, Yvon, 1978. "Peer group effects and educational production functions," Journal of Public Economics, Elsevier, vol. 10(1), pages 97-106, August.
    8. Ryo Nakajima, 2007. "Measuring Peer Effects on Youth Smoking Behaviour," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 897-935.
    9. McManus, Douglas A., 1992. "How common is identification in parametric models?," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 5-23.
    10. 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.
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    12. Mary Corcoran & Roger Gordon & Deborah Laren & Gary Solon, 1992. "The Association between Men's Economic Status and Their Family and Community Origins," Journal of Human Resources, University of Wisconsin Press, vol. 27(4), pages 575-601.
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    Citations

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    Cited by:

    1. Beugnot, Julie & Fortin, Bernard & Lacroix, Guy & Villeval, Marie Claire, 2017. "Gender and Peer Effects in Social Networks," IZA Discussion Papers 10588, Institute for the Study of Labor (IZA).
    2. Fortin, Bernard & Yazbeck, Myra, 2015. "Peer effects, fast food consumption and adolescent weight gain," Journal of Health Economics, Elsevier, vol. 42(C), pages 125-138.
    3. Rokhaya Dieye & Bernard Fortin, 2017. "Gender Peer Effects Heterogeneity in Obesity," Cahiers de recherche 1702, Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques.
    4. Battaglini, Marco & Patacchini, Eleonora, 2016. "Influencing Connected Legislators," CEPR Discussion Papers 11571, C.E.P.R. Discussion Papers.
    5. Boucher, Vincent & Fortin, Bernard, 2015. "Some Challenges in the Empirics of the Effects of Networks," IZA Discussion Papers 8896, Institute for the Study of Labor (IZA).
    6. UI, Takashi, 2015. "Bayesian Nash Equilibrium and Variational Inequalities," Discussion Papers 2015-08, Graduate School of Economics, Hitotsubashi University.
    7. Julie Beugnot & Bernard Fortin & Guy Lacroix & Marie Claire Villeval, 2017. "Gender and Peer Effects on Performance in Social Networks," Working Papers 1711, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    8. Ida Johnsson & Hyungsik Roger Moon, 2017. "Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach," Papers 1709.10024, arXiv.org.
    9. Firmin Doko Tchatoka & Robert Garrard & Virginie Masson, 2017. "Testing for Stochastic Dominance in Social Networks," School of Economics Working Papers 2017-02, University of Adelaide, School of Economics.
    10. George Judge, 2016. "Econometric Information Recovery in Behavioral Networks," Econometrics, MDPI, Open Access Journal, vol. 4(3), pages 1-11, September.
    11. Boucher, Vincent, 2016. "Conformism and self-selection in social networks," Journal of Public Economics, Elsevier, vol. 136(C), pages 30-44.
    12. de Martí, Joan & Zenou, Yves, 2015. "Network games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 221-240.
    13. Yang, Chao & Lee, Lung-fei, 2017. "Social interactions under incomplete information with heterogeneous expectations," Journal of Econometrics, Elsevier, vol. 198(1), pages 65-83.
    14. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    15. repec:eee:jcecon:v:45:y:2017:i:2:p:271-286 is not listed on IDEAS
    16. Aureo de Paula & Imran Rasul & Pedro CL Souza, 2018. "Recovering social networks from panel data: Identification, simulations and an application," DOUMENTOS DE TRABAJO LACEA 016173, THE LATIN AMERICAN AND CARIBBEAN ECONOMIC ASSOCIATION - LACEA.
    17. Arun Advani & Bansi Malde, 2014. "Empirical methods for networks data: social effects, network formation and measurement error," IFS Working Papers W14/34, Institute for Fiscal Studies.
    18. Áureo de Paula & Imran Rasul & Pedro Souza, 2018. "Recovering Social Networks from Panel Data: Identification, Simulations and an Application," Working Papers 2018-013, Human Capital and Economic Opportunity Working Group.

    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • 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
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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