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Approximate variational inference for a model of social interactions

Author

Listed:
  • Angelo Mele

    (Johns Hopkins University - Carey Business School)

Abstract
This paper proposes approximate variational inference methods for estimation of a strategic model of social interactions. Players interact in an exogenous network and sequentially choose a binary action. The utility of an action is a function of the choices of neighbors in the network. I prove that the interaction process can be represented as a potential game and it converges to a unique stationary equilibrium distribution. However, exact inference for this model is infeasible because of a computationally intractable likelihood, which cannot be evaluated even when there are few players. To overcome this problem, I propose variational approximations for the likelihood that allow approximate inference. This technique can be applied to any discrete exponential family, and therefore it is a general tool for inference in models with a large number of players. The methodology is illustrated with several simulated datasets and compared with MCMC methods.

Suggested Citation

  • Angelo Mele, 2013. "Approximate variational inference for a model of social interactions," Working Papers 13-16, NET Institute.
    • Handle: RePEc:net:wpaper:1316
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    File URL: http://www.netinst.org/Mele_13-16.pdf
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    References listed on IDEAS

    as
    1. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    2. Ryo Nakajima, 2007. "Measuring Peer Effects on Youth Smoking Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 897-935.
    3. Angelo Mele, 2010. "A structural model of segregation in social networks," CeMMAP working papers CWP32/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Braun, Michael & McAuliffe, Jon, 2010. "Variational Inference for Large-Scale Models of Discrete Choice," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 324-335.
    5. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    6. Grimmer, Justin, 2011. "An Introduction to Bayesian Inference via Variational Approximations," Political Analysis, Cambridge University Press, vol. 19(1), pages 32-47, January.
    7. Anton Badev, 2014. "Discrete Games in Endogenous Networks: Theory and Policy," 2014 Meeting Papers 901, Society for Economic Dynamics.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Gibbons, Steve & Overman, Henry G. & Patacchini, Eleonora, 2015. "Spatial Methods," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 115-168, Elsevier.

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    More about this item

    Keywords

    Variational approximations; Bayesian Estimation; Social Interactions;
    All these keywords.

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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