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Identification of Peer Using Group Size Variation

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  • Laurent Davezies

    (Crest)

  • Xavier d'Haultfoeuille

    (Crest)

  • Denis Fougère

    (Crest)

Abstract

This paper considers the semiparametric identification of endogenousand exogenous peer effects in the linear-in-means model. We showthat this model is generically identified when at least three differentsizes of peer groups are observed in the sample at hand. While unnecessaryin general, homoskedasticity may be required in special cases torecover all parameters. Extensions to asymmetric responses to peersand binary outcomes are also considered. Once more, most parametersare semiparametrically identified under rather weak conditions.However, recovering all of them requires more stringent assumptions.Finally, we bring theoretical evidence that the model is more adaptedto small groups.

Suggested Citation

  • Laurent Davezies & Xavier d'Haultfoeuille & Denis Fougère, 2007. "Identification of Peer Using Group Size Variation," Working Papers 2007-34, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2007-34
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    References listed on IDEAS

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    1. Bryan S. Graham, 2008. "Identifying Social Interactions Through Conditional Variance Restrictions," Econometrica, Econometric Society, vol. 76(3), pages 643-660, May.
    2. Charles F. Manski, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 531-542.
    3. Joshua D. Angrist & Kevin Lang, 2004. "Does School Integration Generate Peer Effects? Evidence from Boston's Metco Program," American Economic Review, American Economic Association, vol. 94(5), pages 1613-1634, December.
    4. Krauth, Brian V., 2006. "Simulation-based estimation of peer effects," Journal of Econometrics, Elsevier, vol. 133(1), pages 243-271, July.
    5. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    6. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, National Bureau of Economic Research, Inc.
    7. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Oxford University Press, vol. 68(2), pages 235-260.
    8. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
    9. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    10. Joshua Herries & Daniel I. Rees & Jeffrey S. Zax, 2003. "Interdependence in worker productivity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(5), pages 585-604.
    11. Charles F. Manski, 2000. "Economic Analysis of Social Interactions," Journal of Economic Perspectives, American Economic Association, vol. 14(3), pages 115-136, Summer.
    12. Esther Duflo & Emmanuel Saez, 2003. "The Role of Information and Social Interactions in Retirement Plan Decisions: Evidence from a Randomized Experiment," The Quarterly Journal of Economics, Oxford University Press, vol. 118(3), pages 815-842.
    13. Brock, William A. & Durlauf, Steven N., 2007. "Identification of binary choice models with social interactions," Journal of Econometrics, Elsevier, vol. 140(1), pages 52-75, September.
    14. Manski, Charles F, 1987. "Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data," Econometrica, Econometric Society, vol. 55(2), pages 357-362, March.
    15. Graham, Bryan S. & Hahn, Jinyong, 2005. "Identification and estimation of the linear-in-means model of social interactions," Economics Letters, Elsevier, vol. 88(1), pages 1-6, July.
    16. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
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    Cited by:

    1. Bramoullé, Yann & Djebbari, Habiba & Fortin, Bernard, 2009. "Identification of peer effects through social networks," Journal of Econometrics, Elsevier, vol. 150(1), pages 41-55, May.
    2. Alberto Bisin & Andrea Moro & Giorgio Topa, 2011. "The empirical content of models with multiple equilibria in economies with social interactions," Staff Reports 504, Federal Reserve Bank of New York.
    3. Chi, Feng & Yang, Nathan, 2010. "Twitter Adoption in Congress: Who Tweets First?," MPRA Paper 23225, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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