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Identification and Estimation of Social Interactions through Variation in Equilibrium Influence


  • Mikko Packalen

    (Department of Economics, University of Waterloo)


This paper presents a new method for estimating social interaction effects. The proposed approach is based on using network interaction structure induced variation in equilibrium influence to construct conditionally balanced interaction structures. As equilibrium influence is determined by the known interaction structure and the unknown endogenous social interaction parameter, interaction structures are constructed for different imputed values of the unknown parameter. Each constructed interaction structure is conditionally balanced in the sense that when it is combined with observations on the outcome variable to construct a new variable, the constructed variable is a valid instrumental variable for the endogenous social interaction regressor if the true and imputed parameter values are the same. Comparison of each imputed value with the associated instrumental variable estimate thus yields a confidence set estimate for the endogenous social interaction parameter as well as for other model parameters. We provide conditions for point identification and partial identification. The contrast between the proposed and existing approaches is stark. In the existing approach instruments are constructed from observations on exogenous variables, whereas in the proposed approach instruments are constructed from observations on the outcome variable. Both approaches have advantages, and the two approaches complement one another. We demonstrate the feasibility of the proposed approach with analyses of the determinants of subjective college completion and income expectations among adolescents in the Add Health data and with Monte Carlo simulations of Erdös-Rényi and small-world networks.

Suggested Citation

  • Mikko Packalen, 2010. "Identification and Estimation of Social Interactions through Variation in Equilibrium Influence," Working Papers 1013, University of Waterloo, Department of Economics, revised Dec 2010.
  • Handle: RePEc:wat:wpaper:1013

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    References listed on IDEAS

    1. Antoni Calvó-Armengol & Eleonora Patacchini & Yves Zenou, 2009. "Peer Effects and Social Networks in Education," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1239-1267.
    2. Giacomo De Giorgi & Michele Pellizzari & Silvia Redaelli, 2010. "Identification of Social Interactions through Partially Overlapping Peer Groups," American Economic Journal: Applied Economics, American Economic Association, vol. 2(2), pages 241-275, April.
    3. Ethan Cohen-Cole & Giulio Zanella, 2008. "Unpacking Social Interactions," Economic Inquiry, Western Economic Association International, vol. 46(1), pages 19-24, January.
    4. Cohen-Cole, Ethan, 2006. "Multiple groups identification in the linear-in-means model," Economics Letters, Elsevier, vol. 92(2), pages 157-162, August.
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    JEL classification:

    • 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
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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