Identification of Peer Using Group Size Variation

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.