Identification of peer effects using group size variation

This paper studies the econometric properties of a linear-in-means model of social interactions. Under a slightly more restrictive framework than Lee (2007), we show that this model is generally identified when at least three different sizes of peer groups are observed in the sample at hand. While unnecessary in general, homoscedasticity may be required in special cases, for instance when endogenous and exogenous peer effects cancel each other. We extend this analysis to the case where only binary outcomes are observed. Once more, most parameters are semiparametrically identified under weak conditions. However, identifying all of them requires more stringent assumptions, including a homoscedasticity condition. We also develop a parametric estimator for the binary case, which relies on the Geweke-Hajivassiliou-Keane (GHK) simulator. Monte Carlo simulations illustrate the influence of group sizes on the accuracy of the estimation, in line with the results obtained by Lee (2007).