A social interaction model with an extreme order statistic

In this paper, we introduce a social interaction econometric model with an extreme order statistic to model peer effects. We show that the model is a well‐defined system of equations and that it is a static game with complete information. The social interaction model can include exogenous regressors and group effects. Instrumental variables estimators are proposed for the general model that includes exogenous regressors. We also consider distribution‐free methods that use recurrence relations to generate moment conditions for estimation. For a model without exogenous regressors, the maximum likelihood approach is computationally feasible.