Identification of Heterogeneous Peer Effects

We develop a model of peer effects where each peer has a separate effect depending on their rank in the distribution of peers' outcomes. Our model admits a unique equilibrium, and model parameters can be identified using peers' exogenous characteristics. To obtain a more parsimonious model of peer effects, we introduce a tractable specification based on quantile-dependent peer effect coefficients, and develop a specification test. Applying the model to several student outcomes in the Add Health data, we uncover heterogeneous and often non-monotonic spillovers that cannot be captured by existing models. Our results have direct implications for counterfactual analysis, suggesting that a student's influence in a network depends not only on network structure, but also on that student's position in the outcome distribution of their peers.