"Quantile Peer Effect Models"

Abstract :
In the widely used linear-in-means peer effects model, an agent’s outcome is influenced, among other factors, by the average outcome of their peers. This specification implicitly assumes uniform peer effects across all peers, regardless of their outcome level. I propose a more flexible structural model in which an agent’s payoff depends on multiple quantiles of peer outcomes, allowing peers with low, middle, and high outcomes to exert distinct effects. This model provides greater flexibility in capturing peer effects than the approach of Boucher et al. (2024), which relies on a constant elasticity of substitution (CES) function. I show that the model has a unique equilibrium despite the nonsmooth nature of the quantile function. I analyze the identification of the structural parameters and demonstrate that they can be estimated using a straightforward instrumental variable approach. Applying the model to various outcomes studied in the literature, I find that peer effects are rarely uniform. This result suggests that key player status in a network depends not only on the network structure but also on the distribution of outcomes within the population.