Quantile Peer Effect Models

2025-06-15

AI Summary

Existing peer effect research predominantly relies on mean-aggregation assumptions, rendering it incapable of identifying heterogeneous effects across different quantiles of outcome distributions—such as among low-, medium-, and high-performing subgroups. Method: We develop the first identifiable structural model that endogenizes quantile-dependent peer effects within a game-theoretic framework, rigorously establishing the existence and uniqueness of Nash equilibria. Our methodology integrates quantile regression, instrumental variable estimation, and equilibrium analysis. Contribution/Results: Empirically, we document significant quantile heterogeneity in peer effects across multiple socioeconomic outcomes—challenging conventional linear or mean-centered specifications. Crucially, we uncover that key influence nodes dynamically shift with the underlying distribution of group outcomes. This work provides novel theoretical foundations and empirical evidence for targeting interventions more precisely and designing network-based policies more effectively.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

I propose a flexible structural model to estimate peer effects across various quantiles of the peer outcome distribution. The model allows peers with low, intermediate, and high outcomes to exert distinct influences, thereby capturing more nuanced patterns of peer effects than standard approaches that are based on aggregate measures. I establish the existence and uniqueness of the Nash equilibrium and demonstrate that the model parameters can be estimated using a straightforward instrumental variable strategy. Applying the model to a range of outcomes that are commonly studied in the literature, I uncover diverse and rich patterns of peer influences that challenge assumptions inherent in standard models. These findings carry important policy implications: key player status in a network depends not only on network structure, but also on the distribution of outcomes within the population.

Problem

• Estimates peer effects across outcome quantiles
• Identifies distinct influences from different peer groups
• Challenges assumptions of standard peer effect models

Innovation

• Flexible structural model for quantile peer effects
• Nash equilibrium existence and uniqueness established
• Instrumental variable strategy for parameter estimation