Weak Identification in Peer Effects Estimation

2025-08-06

AI Summary

This paper addresses the weak identification problem in estimating peer effects in social networks. Under the “filling-in” asymptotic framework—where the network size grows—the conventional linear mean model suffers from asymptotic collinearity due to the network averaging operation: when node average degree increases with sample size and covariates are i.i.d., standard estimators exhibit bias or slow convergence. To resolve this, the paper proposes a linear sum model, which replaces neighborhood averages with neighborhood sums as the fundamental modeling unit. This formulation avoids identification deterioration induced by growing degrees and requires only nontrivial variation in the degree distribution—a milder condition that accommodates broader network structures. Theoretically, the proposed estimator is shown to be consistent and √n-asymptotically normal, thereby substantially improving inferential reliability.

Technology Category

• Application Domains: Social Networks
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction

Application Category

• Social Networks and Social Media: Social media analysis through the lenses of networks
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Social recommender systems and personalization for the social Web

Abstract

It is commonly accepted that some phenomena are social: for example, individuals' smoking habits often correlate with those of their peers. Such correlations can have a variety of explanations, such as direct contagion or shared socioeconomic circumstances. The network linear-in-means model is a workhorse statistical model which incorporates these peer effects by including average neighborhood characteristics as regressors. Although the model's parameters are identifiable under mild structural conditions on the network, it remains unclear whether identification ensures reliable estimation in the "infill" asymptotic setting, where a single network grows in size. We show that when covariates are i.i.d. and the average network degree of nodes increases with the population size, standard estimators suffer from bias or slow convergence rates due to asymptotic collinearity induced by network averaging. As an alternative, we demonstrate that linear-in-sums models, which are based on aggregate rather than average neighborhood characteristics, do not exhibit such issues as long as the network degrees have some nontrivial variation, a condition satisfied by most network models.

Problem

• Estimating peer effects reliably in growing networks
• Addressing bias in standard network effect estimators
• Proposing alternative models for stable peer effect estimation

Innovation

• Uses network linear-in-means model
• Proposes linear-in-sums models alternative
• Addresses asymptotic collinearity in estimation