Who Matters to Whom? Identifying Peer Effects with Propagation Geometry

TL;DR

This paper introduces a unifying theory of peer effects centered on social norm aggregators, providing a geometric perspective on how influence propagates in networks and offering new tools for identification and inference.

Contribution

It develops a comprehensive framework linking various exposure maps to influence propagation, unifies existing models, and proposes geometry-based instruments for better identification.

Findings

Unified theory of peer influence with diverse aggregators

Operator-based influence propagation characterized by Jacobian matrices

Geometry-inspired instruments improve identification in network models

Abstract

This paper develops a unifying theory of peer effects that treats the peer aggregator (the social norm mapping peers' actions into a scalar exposure) as the central behavioral primitive. We formulate peer influence as a norm game in which payoffs depend on own action and an exposure index, and we provide equilibrium existence and uniqueness for a broad class of aggregators. Using economically interpretable axioms, we organize commonly used exposure maps into a small taxonomy that nests linear-in-means, CES (peer-preference) norms, and smooth ``attention-to-salient-peers'' aggregators; rank-based quantile norms are treated as a complementary class. Building on this unification, we show that each aggregator induces an operator that governs how exogenous variation propagates through the network. Linear-in-means corresponds to constant transport (adjacency matrix), recovering the classic (friends-of-friends) instrument families. For nonlinear norms, operator becomes state- and preference-dependent and is characterized by the Jacobian of the exposure map evaluated at an exogenous predictor. This perspective yields geometry-induced instrument that exploit heterogeneity in marginal influence and nonredundant paths, and can remain informative when one-step moments or adjacency-power instruments become weak. Monte Carlo evidence and an application to NetHealth illustrate the practical implications across alternative aggregators and outcomes.