Beyond the Mean: Peer Effects with Nonlinear Social Benchmarks

Speaker: Dr Yanli Lin

Affiliation: University of Western Australia

Location: Room 212, Chamberlain Building (#35), St Lucia Campus

Abstract: This paper develops a nonlinear peer-effects model in which agents respond to a log-sum-exp (LSE) aggregator of peers' outcomes. Unlike CES-based norms, the LSE specification is well defined on the entire real line, nests the linear-in-means benchmark, and smoothly bridges minimum-, mean-, and maximum-type peer benchmarks. We provide a microfoundation that separates spillover and conformism channels and show that the induced best-response system admits a unique Nash equilibrium under a simple contraction condition. For grouped network data with additive group effects and both connected and isolated individuals, we exploit the translation equivariance of the LSE aggregator to remove group effects exactly before estimation, and propose an orthogonally transformed Gaussian pseudo-maximum-likelihood estimator. The transformation avoids the first-order incidental-parameter problem associated with direct fixed-effect profiling in many-small-groups settings, while isolated individuals separately identify spillover and conformism. We establish identification, consistency, asymptotic normality, and a cluster-robust variance estimator. Finally, we characterize how the peer-norm shape affects equilibrium welfare, document the estimator's finite-sample performance through Monte Carlo simulations, and apply the model to the Add Health (National Longitudinal Study of Adolescent to Adult Health) data.