Estimating peer effects in noisy, low-rank networks via network smoothing

TL;DR

This paper introduces a method for estimating peer effects in noisy networks by leveraging low-rank matrix estimation of the expected adjacency matrix, improving accuracy despite measurement errors.

Contribution

It establishes that peer effects over the true network are asymptotically equivalent to those over the expected low-rank adjacency matrix, enabling more robust estimation.

Findings

Method performs well with egocentric samples and aggregated data

Approach is effective with networks with missing edges

Simulations confirm robustness across various noise structures

Abstract

Peer effect estimation requires precise network measurement, yet most empirical networks are noisy, rendering standard estimators inconsistent. To address measurement error in networks, we propose a method to estimate peer effects in networks whose expected adjacency matrix is low-rank. Our key result shows that peer effects over a true unobserved network are asymptotically equivalent to peer effects over the expected adjacency matrix. This result reduces peer effect estimation in noisy networks to low-rank matrix estimation targeting the expected adjacency matrix. We develop our theory for weighted networks observed with additive noise, but simulations suggest approach can be applied more generally when there is a low-rank estimation method suited to a particular noise structure. We demonstrate via simulations that our approach applies to egocentric samples, aggregated relational data, and networks with missing edges, each requiring a different low-rank estimation method.