On the Estimation of Peer Effects for Sampled Networks

TL;DR

This paper investigates the challenges of estimating peer effects in sampled networks, demonstrating the limitations of design identification, and proposing bias correction methods for incomplete network data.

Contribution

It introduces a new framework for understanding peer effect estimation in sampled networks and develops a bias-corrected estimator under realistic conditions.

Findings

Peer effects cannot be identified without observing links to unsampled units.

The proposed bias correction reduces asymptotic bias in estimates.

Simulation results validate the effectiveness of the bias-corrected estimator.

Abstract

This paper deals with the estimation of exogeneous peer effects for partially observed networks under the new inferential paradigm of design identification, which characterizes the missing data challenge arising with sampled networks with the central idea that two full data versions which are topologically compatible with the observed data may give rise to two different probability distributions. We show that peer effects cannot be identified by design when network links between sampled and unsampled units are not observed. Under realistic modeling conditions, and under the assumption that sampled units report on the size of their network of contacts, the asymptotic bias arising from estimating peer effects with incomplete network data is characterized, and a bias-corrected estimator is proposed. The finite sample performance of our methodology is investigated via simulations.