Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach

TL;DR

This paper introduces a novel control function method with a sieve semiparametric approach to estimate peer effects in social networks, addressing endogeneity caused by unobservable individual traits influencing both network formation and outcomes.

Contribution

It develops two estimators for peer effects that control for endogenous network formation without specifying the control function's form, using a flexible semiparametric approach.

Findings

Proposes a control function estimator for endogenous social networks.

Establishes asymptotic properties of the semiparametric estimator.

Addresses unobservable heterogeneity affecting network links and outcomes.

Abstract

We propose a method of estimating the linear-in-means model of peer effects in which the peer group, defined by a social network, is endogenous in the outcome equation for peer effects. Endogeneity is due to unobservable individual characteristics that influence both link formation in the network and the outcome of interest. We propose two estimators of the peer effect equation that control for the endogeneity of the social connections using a control function approach. We leave the functional form of the control function unspecified and treat it as unknown. To estimate the model, we use a sieve semiparametric approach, and we establish asymptotics of the semiparametric estimator.