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

Abstract

We propose methods 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 inuence 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, estimate the model using a sieve semiparametric approach and establish asymptotics of the semiparametric estimator.

A Structural Model for the Coevolution of Networks and Behavior

“…In our model, agents make decisions on links g ij as well as effort y i , taking into account the direct utility from links, the direct utility from effort, and the social utility. In the social interaction models with endogenous networks (see, e.g., Auerbach, 2019;Johnsson and Moon, 2019), links are assumed to be pairwise independent (conditional on observed and unobserved individual attributes).…”

“…In our model, links are interdependent with externalities given by the congestion and cyclic triangle effects in a i (g, X). Furthermore, Auerbach (2019) and Johnsson and Moon (2019) assume actions depend on links but not the other way around (conditional on observed and unobserved individual attributes). In our model, the social utility component in Equation…”

“…The focus of these papers is to consistently estimate social interaction effects controlling for the unobserved heterogeneity in the network formation process. In particular, Auerbach (2019) and Johnsson and Moon (2019) take a fixed-effect approach and allow the unobserved heterogeneity to affect link formation nonparametrically. Since it is difficult to distinguish link externalities from a flexible form of unobserved heterogeneity (Graham, 2015), link externalities are excluded a priori from their network formation models.…”

Peers, Parents, and Attitudes about School

“…Nonetheless, unobservables could still cause G to be endogenous. To deal with this, I turn to a recently developed estimator for peer effects by Johnsson and Moon (2015). This is a semiparametric control function approach, which estimates a first step network formation model developed in Graham (2017) and then uses information from the first step to estimate peer effects controlling for endogenous network formation.…”

“…To address this, I use a two-step procedure, estimating a network formation model developed by Graham (2017) in a first step. In the second step, I implement a recently developed semiparametric estimator in the outcome equation, using information from the network formation model to correct for bias from the network endogeneity (Johnsson and Moon 2015). This approach allows for an unobservable, individual fixed effect in the choice of friendship between two dyads (adolescents) that is also correlated with attitudes.…”