Unrequited friendship? How reciprocity mediates adolescent peer effects

Researchers using directed network data to estimate peer effects must somehow handle unreciprocated nominations. To better understand how peer effects operate and how best to estimate their effects, this paper investigates how the reciprocation of friendship mediates peer effects. We begin by characterizing how reciprocated and unreciprocated friendships compare in terms of the amount of interaction and social distance. We then use a higher order spatial autoregressive (SAR) model to investigate the differential effects of reciprocated friends, unreciprocated friends, and unchosen friends (i.e. an incoming friendship nomination that is not reciprocated) on adolescents' behaviors and outcomes using data from the Add Health study. We find that adolescents experience heterogenous influences from friends, with the greatest effect from reciprocated friends, intermediate effects from unreciprocated friends, and the smallest, but positive effects from unchosen friends. Our results indicate that it is misleading to assign equal weight to all friends or to impose symmetry on unreciprocated friendship nominations, as is often done.