Peer effects in education, sport and screen activities: local aggregate or local average?

We develop two different social network models with different economic foundations. In the local-aggregate model, it is the sum of friends' efforts in some activity that affects the utility of each individual while, in the local-average model, it is costly to deviate from the average effort of friends. Even though the two models are fundamentally different in terms of behavioral foundation, their implications in terms of Nash equilibrium are relatively close since only the adjacency (social interaction) matrix differs in equilibrium, one being the row-normalized version of the other. We test these alternative mechanisms of social interactions to study peer effects in education, sport and screen activities for adolescents in the United States using the AddHealth data. We extend Kelejian's (2008) J test for spatial econometric models helping differentiate between these two behavioral models. We find that peer effects are not significant for screen activities (like e.g. video games). On the contrary, for sport activities, we find that students are mostly influenced by the aggregate activity of their friends (localaggregate model) while, for education, we show that both the aggregate performance at school of friends and conformism matter, even though the magnitude of the effect is higher for the latter