اثرات همسالان داخلی: مجموع محلی و یا متوسط محلی؟

We develop a unified model embedding different behavioral mechanisms of social interactions and design a statistical model selection test to differentiate between them in empirical applications. This framework is applied to study peer effects in education (effort in studying) and sport activities for adolescents in the United States. We find that, for education, students tend to conform to the social norm of their friends while, for sport activities, both the social multiplier and the social norm effect matter.

In many circumstances, the decision of agents to exert effort in education, or some other activity, cannot adequately be explained by their characteristics and by the intrinsic utility derived from it. Rather, its rationale may be found in how peers and others value this activity. There is indeed strong evidence that the behavior of individual agents is affected by that of their peers. This is particularly true in education, crime, labor markets, fertility, participation in welfare programs, etc. (for surveys, see, Glaeser and Scheinkman, 2001, Moffitt, 2001, Durlauf, 2004, Ioannides and Loury, 2004 and Ioannides, 2012). The way peer effects operate is, however, unclear. Are students working hard at school because some of their friends work hard or because they do not want to be different from the majority of their peers who work hard? The aim of this paper is to help our understanding of social interaction mechanisms of peer effects. For that, we begin by developing a social network model aiming at capturing how peer effects operate through social networks. 1 We characterize the Nash equilibrium and show under which condition an interior Nash equilibrium exists and is unique. Such a model encompasses the most popular peer effects models on networks: the local-aggregate and the local-average models. In the local-aggregate model (see, in particular, Ballester et al., 2006, Ballester et al., 2010, Bramoullé and Kranton, 2007, Galeotti et al., 2009 and Calvó-Armengol et al., 2009), endogenous peer effects are captured by the sum of friends’ efforts in some activity so that the more active friends an individual has, the higher is her marginal utility of exerting effort. In the local-average model (e.g. Glaeser and Scheinkman, 2003, Patacchini and Zenou, 2012 and Boucher et al., 2014), peers’ choices are viewed as a social norm and individuals pay a cost for deviating from this norm. In this model, each individual wants to conform as much as possible to the social norm of her reference group, which is defined as the average effort of her friends. 2 Ghiglino and Goyal (2010) develop a theoretical model where they compare the local aggregate and local average models in the context of a pure exchange economy where individuals trade in markets and are influenced by their neighbors. They found that with aggregate comparisons, networks matter even if all people are equally wealthy. With average comparisons, networks are irrelevant when individuals are equally wealthy. The two models are, however, similar if there is heterogeneity in wealth. 3 We are not aware of a paper where both local-aggregate and local-average effects are incorporated in a unified network model. Next, we study the econometric counterpart of the theoretical model. In the spatial econometric literature, the local-average and the local-aggregate model are well-known and their main difference (from an econometric viewpoint) is due to the fact that the adjacency matrix is row-normalized in the former but not in the latter. Our theoretical analysis provides a microfoundation for these two models. For the local-average model, Bramoullé et al. (2009) show that intransitivity in network connections can be used as an exclusion restriction to identify the endogenous peer effect from contextual and correlated effects. In this paper, we show that, for the local-aggregate model, different positions of the agents in a network captured by the Bonacich (1987) centrality can be used as additional instruments to improve identification and estimation efficiency. We also give identification conditions for a general econometric network model that incorporates both local-aggregate and local-average endogenous peer effects. Finally, we extend Kelejian's (2008)J test for spatial econometric models to differentiate between the local-aggregate and the local-average endogenous peer effects in an econometric network model with network fixed-effects. We illustrate our methodology using data from the U.S. National Longitudinal Survey of Adolescent Health (AddHealth), which contains unique detailed information on friendship relationships among teenagers. In line with a number of recent studies based on the AddHealth data (e.g. Calvó-Armengol et al., 2009, Lin, 2010, Patacchini and Zenou, 2012 and Liu et al., 2012), we exploit the structure of the network as well as network fixed effects to identify peer effects from contextual and correlated effects. 4 We find that, for study effort, students tend to conform to the social norm of their friends while, for sport activities, both the social multiplier and the social norm effect matter. Our results also show that the local-average peer effect is overstated if the local-aggregate effect is ignored and vice versa. In this respect, our analysis reveals that caution is warranted in the assessment of peer effects when social interactions can take different forms. We believe that it is important to be able to disentangle empirically different behavioral mechanisms of endogenous peer effects because they imply different policy implications. In the local-average model, the only way to affect individuals’ behavior and thus their outcomes is to change the social norm of the group. In other words, one needs to affect most people in the group for the policy to be effective. As a result, group-based policies should be implemented in the context of this model. On the other hand, for the local-aggregate model, one can target only one individual and still effectively influence the whole network. In other words, in the local-aggregate model there is a more salient social multiplier effect than in the local-average model, and hence, individual-based policies could be implemented. 5 The rest of paper is organized as follows. Section 2 introduces the theoretical framework for the network models. Section 3 discusses the identification conditions of the corresponding econometric models. We extend the J test of Kelejian and Piras (2011) to network models with network fixed effects in Section 4 and empirically test the network models using the AddHealth data in Section 5. Section 5.4 discusses the policy implications of our results. Finally, Section 6 concludes. All proofs of propositions can be found in Appendix A.

Identifying the nature of peer effects is a topic as important for policy purposes as difficult to study empirically. While a variety of mechanisms have been put forward in the theoretical literature, the econometrics of networks is lagging behind. This paper develops a unified econometric framework to estimate two types of social interaction (peer group) effects based on a given network structure. We provide a micro foundation by exploring different types of utility functions and illustrate the methodology using an application to education and sport activities. Our results show that different forms of social interactions may drive peer effects in different outcomes. Furthermore, they show that even for the same outcome there might be different mechanisms of peer effects at work. In this respect, our findings suggest some notes of caveat in the empirical analysis of peer effects. Peer effects are a complex phenomenon and their assessment should be considered with caution. If more than one mechanism is driving social interactions, then neglecting one of them can produce biased inferential results.