March 2007 | Yann Bramoullé, Habiba Djebbari, Bernard Fortin
This paper presents new results on the identification of peer effects through social networks. The authors extend the linear-in-means model by allowing each individual to have their own specific reference group, defined by individuals whose mean outcome and characteristics influence their own outcome. Interactions are structured through a directed social network. They show that relaxing the assumption of group interactions generally allows for the separation of endogenous and exogenous effects. This result is important because distinguishing between peer effects is necessary to evaluate the impact of policies on outcomes of networks with different structures. It also helps to detect which mechanism is at work within a network.
The authors determine the structures under which endogenous and exogenous effects are identifiable, both in the absence of correlated effects and when controlling for correlated effects in the form of component fixed effects. They provide easy-to-check necessary and sufficient conditions for identification. When there are no correlated effects, endogenous and exogenous effects are identified as soon as individuals do not interact in groups. Thus, even the slightest departure from a groupwise structure is sufficient to obtain identification. In many networks, identification originates from natural exclusion restrictions induced by the structure. For instance, identification is guaranteed if an individual has a friend's friend who is not his friend (i.e., the network has an intransitive triad).
When correlated effects are present at the component level, the authors show that the global transformation imposes less restrictive conditions to obtain identification. However, degrees of freedom are lost, and identification fails on some networks, such as the star. They find that endogenous and exogenous effects can be distinguished on most networks.
The paper also discusses the implications of these results for existing models. It shows that the results of Manski (1993), Moffitt (2001), and Lee (2006) directly follow from the general conditions. These authors analyze different versions of the standard model with group interactions. The paper also provides Monte Carlo simulations to analyze the effects of important characteristics of a network, such as its density and its level of transitivity, on the quality of estimates of peer effects. The simulations show that structural parameters are better estimated when the density of the graph is small. The impact of transitivity on the precision of estimators is more complex and can be used as a tool for understanding the relationship between the density of the graph and the actual data.This paper presents new results on the identification of peer effects through social networks. The authors extend the linear-in-means model by allowing each individual to have their own specific reference group, defined by individuals whose mean outcome and characteristics influence their own outcome. Interactions are structured through a directed social network. They show that relaxing the assumption of group interactions generally allows for the separation of endogenous and exogenous effects. This result is important because distinguishing between peer effects is necessary to evaluate the impact of policies on outcomes of networks with different structures. It also helps to detect which mechanism is at work within a network.
The authors determine the structures under which endogenous and exogenous effects are identifiable, both in the absence of correlated effects and when controlling for correlated effects in the form of component fixed effects. They provide easy-to-check necessary and sufficient conditions for identification. When there are no correlated effects, endogenous and exogenous effects are identified as soon as individuals do not interact in groups. Thus, even the slightest departure from a groupwise structure is sufficient to obtain identification. In many networks, identification originates from natural exclusion restrictions induced by the structure. For instance, identification is guaranteed if an individual has a friend's friend who is not his friend (i.e., the network has an intransitive triad).
When correlated effects are present at the component level, the authors show that the global transformation imposes less restrictive conditions to obtain identification. However, degrees of freedom are lost, and identification fails on some networks, such as the star. They find that endogenous and exogenous effects can be distinguished on most networks.
The paper also discusses the implications of these results for existing models. It shows that the results of Manski (1993), Moffitt (2001), and Lee (2006) directly follow from the general conditions. These authors analyze different versions of the standard model with group interactions. The paper also provides Monte Carlo simulations to analyze the effects of important characteristics of a network, such as its density and its level of transitivity, on the quality of estimates of peer effects. The simulations show that structural parameters are better estimated when the density of the graph is small. The impact of transitivity on the precision of estimators is more complex and can be used as a tool for understanding the relationship between the density of the graph and the actual data.