Identification and Estimation of Heterogeneous Peer Effects on Social Networking Platforms

For social networking platforms like Facebook, understanding the peer effects on it can be valuable to many applications, such as designing efficient advertisements with social endorsement. Therefore, we propose a statistical methodology that provides such understanding. These platforms contain heterogeneous users who may form various links based on their own attributes and interests, which leads to the heterogeneity of peer effects. To understand such heterogeneity, we introduce the concept of community, which is a set of individuals who share some common attributes, observed or not, and who are well connected among themselves because they form links that are characterized by these common attributes. Then we propose a model of informational conformity, which suggests that it is reasonable to assume peer effects to be homogeneous within communities but heterogeneous across communities. Then we propose such a model of peer effects and derive sufficient conditions for identification. The community structure is typically not observable, therefore, we propose a network formation model to uncover it and computationally employ an unsupervised machine learning algorithm to solve the model. Since naturally the community structure is not unique, we use a cross validation procedure to find the most efficient one for estimation. We apply this methodology to the same dataset as previous literature to contrast and show when our methodology outperforms. We use simulation to show that in more realistic social networking platform settings, the importance of introducing heterogeneity into peer effects