Do Your Online Friends Make You Pay? A Randomized Field Experiment on Peer Influence in Online Social Networks - Online E-Companion Appendix

Demonstrating compelling causal evidence of the existence and strength of peer to peer influence has become the holy grail of modern research in online social networks. In these networks, it has been consistently demonstrated that user characteristics and behavior tend to cluster both in space and in time. There are multiple well-known rival mechanisms that compete to be the explanation for this observed clustering. These range from peer influence to homophily to other unobservable external stimuli. These multiple mechanisms lead to similar observational data, yet have vastly different policy implications. In this paper, we present a novel randomized experiment that tests the existence of causal peer influence in the general population -- one that did not involve subject recruitment for experimentation -- of a particular large-scale online social network. We utilize a unique social feature to exogenously induce adoption of a paid service amongst a group of randomly selected users, and in the process develop a clean exogenous randomization of treatment and control groups. A variety of nonparametric, semiparametric and parametric approaches, ranging from resampling-based inference to ego-level random effects to logistic regression to survival models, yield close to identical, statistically and economically significant estimates of peer influence in the general population of a freemium social network. Our estimates show that peer influence causes more than a 60% increase in odds of buying the service due to the influence coming from an adopting friend. In addition, we find that users with a smaller number of friends experience stronger relative increase in the adoption likelihood due to influence from their peers as compared to the users with a larger number of friends. Our nonparametric resampling procedure based estimates are helpful in situations of networked data that violate independence assumptions. We establish that peer influence is a powerful force in getting users from free to premium levels, a known challenge in freemium communities