My Friend Far Far Away: Asymptotic Properties of Pairwise Stable Networks

We explore the asymptotic properties of pairwise stables networks (Jackson and Wolinsky, 1996). Specifically, we want to recover a set of parameters from the individuals' utility functions using the observation of a single pairwise stable network. We develop Pseudo Maximum Likelihood estimator and show that it is consistent and asymptotically normally distributed under a very weak version of homophily. The approach is compelling as it provides explicit, easy-to-check conditions on the admissible set of preferences. Moreover, the method is easily implementable using pre-programmed estimators available in most statistical packages. We provide an application of our method using the Add Health database.