Identification of Preferences in Network Formation Games

Given data on a large network, this paper provides a framework for identification of preferences under the assumption of pairwise stability of network links. Network data present difficulties for identification, especially when one allows for links between nodes in a network to be interdependent; e.g., where friends of friends matter. Given a preference specification, we use the observed proportions of various possible payoff-relevant local network structures to learn about the underlying parameters. We show how one can map the observed proportions of these local structures to sets of parameters that are consistent with the model and the data. Our main result provides necessary conditions for a set of parameters to contain the identified set, under general specifications of preferences. We also provide sufficient conditions—and hence a characterization of the identified set—for two empirically relevant classes of specifications. The paper then provides a quadratic programming algorithm that can be used to construct the identified sets. This algorithm is illustrated in a set of Monte Carlo experiments.