Two-step estimation of network-formation models with incomplete information

We model network formation as a simultaneous game of incomplete information, allowing linking decisions to depend on the structure of the network as well as the attributes of agents. When the data is rationalized by a symmetric equilibrium, meaning observationally equivalent agents choose the same ex-ante strategies, the model can be estimated using a computationally simple two-step estimator. We derive its asymptotic properties under a sequence of models sending the number of agents to infinity, which enables inference with only a single network observation. Our procedure generalizes dyadic regression, allowing the latent index to be a function of endogenous regressors that depend on the network. We apply the estimator to study trust networks in rural Indian villages.