Semiparametric Analysis of Network Formation

We consider a statistical model for network formation that features both node-specific heterogeneity parameters and common parameters that reflect homophily among nodes. The goal is to perform statistical inference on the homophily parameters while allowing the distribution of the node heterogeneity to be unrestricted, that is, by treating the node-specific parameters as fixed effects. Jointly estimating all the parameters leads to asymptotic bias that renders conventional confidence intervals incorrectly centered. As an alternative, we develop an approach based on a sufficient statistic that separates inference on the homophily parameters from estimation of the fixed effects. This estimator is easy to compute and is shown to have desirable asymptotic properties. In numerical experiments we find that the asymptotic results provide a good approximation to the small-sample behavior of the estimator. As an empirical illustration, the technique is applied to explain the import and export patterns in a cross-section of countries.