Estimating Nonlinear Network Data Models with Fixed Effects

This paper considers estimation of a directed network model in which outcomes are driven by dyad-specific variables (such as measures of homophily) as well as unobserved agent-specific parameters that capture degree heterogeneity. I develop a jackknife bias correction to deal with the incidental parameters problem that arises from fixed effect estimation of the model. In contrast to previous proposals, the jackknife approach is easily adaptable to different models and allows for non-binary outcome variables. Additionally, since the jackknife estimates all parameters in the model, including fixed effects, it allows researchers to construct estimates of average effects and counterfactual outcomes. I also show how the jackknife can be used to bias-correct fixed effect averages over functions that depend on multiple nodes, e.g. triads or tetrads in the network. As an example, I implement specification tests for dependence across dyads, such as reciprocity or transitivity. Finally, I demonstrate the usefulness of the estimator in an application to a gravity model for import/export relationships across countries.