Semiparametric Estimation in Network Formation Models with Homophily and Degree Heterogeneity

This paper considers a semiparametric version of the network formation model of Graham (2017). The two-way fixed-effects binary choice model allows for homophily and degree heterogeneity, but unlike Graham (2017) leaves the distribution of pair-specific unobservables unspecified. Identification of the slope parameters and fixed effects follows from a novel approach that does not rely on distributional assumptions. The identification strategy suggests an estimator for the slope parameters based upon tetrads of nodes within the network. A computationally simple version of this estimator is shown to be consistent with a non-parametric convergence rate. A consistent estimator of the fixed effects is also provided. Partial identification, for the case of discrete covariate support, and an extension to nonlinear fixed effects are also considered.