  This paper analyzes a semiparametric model of network formation in the
presence of unobserved agent-specific heterogeneity. The objective is to
identify and estimate the preference parameters associated with homophily on
observed attributes when the distributions of the unobserved factors are not
parametrically specified. This paper offers two main contributions to the
literature on network formation. First, it establishes a new point
identification result for the vector of parameters that relies on the existence
of a special repressor. The identification proof is constructive and
characterizes a closed-form for the parameter of interest. Second, it
introduces a simple two-step semiparametric estimator for the vector of
parameters with a first-step kernel estimator. The estimator is computationally
tractable and can be applied to both dense and sparse networks. Moreover, I
show that the estimator is consistent and has a limiting normal distribution as
the number of individuals in the network increases. Monte Carlo experiments
demonstrate that the estimator performs well in finite samples and in networks
with different levels of sparsity.
