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This paper analyzes a semiparametric model of network formation in thepresence of unobserved agent-specific heterogeneity. The objective is toidentify and estimate the preference parameters associated with homophily onobserved attributes when the distributions of the unobserved factors are notparametrically specified. This paper offers two main contributions to theliterature on network formation. First, it establishes a new pointidentification result for the vector of parameters that relies on the existenceof a special repressor. The identification proof is constructive andcharacterizes a closed-form for the parameter of interest. Second, itintroduces a simple two-step semiparametric estimator for the vector ofparameters with a first-step kernel estimator. The estimator is computationallytractable and can be applied to both dense and sparse networks. Moreover, Ishow that the estimator is consistent and has a limiting normal distribution asthe number of individuals in the network increases. Monte Carlo experimentsdemonstrate that the estimator performs well in finite samples and in networkswith different levels of sparsity.

A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity