Two-Step Estimation of a Strategic Network Formation Model with Clustering

This paper explores strategic network formation under incomplete information using data from a single large network. We allow the utility function to be nonseparable in an individual's link choices to capture the spillover effects from friends in common. In a network with n individuals, an individual with a nonseparable utility function chooses between 2^{n-1} overlapping portfolios of links. We develop a novel approach that applies the Legendre transform to the utility function so that the optimal link choices can be represented as a sequence of correlated binary choices. The link dependence that results from the preference for friends in common is captured by an auxiliary variable introduced by the Legendre transform. We propose a two-step estimator that is consistent and asymptotically normal. We also derive a limiting approximation of the game as n grows large that simplifies the computation in large networks. We apply these methods to favor exchange networks in rural India and find that the direction of support from a mutual link matters in facilitating favor provision.