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, the nonseparable utility drives an individual to choose 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 decision of an individual 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 can help simplify the computation in very 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.