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A Weak Law for Moments of Pairwise-Stable Networks

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SNAW01 - Graph Limits and Statistics

We develop asymptotic theory for strategic network-formation models under the assumption that the econometrician observes a single large pairwise-stable network. Drawing on techniques from the literature on random graphs, we derive primitive restrictions on the model that establish a weak law of large numbers for a useful class of network moments. Under these restrictions, we show that the model generates realistic networks that are sparse and may contain “giant” connected subnetworks, two well-known properties of real-world social networks. The restrictions also conveniently suggest a new method to simulate counterfactual networks that avoids a well-known curse of dimensionality. Additionally, we characterize the identified set of structural parameters based on a tractable class of dyad-level network moments and construct consistent set estimators.

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