Michael Leung (University of Southern California)
Normal Approximation in Strategic Network Formation
Abstract: We prove a general central limit theorem for network statistics satisfying a high-level "stabilization" condition. The condition essentially requires that the contribution of each node to the statistic only depends on a small number of nodes in the network and therefore can be interpreted as a weak-dependence condition. We apply this result to static and dynamic models of network formation with strategic interactions and derive primitive sufficient conditions under which important classes of network moments satisfy stabilization. In static models, stabilization holds, in part, under a restriction on the strength of strategic interactions, analogous to restrictions on the marginal effect of spatial or temporal lags in spatial and time-series econometrics. In dynamic models, stabilization holds under restrictions on the initial condition, which may not require limits on strategic interactions.