Central Limit Theory for Models of Strategic Network Formation

TL;DR

This paper develops a central limit theorem for large, sparse, strategically formed networks, providing asymptotic distribution approximations for network statistics with applications in inference.

Contribution

It introduces a novel asymptotic approximation framework for strategic network formation models allowing for endogenous incentives and dependence, extending previous work with Gaussian error characterization.

Findings

Asymptotic distribution of network statistics is Gaussian.

Bias and variance can be consistently estimated from a single network.

Framework applies to large, sparse networks with strategic link formation.

Abstract

We provide asymptotic approximations to the distribution of statistics that are obtained from network data for limiting sequences that let the number of nodes (agents) in the network grow large. Network formation is permitted to be strategic in that agents' incentives for link formation may depend on the ego and alter's positions in that endogenous network. Our framework does not limit the strength of these interaction effects, but assumes that the network is sparse. We show that the model can be approximated by a sampling experiment in which subnetworks are generated independently from a common equilibrium distribution, and any dependence across subnetworks is captured by state variables at the level of the entire network. Under many-player asymptotics, the leading term of the approximation error to the limiting model established in Menzel (2015b) is shown to be Gaussian, with an asymptotic bias and variance that can be estimated consistently from a single network.