A Network Formation Model Based on Subgraphs
101 Pages Posted: 9 Oct 2015 Last revised: 10 Jul 2018
Date Written: November 1, 2016
We develop a new class of random-graph models for the statistical estimation of network formation that allow for substantial correlation in links. Various subgraphs (e.g., links, triangles, cliques, and stars) are generated and their union results in a network. We provide estimation techniques for recovering the rates at which the underlying subgraphs were formed. We illustrate the models via a series of applications including testing for incentives to form cross-caste relationships in rural India, testing to see whether network structure is used to enforce risk-sharing, testing as to whether networks change in response to a community's exposure to microcredit, and show that these models significantly outperform stochastic block models in matching observed network characteristics. We also establish asymptotic properties of the models and various estimators, which requires proving a new Central Limit Theorem for correlated random variables.
Keywords: Subgraphs, Random Networks, Random Graphs, Exponential Random Graph Models, Exponential Family, Social Networks, Network Formation, Consistency, Sparse Networks
JEL Classification: D85, C51, C01, Z13
Suggested Citation: Suggested Citation