A Network Formation Model Based on Subgraphs

TL;DR

This paper introduces subgraph generated models (SUGMs) for network formation, demonstrating their identification, consistency, and superior fit to empirical networks compared to traditional models, with applications to rural Indian networks.

Contribution

The paper develops a new class of network models based on subgraphs, proving their statistical properties and showing they outperform existing models in capturing network patterns.

Findings

SUGMs are identified and estimators are consistent and asymptotically normal.

A four-parameter SUGM fits empirical networks better than standard models.

Applications reveal insights into risk-sharing and private interactions in rural India.

Abstract

We develop a new class of random graph models for the statistical estimation of network formation -- subgraph generated models (SUGMs). Various subgraphs -- e.g., links, triangles, cliques, stars -- are generated and their union results in a network. We show that SUGMs are identified and establish the consistency and asymptotic distribution of parameter estimators in empirically relevant cases. We show that a simple four-parameter SUGM matches basic patterns in empirical networks more closely than four standard models (with many more dimensions): (i) stochastic block models; (ii) models with node-level unobserved heterogeneity; (iii) latent space models; (iv) exponential random graphs. We illustrate the framework's value via several applications using networks from rural India. We study whether network structure helps enforce risk-sharing and whether cross-caste interactions are more likely to be private. We also develop a new central limit theorem for correlated random variables, which is required to prove our results and is of independent interest.