A Network Formation Model Based on Subgraphs

We develop a new class of random-graph models for the statistical estimation of network formation---subgraph generated models (SUGMs)---that allow for substantial correlation in links. Various subgraphs (e.g., links, triangles, cliques, stars) are generated and their union results in a network. We show that all SUGMs are identified and, further, establish the consistency and asymptotic distribution of parameter estimates in empirically relevant cases. We show that a simple four-parameter SUGM matches basic patterns in observed 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 further via several applications using networks from rural India. We study whether network structure helps enforce risk-sharing, whether cross-caste interactions are more likely to be private, and how the introduction of microcredit changes network formation incentives. We also develop a new central limit theorem for correlated random variables, which is required to prove our results and is of independent interest