A Network Formation Model Based on Subgraphs

71 Pages Posted: 9 Oct 2015 Last revised: 26 Mar 2021

See all articles by Arun G. Chandrasekhar

Arun G. Chandrasekhar

Stanford University - Department of Economics

Matthew O. Jackson

Stanford University - Department of Economics; Santa Fe Institute

Date Written: November 1, 2016

Abstract

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.

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

Chandrasekhar, Arun G. and Jackson, Matthew O., A Network Formation Model Based on Subgraphs (November 1, 2016). Available at SSRN: https://ssrn.com/abstract=2660381 or http://dx.doi.org/10.2139/ssrn.2660381

Arun G. Chandrasekhar

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States

Matthew O. Jackson (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States
1-650-723-3544 (Phone)

HOME PAGE: http://www.stanford.edu/~jacksonm

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

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