A Network Formation Model Based on Subgraphs
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arXiv
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| Format: | Preprint |
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2016
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| _version_ | 1866909404273573888 |
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| author | Chandrasekhar, Arun G. Jackson, Matthew O. |
| author_facet | Chandrasekhar, Arun G. Jackson, Matthew O. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1611_07658 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | A Network Formation Model Based on Subgraphs Chandrasekhar, Arun G. Jackson, Matthew O. Physics and Society Social and Information Networks 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. |
| title | A Network Formation Model Based on Subgraphs |
| topic | Physics and Society Social and Information Networks |
| url | https://arxiv.org/abs/1611.07658 |