NATIONAL BUREAU OF ECONOMIC RESEARCH

# An econometric model of link formation with degree heterogeneity

## Bryan S. Graham

NBER Working Paper No. 20341
Issued in July 2014, Revised in February 2017
NBER Program(s):Development Economics, Industrial Organization, Labor Studies, Technical Working Papers

I introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics (homophily) as well as unrestricted agent level heterogeneity in link surplus (degree heterogeneity). Like in fixed effects panel data analyses, the joint distribution of observed and unobserved agent-level characteristics is left unrestricted. Two estimators for the (common) homophily parameter, beta_0, are developed and their properties studied under an asymptotic sequence involving a single network growing large. The first, tetrad logit (TL), estimator conditions on a sufficient statistic for the degree heterogeneity. The second, joint maximum likelihood (JML), estimator treats the degree heterogeneity  {A_(i0)}_(i=1)^N as additional (incidental) parameters to be estimated. The TL estimate is consistent under both sparse and dense graph sequences, whereas consistency of the JML estimate is shown only under dense graph sequences.

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Document Object Identifier (DOI): 10.3386/w20341

Published: An Econometric Model of Network Formation with Degree Heterogeneity. Econometrica: Jul 2017, Volume 85, Issue 4. DOI: 10.3982/ECTA12679

 Graham w20414 Methods of Identification in Social Networks Christakis, Fowler, Imbens, and Kalyanaraman w16039 An Empirical Model for Strategic Network Formation Abadie, Athey, Imbens, and Wooldridge w20325 Finite Population Causal Standard Errors Graham w22186 Homophily and Transitivity in Dynamic Network Formation Banerjee, Chandrasekhar, Duflo, and Jackson w20422 Gossip: Identifying Central Individuals in a Social Network

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