Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 2017, Volume 85, Issue 4

An Econometric Model of Network Formation with Degree Heterogeneity
p. 1033-1063

Bryan S. Graham

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,β0, 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 {Ai0}Ni=1 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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Supplemental Material

Supplement to "An Econometric Model of Network Formation with Degree Heterogeneity"

This zip file contains the replication files for the manuscript.

Supplement to "An Econometric Model of Network Formation with Degree Heterogeneity"

This appendix presents proofs of Theorems 2, 3 and 4. It also summarizes the results of a series of Monte Carlo experiments designed to evaluate the finite sample properties of the tetrad logit and joint maximum likelihood estimates of 0. All notation is as defined in the main test unless stated otherwise. Equation number continues in sequence with that established in the main text.