An econometric model of network formation with degree heterogeneity - Bryan S. Graham (Centre for Microdata Methods and Practice (cemmap), 2017)
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, ß0 , 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 Ai0Ni=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.
Keywords: C31; C33; C35; 330; Network formation; homophily; degree heterogeneity; scale-free networks; incidental parameters; asymptotic bias; fixed effects; conditional likelihood; dependent U-Process