Working Paper: NBER ID: w20341
Authors: Bryan S. Graham
Abstract: 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.\n
Keywords: Homophily; Degree Heterogeneity; Link Formation; Network Analysis
JEL Codes: C31; C35
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| unobserved heterogeneity (C21) | estimation of parameters related to homophily and network connections (D85) |
| assortative matching based on observed agent characteristics (C78) | link formation (D85) |
| presence of hub agents (L85) | measured homophily in the network (D85) |
| network structure (D85) | estimation of homophily (C13) |
| JML estimator (C51) | estimates of incidental and common parameters (C51) |