Estimation of a Scale-Free Network Formation Model

Abstract

Growing evidence suggests that many social and economic networks are scale free in that their degree distribution P(d) is approximately proportional to d^{-γ}. The most widespread explanation for this phenomenon is a random network formation process with preferential attachment. For a general version of such a process, we develop a class of GMM estimators. We show formally that these GMM estimators give consistent estimates of model parameters. Simulations suggest that the GMM estimates are asymptotically normally distributed. The commonly used NLLS estimator gives highly biased and inconsistent estimates; Hill (1975) estimator performs even worse.

Keywords: consistency, degree distribution, network formation, scale-free network

JEL Classification: C15, C45, C51, D85