Essays on identification and estimation of networks

This thesis consists of three chapters that explore the estimation and identification of networks from observable outcomes and covariates only. This problem is equivalent to estimating the spatial neighbouring matrix from a spatial econometric model. Under three settings, I show how the networks can be recovered entirely from observable non-network data. In the first chapter, networks are treated as a source of unobserved heterogeneity and dealt with data collected from observing many groups in one period of time. The proposed method estimates the probability that pairs of individuals form connections, which may depend on exogenous factors such as common gender. I derive a maximum likelihood estimator for network effects that is not conditional on network observation, accomplished with recourse to a spatial econometric model with unobserved and stochastic networks. I apply the model to estimate network effects in the context of a program evaluation. The second chapter assumes the observation of one group over many periods of time and estimates the networks as a collection of pairwise links. We estimate the spatial neighbouring matrix with recourse to the Adaptive Lasso. Non-asymptotic Oracle inequalities, together with the asymptotic sign consistency of the estimators, are presented and proved. The third chapter shows how the procedure developed in the preceding paper can be used to classify individuals into groups based on similarity of observed behavior. We propose a Lasso estimator that captures the block structure of the spatial neighboring matrix. The main results show that off-diagonal block elements are estimated as zeros with high probability. We correctly identified US Senate’s blocks based on party affiliation using only voting data. Empirical research on social and economic networks has been constrained by the limited availability of data regarding such networks. This collection of papers may therefore provide an useful tool for applied research.