Econometric methods for network data [electronic resource]
Keywords: Economics.

This dissertation studies inference in network-formation models with game-theoretic foundations. These are discrete-choice models in which the binary outcome represents whether or not a pair of nodes forms a link. Strategic interactions result from "network externalities, " meaning that the surplus that a node pair enjoys from forming a link may depend on the existence of other links in the network. Estimation of strategic models faces two core difficulties. The first is that network externalities can generate link "autocorrelation, " since an ego's decision to form a link with an alter may depend on the alter's other link-formation decisions and vice versa. Moreover, we typically observe only a few networks in the data and often only a single network. Hence, it is nontrivial to obtain a central limit theorem in the strategic context. The development of a sampling theory for large networks remains an open problem and is a central theme of this dissertation. The second core difficulty is incompleteness due to multiple equilibria. For a fixed vector of node primitives there may be multiple networks consistent with the equilibrium restrictions imposed by the model. If the econometrician is unwilling to take a stance on the mechanism by which nodes coordinate on a particular equilibrium, then the model likelihood depends on an infinite-dimensional nuisance parameter, and the model may only be partially identified. The first chapter of this dissertation analyzes strategic models of network formation with incomplete information. We show that in a setting without unobserved heterogeneity, by conditioning on commonly known attributes, we can eliminate autocorrelation among links. Moreover, we show that equilibrium beliefs can be estimated directly from the data under the restriction that the observed equilibrium is symmetric. Then the structural parameters can be estimated using a simple two-step estimator that augments commonly used "dyadic regression" models with an additional nonparametric first step to account for network externalities. The second chapter studies models with complete information, allowing for unobserved heterogeneity. This chapter considers models that obey a weak "component externalities" restriction on network externalities. We derive conditions under which certain node-level functions of the network constitute alpha-mixing random fields, objects for which central limit theorems exist. In particular, homophily plays an important role in reducing autocorrelation. Our results enable the estimation of certain network moments that are useful for inference. The third chapter studies models with complete information under a stronger "local externalities" restriction on network externalities. Whereas a central limit theorem under component externalities requires a "subcritical" network comprised of a large number of small components, we show that a class of models obeying local externalities can generate sparse networks with giant components, properties consistent with real-world social networks. Further, we develop conditions under which certain network statistics, converge to their expectations as the size of the network goes to infinity. A key requirement is that nodes are homophilous with respect to a set of attributes and that the degree of homophily increases with the size of the network at a particular rate. That is, nodes are increasingly selective about their partners the larger the pool of available partners. The rate at which selectivity increases in part determines the "realism" of global properties of large networks and the possibility of a law of large numbers. We derive rates that are compatible with both objectives. We also develop moment inequalities for inference that are "sharp" in the sense that they fully exhaust the empirical implications of the equilibrium restrictions.