UC Berkeley

This dissertation studies two frameworks for incorporating network data into economic modeling.

In the first chapter I consider the latent space framework of Holland and Leinhardt (1981) in which the existence of a link between two agents depends on their position in a latent space. I use this framework to estimate the parameters of a linear model in which the regressors and errors covary with the agents latent positions. Neither the endogenous relationship between the regressors and errors nor the distribution of network links are restricted parametrically. Instead, the model is identified by variation in the regressors unexplained by the agents latent positions. I first demonstrate that agents with similar columns of the squared adjacency matrix, the ijth entry of which contains the number of other agents linked to both agents i and j, necessarily have a similar distribution of network links. I then propose a semi parametric estimator based on matching pairs of agents with similar columns of the squared adjacency matrix. I find sufficient conditions for the estimator to be consistent and asymptotically normal, and provide a consistent estimator for its asymptotic variance.

In the second chapter I consider the rooted network framework of Aldous and Steele (2004). I use this framework to specify a nonparametric regression of a scalar outcome on a sparse network. The main assumption is that the outcome depends predominately on the configuration of agents and links nearby a distinguished agent. I first establish notion of distance between such configurations and then use it to construct a nearest-neighbor estimator of the regression function.

In the third chapter I revisit the latent space setting of the first chapter. I first specify a semi parametric model of link formation in which the existence of a link between a pair of agents depend on their positions in some latent space, an idiosyncratic error, and some linear combination of observed link covariates. I then proposes an estimator for the infinite- dimensional component of the model using a variation on the matching strategy outlined in the first chapter ands characterize the rate of convergence of the estimator using large- deviation arguments.