Alexandre Belloni, Duke University 

S. S. Wilks Memorial Seminar in Statistics

Abstract: There is an increasing literature on social networks that is concerned with estimation of various effects when the network structure is known. In this work, based on available data, we aim to estimate the network structure/externalities. However, we consider the case in which only a subset of the network is observed but the interaction in the network is impacted by (unobserved) latent agents. We characterize the impact of such latent agents and propose estimators for the effective externality network. Our results cover the high-dimensional case and leads to simultaneous confidence intervals even if the number of observable agents is substantially larger than the sample size. (Our estimation and results are new even if there are no latent agents.) We discuss identification issues and additional results under binary network connections. As a motivating example we study in detail how a seller estimates the impact of the social network on agents' consumption and makes pricing decisions when there are additional latent agents which are not observed by the seller. We establish structural results, compute optimal pricing rules based on observable quantities, and estimate the effective externality network. This work is co-authored with Baris Ata and Ozan Candogan.