Improving Control over Unobservables with Network Data

Abstract
Unobserved variables often threaten the causal interpretation of empirical estimates. An opportunity to alleviate this concern lies in network datasets, which provide a rich source of information about individual characteristics insofar as they influence network formation. This paper develops the idea of controlling for unobserved confounders by leveraging network structures that exhibit homophily, a frequently observed tendency to form edges with similar nodes. This is formally accomplished under two main frameworks. First, I introduce a concept of strong homophily, according to which individuals' selectivity is at scale with the size of the potential connection pool. This contributes to the network formation literature with a model that can accommodate common features of empirical networks such as homophily, sparsity, and clustering, and allows me to show that an estimator that considers neighbors as a comparison group is consistent for the Conditional Average Treatment Effect (CATE). I then consider a setting without strong homophily and show how selecting connected individuals whose observed characteristics made such a connection less likely delivers an estimator with similar properties. Overall, the method allows nonparametric treatment effect inference for both CATE and Average Treatment Effect (ATE) under a version of unconfoundedness that conditions on unobservables, which is often more credible than selection on observables alone. In an application, I recover an estimate of the effect of parental involvement on students' test scores that is greater than that of OLS, arguably due to the estimator's ability to account for unobserved ability and effort.