It is almost self-evident that social interactions can determine economic behavior and outcomes. Yet, information on social ties does not exist in most publicly available and widely used datasets. We present methods to recover information on the entire structure of social networks from observational panel data that contains no information on social ties between individuals. In the context of a canonical social interactions model, we provide sufficient conditions under which the social interactions matrix, endogenous and exogenous social effect parameters are all globally identified. We describe how high-dimensional estimation techniques can be used to estimate the model based on the Adaptive Elastic Net GMM method. We showcase our method in Monte Carlo simulations using two stylized and two real world network structures. Finally, we employ our method to study tax competition across US states. We find the identified network structure of tax competition differs markedly from the common assumption of tax competition between geographically neighboring states: the majority of geographic neighboring states (63%) are found not to be relevant for tax setting. We analyze the identified social interactions matrix to provide novel insights into the longstanding debate on the relative roles of factor mobility and yardstick competition in driving tax setting behavior across states. Most broadly, our method shows how the analysis of social interactions can be usefully extended to economic realms where no network data exists.