Social interactions determine many economic behaviors, but information on social ties does not exist in most publicly available and widely used datasets. We present results on the identification of social networks from observational panel data that contains no information on social ties between agents. 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 globally identified if networks are constant over time. We also provide an extension of the method for time-varying networks. We then describe how high-dimensional estimation techniques can be used to estimate the interactions model based on the Adaptive Elastic Net Generalized Method of Moments. We employ the method to study tax competition across US states. The identified social interactions matrix implies that tax competition differs markedly from the common assumption of competition between geographically neighboring states, providing further insights into the long-standing debate on the relative roles of factor mobility and yardstick competition in driving tax setting behavior across states. Most broadly, our identification and application show that the analysis of social interactions can be extended to economic realms where no network data exists.