Information propagation in online social networks is facilitated by two types of influence - endogenous (peer) influence that acts between users of the social network and exogenous (external) that corresponds to various external mediators such as online news media. However, inference of these influences from data remains a challenge, especially when data on the activation of users is scarce. In this paper we propose a methodology that yields estimates of both endogenous and exogenous influence using only a social network structure and a single activation cascade. Our method exploits the statistical differences between the two types of influence - endogenous is dependent on the social network structure and current state of each user while exogenous is independent of these. We evaluate our methodology on simulated activation cascades as well as on cascades obtained from several large Facebook political survey applications. We show that our methodology is able to provide estimates of endogenous and exogenous influence in online social networks, characterize activation of each individual user as being endogenously or exogenously driven, and identify most influential groups of users.