Humans use language to refer to entities in the external world. Motivated by this, in recent years several models that incorporate a bias towards learning entity representations have been proposed. Such entity-centric models have shown empirical success, but we still know little about why. In this paper we analyze the behavior of two recently proposed entity-centric models in a referential task, Entity Linking in Multi-party Dialogue (SemEval 2018 Task 4). We show that these models outperform the state of the art on this task, and that they do better on lower frequency entities than a counterpart model that is not entity-centric, with the same model size. We argue that making models entity-centric naturally fosters good architectural decisions. However, we also show that these models do not really build entity representations and that they make poor use of linguistic context. These negative results underscore the need for model analysis, to test whether the motivations for particular architectures are borne out in how models behave when deployed.