Group membership affects an agent's individual behavior. We determine how, by testing two competing hypotheses. One is that group membership operates through social identity, and the other is that group membership implements a correlation among the actions of in-group members in response to an implicit signal. We introduce two novel features in the experimental design. The first feature is the display of group outcomes. This allows us to assess directly the importance of relative group performance on subjects' decisions. The second is a careful manipulation of the Dictator game and the Trust game. More specifically, we choose parameters strategically so as to ensure no change in the pecuniary incentives across the two games. For a precise quantitative test of the two hypotheses we develop a structural model to describe an agent's behavior across treatments. Our findings suggest that the role of social identity on motivating agents' decisions has been exaggerated. The display of group outcomes induces a group effect, but a careful analysis of this effect reveals that participants use group outcomes as a signal to coordinate in-group members on favorable outcomes. Furthermore, we find evidence in support of recent experimental studies which demonstrate that an agent's allocation choice is sensitive to the behavior of the agent that generated the choice set.