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I present a stochastic version of Tirole's (1996) collective reputation model. In equilibrium, group behavior is persistent due to a complementarity between the group's reputation, which depends on the past behavior of the group's members, and current incentives. A group can maintain a strong reputation even as conditions become unfavorable, while an improvement in the environment may not help a group with a poor reputation. I also connect the model to the theory of statistical discrimination and show that the same mechanism can explain why discrimination might persist over time.