Leading equilibrium concepts require agents’ beliefs to coincide with the model’s true probabilities and thus be free of systematic errors. This implicitly assumes a criterion that tests beliefs against the observed outcomes generated by the model. We formalize this requirement in stationary environments. We show that there is a tension between requiring that beliefs can be tested against systematic errors and allowing agents to disagree or be uncertain about the long-run fundamentals. We discuss the application of our analysis to asset pricing, Markov perfect equilibria, and dynamic games.