The authors consider the following scenario: Two agents construct models of an endogenous price process. One agent thinks the data are stationary, the other thinks the data are nonstationary. A policymaker combines forecasts from the two models using a recursive Bayesian model averaging procedure. The actual (but unknown) price process depends on the policymaker’s forecasts. The authors find that if the policymaker has complete faith in the stationary model, then beliefs and outcomes converge to the stationary rational expectations equilibrium. However, even a grain of doubt about stationarity will cause beliefs to settle on the nonstationary model, where prices experience large self-confirming deviations away from the stationary equilibrium. The authors show that it would take centuries of data before agents were able to detect their model misspecifications.