This paper studies adaptive learning with multiple models. An agent operating in a self-referential environment is aware of potential model misspecification, and tries to detect it, in real-time, using an econometric specification test. If the current model passes the test, it is used to construct an optimal policy. If it fails the test, a new model is selected. As the rate of coefficient updating decreases, one model becomes dominant, and is used “almost always”. Dominant models can be characterized using the tools of large deviations theory. The analysis is used to address two questions posed by Sargent's Phillips Curve model.