  Individuals use models to guide decisions, but many models are wrong. This
paper studies which misspecified models are likely to persist when individuals
also entertain alternative models. Consider an agent who uses her model to
learn the relationship between action choices and outcomes. The agent exhibits
sticky model switching, captured by a threshold rule such that she switches to
an alternative model when it is a sufficiently better fit for the data she
observes. The main result provides a characterization of whether a model
persists based on two key features that are straightforward to derive from the
primitives of the learning environment, namely, the model's asymptotic accuracy
in predicting the equilibrium pattern of observed outcomes and the 'tightness'
of the prior around this equilibrium. I show that misspecified models can be
robust in that they persist against a wide range of competing models --
including the correct model -- despite individuals observing an infinite amount
of data. Moreover, simple misspecified models with entrenched priors can be
even more robust than correctly specified models. I use this characterization
to provide a learning foundation for the persistence of systemic biases in two
applications. First, in an effort-choice problem, I show that overconfidence in
one's ability is more robust than underconfidence. Second, a simplistic binary
view of politics is more robust than the more complex correct view when
individuals consume media without fully recognizing the reporting bias.
