  We consider an agent who represents uncertainty about the environment via a
possibly misspecified model. Each period, the agent takes an action, observes a
consequence, and uses Bayes' rule to update her belief about the environment.
This framework has become increasingly popular in economics to study behavior
driven by incorrect or biased beliefs. Current literature has characterized
asymptotic behavior under fairly specific assumptions. By first showing that
the key element to predict the agent's behavior is the frequency of her past
actions, we are able to characterize asymptotic behavior in general settings in
terms of the solutions of a generalization of a differential equation that
describes the evolution of the frequency of actions. We then present a series
of implications that can be readily applied to economic applications, thus
providing off-the-shelf tools that can be used to characterize behavior under
misspecified learning.
