We link two approaches to biased belief formation: non-Bayesian updating and misspecified models. The former parameterizes a bias with an updating rule mapping signals to posterior beliefs or a belief forecast describing anticipated beliefs; the latter is an incorrect model of the signal generating process. Our main result derives necessary and sufficient conditions for an updating rule and belief forecast to have a misspecified model representation, shows that these two components uniquely pin down a representation, and constructs it. This clarifies the belief restrictions implicit in the misspecified model approach. It also allows leveraging of the distinct advantages of each approach by decomposing a model into empirically identifiable components, showing these components isolate the two forms of bias that the model encodes—the retrospective bias after information arrives and the prospective bias beforehand, and rendering off-the-shelf tools to characterize asymptotic learning and equilibrium predictions
in misspecified models applicable to non-Bayesian updating.