Abstract
Many asset prices exhibit large and highly persistent deviations from their fundamental values, yielding potential long-run predictability.¹ That asset prices can move from simple benchmark rational pricing levels and then stay far from these levels for some time is a major puzzle. The swings can be both short or long in duration, and their time series shows few regular patterns when one analyzes their long-range behavior. Many explanations have been proposed involving varying levels of rationality, knowledge, and learning, but no one explanation has dominated the debate. This chapter explores an underparameterized learning model with heterogeneous gain parameters and traders