Market selection and learning under model misspecification

Abstract

This paper studies market selection in an Arrow-Debreu economy with complete markets where agents learn over misspecified models. In this setting, standard Bayesian learning loses its formal justification and biased learning processes may provide a selection advantage. Studying two cases of model misspecification and four learning processes, our analysis reveals that, differently from correctly specified settings, the ecology of traders populating the market crucially affects selection dynamics and, thus, long-run asset valuation. In fact, model misspecification implies a general difficulty in ranking learning behaviors with respect to their survival prospects. For instance, prediction averaging shows an advantage when the true data generating process belongs to the same family of models that agents use to learn. This advantage partially disappears when the true model belongs to a more general class, as a trade off emerges between approximating the projection of the true model on the space on which the agents learn and adapting to the part of the true model that cannot be represented in that space. Rules that guarantee survival are possible, but they exploit imitative mechanisms that require information about all the other market participants.