The Role of Priors in Active Bayesian Learning in the Sequential Statistical Decision Framework

Abstract

This chapter introduces the notions of rational expectations and optimal learning extensively used in economic theory.* It has become well known from recent literature that in active learning situations (where the actions of the statistician, or the person learning about some parameters, influences the draws from the distribution about which he/she is learning), full learning may not take place. This challenges the use of the rational expectations hypothesis which is justified on the basis that agents operating in an economy eventually all learn the true structure of the economy and optimize accordingly. In El-Gamal and Sundaram (1989, 1990) we presented a framework where a Bayesian economist imposes priors on agent-priors and we then study the evolution of those economist beliefs. We showed that generically, the economist limit beliefs generically do not have point mass at any particular agent-belief, let alone the true rational expectations belief. We show, however, that in most cases where there is sufficient variability in the law of motion that the agents are trying to learn, in sequential models that are extensively used in the economic literature, the rational expectations hypothesis may indeed be justified on the basis of optimizing and optimally updating agents.