Interactive Learning and Behavioral Sunspots

This paper shows how to extend the adaptive learning approach to a truly behavioral uncertainty problem. It investigates the simplest case of a first order self-referential model where two agents have a non-negligible impact on aggregate expectations. Unlike the standard setting, agents are not boundedly rational in that they acknowledge their own influence on output and they are perfectly informed about the exogenous determinants of the economy. Nevertheless no common knowledge is assumed; agents are epistemically isolated and they can only have noisy perceptions of the other agent's simultaneous expectation. In order to have consistent forecasts, each agent has to learn how the other agent's expectations will affect the economy. I prove there exist two types of learnable equilibria: (a) a unique rational expectation equilibrium (REE) and (b) at least one behavioral sunspot equilibrium (BSE). The latter may arise because the learning dynamics can generate the self-fulfilling reciprocal belief that the other agent is irrationally exuberant. Finally, numerical simulations illustrate how an unpredictable switch from the REE to a BSE may occur endogenously when both coexist and are learnable.