Continuous Beliefs Dynamics

Abstract

We propose a general framework for studying the evolution of heterogeneous beliefs in a dynamic feedback setting. Beliefs distributions are defined on a continuous space representing the possible strategies agents can choose from. Agents base their choices on past performances. As new information becomes available strategies are re-evaluated and the beliefs distribution is updated using a continuous choice model. This approach gives rise to price dynamics in which the beliefs distribution evolves together with realized prices. The statistical properties of the endogenous random price fluctuations are fully determined by the model. The structure of the macroscopic model depends on the class of predictors and on the performance measure used by the agents. Whenever a well-known econometric model is obtained, an economic interpretation of the model parameters can be given, as is shown here for an ARCH model. The approach is illustrated with several examples and empirical applications.