On rational belief equilibria

Summary We study equilibria in which agent's belief are rational in the sense of Kurz 1994]. The market is formulated by specifying a stochastic demand function and a continuum of producers, each with a quadratic cost function who must select their output before knowing prices. Holding Rational Beliefs about future prices, producers maximize expected profits. In a Rational Belief Equilibrium (RBE) agents select diverse forecast functions but each one is rational in the sense that it is based on a theory which cannot be rejected by the data. It is shown that there exists a continuum of RBE's and they could entail very different patterns of time series for the economy and consequently different aggregate levels of longterm volatility. Since the model contains exogenously specified random variables, the difference in the level of long-term volatility of prices among the different RBE's arises endogenously as an amplification of the volatility of exogenous variables. The paper derives exact bounds on the possible levels of such amplification.This research was supported by NSF Grant IRI-8814954 to Stanford University. The author is thankful to Steven N. Durlauf and Carsten K. Nielsen for useful comments on an earlier draft.