An Introduction to the Theory of Rational Expectations Under Asymmetric Information

TLDR: In this article, the authors show that rational expectations models are radically different from the standard Marshallian or Walrasian model of competitive equilibrium in an economy where traders have diverse information, and show that if there is a complete set of insurance markets and utility is additively separable over time, then there exists a rational expectations equilibrium which gives consumers the same allocation as if each consumer has access to all of the information.

Abstract: Every good economics textbook contains the cliche that market prices provide signals which facilitate the allocation of resources to their best use. In a world not subject to random shocks, consumers and producers when faced with competitive prices need look no further than their own preferences or production technology to be able to make a decision. They need give no thought to the tastes, endowments or technology of other agents. However, in a world subject to random shocks, this is no longer the case. Agents are faced with the problem of forecasting future states of nature and more importantly of forecasting the impact of these states on the actions of other agents. Rational expectations theories provide a model of how agents make those forecasts. In a world subject to random shocks, it will be the case that agents acquire (or at least attempt to acquire) information about the future realization of the shocks. It will, in general, be the case that different agents have access to different information. The fact that information is dispersed throughout the economy has the potential to cause a misallocation of resources relative to what would be the case if all agents knew everything. An efficient allocation of resources will in general require the transfer of information from consumers who have some information about their future demands to producers who can take current actions to mitigate avoidable scarcities or surpluses. Though many classical and neo-classical writers emphasize the informational role of prices, the standard Marshallian or Walrasian model of competitive equilibrium does not involve prices transferring information across traders. The purpose of this paper is to show that rational expectations models are radically different from Walrasian models in an economy where traders have diverse information. This is demonstrated by showing that unlike what occurs in a Walrasian equilibrium of an economy with heterogeneous information, if there is a complete set of insurance markets and utility is additively separable over time, then there exists a rational expectations equilibrium which gives consumers the same allocation as if each consumer has access to all of the economy's information. This implies that, under the above assumptions, a central planner with all the economy's information could not Pareto dominate the competitive allocation achieved when traders have diverse information and rational expectations. This paper makes no attempt to survey the literature on rational expectations. The reader is referred to Shiller (1978), Barro (1981) for a survey of macroeconomics and rational expectations, and Radner (1980) for a survey of the microeconomics and mathematical theory of rational expectations. This paper will, however, try to outline the evolution of the rational expectations concept from a notion of optimal forecasting to a virtually complete departure from the Walrasian model of equilibrium. The rest of this section is devoted to a discussion of pre-rational expectations ideas.