Rational Expectations in the Aggregate

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RATIONAL EXPECTATIONS IN THE AGGREGATE

I. INTRODUCTION

One of the major recent innovations in economic theory is the emergence of the rational expectations hypothesis, the hypothesis that expectations of agents tend to be consistent with the predictions of the relevant economic theory. This paper considers the relationship between the way rational expectations is typically employed in practice and the argument frequently put forth to justify its use.

Rational expectations has typically meant what we will refer to as standard rational expectations: the expectation of each agent taken separately is by itself consistent with the predictions of the relevant theory. This, however, is different from the argument frequently put forth by proponents of the rational expectations hypothesis to justify its use. This argument is that on an aggregate level expectations should be consistent with the predictions of the relevant theory. This justification recently in the works of Kantor [1979], Maddaock and Carter [1982], and Hoover [1984]; it was first expressed by Muth [1961, 316]:

The hypothesis can be rephrased a little more precisely as follows: that expectations of firms (or, more generally, the subjective probability distribution of outcomes) tend to be distributed, for the same information set, about the predictions of the theory (or the "objective" probability distributions of outcomes).

Underlying the above argument is a belief that if expectations are rational in the aggregate, then expectational deviations across agents will tend to cancel out. The statement of this belief also appeared in Muth [1961, 321]:

...Allowing for cross-sectional differences in expectations is a simple matter, because their aggregate effect is negligible as long as the deviation from the rational forecast for an individual firm is not strongly correlated with those of the others...

Charles Schultze [1985, 10] expressed the same notion in his 1984 presidential address to the American Economic Association: (1)

In a word of auction markets, the fact that forecasts of individual agents are widely distributed around the "true" mean is for most purposes irrelevant...

This paper formally investigates the relationship between standard rational expectations and what occurs when expectations are rational only in the aggregate, i.e., what will be referred to here as aggregate rational expectation. (2) The goal is two fold. First it is to show that the above view is overly simple. It is generally not the case that an aggregate rational expectations world can e accurately modeled using a standard rational expectations assumption. The second objective is to consider environments where standard and aggregate rational expectations equilibria differ, and investigate what factors affect the size of the difference.

These issues are examined by analyzing a model wherein agents choose between alternative activities. A crucial factor in determining the relationsip between standard and aggregate rational expectations equilibria is the nature of the interaction among agents. This interaction is characterized as being either of two types. First, activities can exhibit congestion, i.e., the larger is the total number of agents who choose to participate in a given activity, the lower is the incentive for agent i to choose that activity. Examples of situations which exhibit congestion are the problem of agents choosing between different roads which lead to the same final destination, and market decisions such as the problem of carrer choice or the problem of firms deciding where to locate. Second, the activities can exhibit synergism, i.e., the larger is the total number of agents who choose to participate in a given activity, the higher is the incentive for agent i to choose that activity. An example of a situation which exhibits synergism is the problem faced by consumers in choosing a computer hardware system; the larger is the number of individuals who purchase a particular system, the greater will be the subsequent availability of computer peripherals and software for that system. …