Muth’s Rational Expectations

John F. Muth Rational Expectations and the Theory of Price Movements Econometrica, Vol. 29, No. 3. (Jul., 1961), pp. 315-335.

Two major conclusions from studies of expectations data are the following:
1. Averages of expectations in an industry are more accurate than naive models and as accurate as elaborate equation systems, although there are considerable cross-sectional differences of opinion.
2. Reported expectations generally underestimate the extent of changes that actually take place.

[Expectations}, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory. …

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 prediction of the theory (or the “objective” probability distributions of outcomes).

The rational expectations hypothesis states that, in the aggregate, the expected price is an unbiased predictor of the actual price.

 Comment

It assumed that an unbiased predictor exists, and nowhere are economies out of equilibrium considered. It is also implicitly assumed that the theory is broadly correct. Thus a pedant (like me) can consider two variants of the theory:

  • If firms believe in some theory, then their predictions will tend to be those of the theory, and they will expect their predictions to be roughly correct.
  • If a theory is correct, then under competition we may expect the predicitions of firms to be roughly those of the theory, whether or not firms know of the theory. Moreover, the predicitons will tend to be optimal in some sense.

In particular:

If there is a dominant theory, then the subjective probability distribution of outcomes tends to be distributed, for the same information set, about that theory’s probability distributions.

By dominant theory I mean one that is believed to be correct by those who influence the subjective probability distribution. It is not enough that a firm believes a theory, since the firm will often adapt to the behaviour of others, which can lead to inconsistent behaviour. But broadly what is being suggested is that firms act in approximate accord with their beliefs, and do not systematically deviate from them. This begs the following questions:

  • Is what is believed always correct, and could it incorporate systematic biases?
  • Do firms necessarily believe in theories that are represented by probability distributions?
  • In a free competition, do theories that can be represented by probability distributions have an advantage?

We could ask similar questions about individual rationality, perhaps looking to logic for some insights. Whitehead introduced the concept of an epoch, within which classical concepts, such as probability distributions, applied. Using this term we may say that:

  • There are objective mechanisms by which reasoning agents with enough relevant information will tend to converge to the actual theory of the epoch.
  • Acting on the above theories will be an optimal strategy for that epoch.

With this in mind it seems reasonable to limit Muth’s thesis to short-term expectations. Thus if one thinks there might be a financial crisis, one cannot rely on Muth’s argument to suppose that one can ‘predict’ the future by canvasing firms’ opinions.

Dave Marsay

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