# THE RATIONALITY OF RATIONAL EXPECTATIONS

Cloda Lane
Junior Sophister
_____________________________
The advent of rational expectations in econometric models has marked a revolution in economic thinking that is comparable in the magnitude of its impact on the economics profession to the Keynesian revolution of a half century ago.[6]
The purpose of this essay is not to defend the numerous models and policy prescriptions which are based on the rational expectations hypothesis but to provide an insight into why the hypothesis coincides with optimising economic behaviour. As Simon (1978, p 12) outlines, Economics, whether normative or positive, has not simply been the study of the allocation of scarce resources, it has been the study of the rational allocation of scarce resources. Expectations often form a major part of the decisions which are made in the economy and as such they should also come under the doctrine of rationality. In line with other rational economic behaviour[7]we must see if the rational expectations hypothesis is the best (the objective) available (the constraint) method of modelling expectations. To show that this hypothesis is rational I will outline the theory itself and then I will show how it can withstand both theoretical and empirical criticisms.

## The Rational Expectations Hypothesis

The premise of the rational expectations hypothesis is that economic variables are generated by systematic processes. Over time, economic agents learn what the process determining a variable is and they will use this knowledge to form expectations of that variable. Individuals learn about the variable generating process by using all the information available to them that is related to the variable. The end result is that the expectations of firms (or, more generally, the subjective probability distribution of outcomes) tend to be distributed, for some information set, about the prediction of the theory (or the objective probability distribution of outcomes).[8]

To see how the hypothesis works imagine an economic variable, Y, whose value is determined by its own lagged value, by the lagged value of two other variables, X and Z, and by a random variable U. This provides us with the simple linear process:

Yt = 0 + 1Yt-1 + 2Xt-1 + 3Z t-1 + Ut

The expected values of Yt is found by finding the mathematical expectation of Yt . Since Yt-1, Xt-1 and Z t-1 are lagged, their values are known at the end of period t-1 (when the forecast is being made). The values of Ut, however, only becomes known at the end of period t so the rational forecaster must form some expectation of its value at the end of period t-1. This means that:

Et-1(Yt ) = 0 + 1Yt-1 + 2 Xt-1 + 3Z t-1 +Et-1 (Ut)

The random variable is assumed to be distributed with mean zero and variance 2. The best estimate that can be made of the expected value of Ut is to use its mean value, zero. This leaves us with a formula for the expected value of Y as:

Et-1(Yt ) = 0 + 1Yt-1 + 2 Xt-1 + 3Zt-1

Thus, the rational expectation of the variable Y in period t is its mathematical expectation given the available information. Thus, as Muth (1961) explained, rational expectations should be generated by the same (stochastic) process that generates the variable to be forecast.[9]

The rational expectations hypothesis does not argue that agents are always right in their expectations of future variables. In fact, the forecast error is exactly equal to the random variable that determines Yt. This random variable is uncorrelated with the other variables in the process and with the information set available to the agent. This makes sense because if such correlation existed, it would logically be included in arriving at the initial expectation.[10] These random variables, and hence any forecast errors, are surprises or news in the system. They are random, they exhibit no definite pattern, they have a mean value of zero and they have a variance less than that associated with any other model of forecasting.[11] This means that, on average, rational expectations will be correct because the mean value of the forecast error is zero and it also means that they are the most efficient (in a statistical sense) means of forming expectations because their forecast errors have the property of minimum variance.

The rational expectations hypothesis thus puts forward a means of forming expectations which is based on agents taking account of all necessary available information to make their forecasts. The information is used efficiently to determine the process which generates the variable in question and the process is then used to formulate an expected value of that variable. The end result is that, Rational expectations, by Muths definition, yield predictions of future events which differ from the corresponding eventual outcomes only by errors which are themselves independent of the variables used to generate the predictions.[12]

Rational expectations are best in a statistical sense but do they stand up to theoretical and empirical scrutiny? In answer to this question the following discussion will focus on some of the major theoretical criticisms of the hypothesis and some of the empirical evidence concerned with the formation of expectations.

## Theoretical Analysis

One of the main criticisms of the rational expectations hypothesis is that, as Arrow (1978) outlines, Economic agents are required to be superior statisticians, capable of analysing the future general equilibria of the economy.[13] This criticism stems from the mis-conception that Muth was proposing that economic agents use the exact model used by economists.[14] The fact of the matter, however, is that the rational expectations hypothesis argues that trained economists and economic agents produce the same expectations but it does not argue that they come to that conclusion by using the exact same method. In fact for the hypothesis to hold it is sufficient that in the light of past observation and experience they possess some concept of a reduced-form approach to economic modelling to permit them to make reasonable predictions.[15] This criticism of economic agents needing to be qualified economists for the hypothesis to be viable does not, therefore, withstand closer scrutiny of Muth's thesis.

A closely related criticism is the one that argues that the idea of rationality is implausible in itself. Can we really assume that all decision-makers are intelligent enough to use and fully understand all the available information? Once again, this criticism is based on a misconception of what the hypothesis is saying. The hypothesis does not apply to every individual in the economy. Rather, it claims that on the average expectations are rational. Thus, some agents may irrationally overpredict and some may underpredict but this does not mean that on average the expectations in the market cant be rational.

We must also remember that the hypothesis doesnt require that every single agent in the market gathers and formulates the information themselves and makes the expectations for themselves. In many cases individuals let other people form their expectations for them. For example, peoples expectations of inflation are often based on the expectations that have been carefully constructed by economists in the Central Bank, the ESRI or the Department of Finance. These expectations are based on full information and are rational. Thus, the market as a whole has rational expectations even though these expectations have been formed by only a subset of society.[16] Another situation where individuals allow others to form their expectations for them is in the labour market: Here, many such agents are perfectly willing to delegate the model-analysing role of their elected or appointed trade union representatives who do indeed invoke former models and often employ expert financial specialists and consultants to assist them.[17] Thus, the expectations of the market as a whole can be rational without making the highly unlikely assumption that every single individual forms rational expectations.

Finally, the criticism of the hypothesis on the grounds of rationality undermines the basis of economics: The idea that the typical individual is capable of making the best of the opportunities open to him is a common one in economics.[18] Thus, to claim that agents are not rational when making forecasts is equivalent to claiming that the core of economic argument, that economic agents are rational decision-makers, is incorrect.

A third criticism of the rational expectations hypothesis is that the information necessary to form expectations is not always available and when it is it may be very costly to use it. It is true that individuals can not automatically know which variables are important in the variable generating process or know what the size of the coefficients in that process are but it is also true that the rational expectations hypothesis doesnt claim that they do. What the hypothesis argues is that on average and after a period of time, economic agents will learn from past experience what the process is. They will combine this developed knowledge with current available information to form their expectations. This is why the rational expectations hypothesis is best seen as a long-run argument. It is based on a learning process which takes time but once the necessary knowledge is acquired the process determining a variable will be known. It must be noted, however, that Friedman (1979, p 24) is right to point out that what is typically missing in Rational Expectations models, however, is a clear outline of the way in which economic agents derive the knowledge which they then use to formulate expectations meeting the requirement. This is something which needs to be developed in models that are based on rational expectations but we must remember that the models are based on the hypothesis, and are not the same as it. Thus, although a knowledge of the learning process of economic agents would make economic models more concise, the absence of it does not take away from the hypothesis itself.

The other side of this information criticism is that even when information is available it is costly to use. This criticism, however, does not take away from the rational expectations hypothesis. The crux of the hypothesis is not that a rational agent should simply use all the available information but that he should use all the available information in an efficient manner. That is, an efficient and rational individual will carry out a form of cost benefit analysis on the information, using only that which is of net benefit to him. Thus, in fact, the limitation imposed by costly information coincides with the efficiency standpoint of the hypothesis. There is also the argument that when information, that is absolutely necessary, gets too costly, agents can pool together to obtain that information or the government can obtain it and provide it to the public. Both of these methods ensure that agents still get the information and thus they can still form rational expectations.

A fourth criticism of the hypothesis is that it has limited applicability. As it is not always easy to determine the process by which a variable is generated it may not always be possible to form rational expectations. However, as Attfield, Demery and Duck (1985, p 28) outline a rational expectation can still be formed without knowing the exact process. In fact, we can still form expectations from an intelligent appraisal of circumstances, though the process behind such circumstances may be a bit harder to discern. Thus, rational expectations can be made even when variables are generated by unique and unusual processes because the economic agent will have enough information to make an intelligent estimate of the process.

The final criticism of the rational expectations hypothesis is the argument that the hypothesis is not testable. The obvious retort to this criticism is that although expectations are inherently immeasurable, there have been numerous attempts made to incorporate them into econometric models and to test their validity in these models. This fact holds for all proposed means of expectations formation (including adaptive and rational). Although the attempts made to test these hypotheses are not perfect, they are no worse for the rational expectations hypothesis than they are for any other expectations hypothesis. To see how the hypothesis holds up under these tests we must look at some of the empirical work that has been carried out on it.

## Empirical Analysis

Since Muths seminal article was published, numerous attempts have been made to prove and disprove the rational expectations hypothesis. The hypothesis has been supported by much empirical work in the financial markets and commodity exchanges.[19] For example, Mishkin (1983, p 157) found that on balance the results justify using the assumption of rational expectations in empirical work, especially when financial markets are studied. The results for these specialised markets are very robust but there is much truth in the argument that the hypothesis holding true in these markets does not prove that it is the ideal way of forming expectations across the economy. While no major favourable insights of rational expectations in other markets have abounded, those empirical studies that have claimed to disprove the hypothesis have not been technically strong.

For example, many of these empirical tests of the rational expectations hypothesis have used survey data to proxy expectations.[20] Using survey data, however, presupposes that for market expectations to be rational all agents surveyed must be forming rational expectations. We know, however, that the hypothesis is based on the market, on average, having rational expectations and not on every individual forming such expectations. There is thus a data identification problem here and we must conclude that survey forecasts do not necessarily describe the forecasts inherent in market behaviour, and irrationality of survey forecasts does not in itself imply that market forecasts are also irrational.[21] Thus, any empirical attack on the rational expectations hypothesis which is based on survey data can not be taken as absolute.

Another problem with many of the empirical criticisms of the rational expectations hypothesis is that they have been based on tests which do not satisfy important statistical criterion. The most notable of such tests is the Chow Test.[22] This test has been used by many economists to test the rational expectations hypothesis but often their data fail to be consistent.[23] When alternative testing methods are used what the Chow Test showed to be irrational has often been shown as rational.[24] Thus, any conclusion about the irrationality of the rational expectations hypothesis based on these tests can not be assumed to be accurate.

These are just two examples which highlight some of the many problems that arise in empirical work concerned with expectations. No overall conclusion about whether expectations in the market are rational can be obtained from empirical work as it is so imperfect. All that we can do is realise that in the case of the financial markets there is widespread evidence to support the rational expectations hypothesis while in the case of other markets there is not sufficiently strong evidence to completely disprove this theory. Until this hypothesis has been empirically falsified it can not be dismissed as irrational.

## Conclusion

Rational expectations are the best available models that economics has for modelling economic expectations. At a statistical level, they are efficient because they have an error term whose variance is less than that of any other method of modelling expectations and which has a mean value that predicts that on average, the error variable will be zero. The rational expectations hypothesis is also best because, unlike other hypotheses, it coincides perfectly with the concept of homo economicus and of the utility-maximising individual.[25] Finally, there is more information available that discredits other expectations models than there is to disprove the rational expectations hypothesis. Thus, the hypothesis that expectations are rational must be taken seriously, if only because its alternatives, for example various fixed-weight autoregressive models, are subject to so many objections.[26] The main point to be made is that the rational expectations hypothesis is not perfect but, given that expectations need to be incorporated into economic models, it is the best available method that we have for modelling these expectations. It therefore fits the loose economic criterion of rationality.

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