[Note for bibliographic reference: Melberg, Hans O. (1997), Why (dis)believe
rational expectations? A review of Sheffrin's Rational Expectations, http://www.oocities.com/hmelberg/papers/970307.htm]
Why (dis)belive rational expectations?
A Review of Steven M. Sheffrin's Rational Expectations
by Hans O. Melberg
Steven M. Sheffrin, Rational Expectations, Cambridge: Cambridge University
Press, 1996 (2nd edition, first: 1983), ISBN: 0-521-47939-8, 184 pages
Why should we care about rational expectations? As with any other approach I believe there
are two criteria which determine whether it is worth our attention. First, we should ask
whether the approach is reliable. In short, is the theory true? Second, we should ask if
the approach is relevant. To what degree does it affect actual policies? If the theory is
both true and relevant, then it is worth our attention.
At first sight Sheffrin seems to disagree with the above criteria. In his book Rational
Expectations he argues that the rational expectations approach should be judged in
terms of its fruitfulness in generating further research. As he writes "The 'test'
that will be used is whether thinking in substantive areas has changed because of the
influence from the rational expectations approach" (p. 24). However, a reading of his
book shows that Sheffrin is using a survey of the literature generated by rational
expectations as a veichle to discuss the truth and relevance of rational expectations.
This is good. It would be disappointing indeed if Sheffrin merely surveyed the field
without pronouncing some kind of judgement on the quality of the articles surveyed and on
the relevance of rational expectations in general.
We may divide Sheffrin's text into three. First, Sheffrin explains rational
expectations, stable stochastic systems and many other concepts. Second, there is a survey
of the literature employing rational expectations. Third, Sheffrin evaluates these
arguments in order to make an aggregate judgement on rational expectations. I shall argue
that the first two parts are very well done. In the words of another reviewer,
"Sheffrin is particularly succesful atreducing the complex mathematics and
econometrics to a reasonable level without unduly shortchanging the reader." (J. S.
McCallum in JEL 22 (1984), p. 1636). I am, however, more critical of some of Sheffrin's
arguments relating to whether the articles support or subvert the rational expectations
approach. The main problem being that he does not seriously discuss the weak power of
statistical tests when rational expectations is specified as the null hypothesis. It is
not very convincing to argue that we should believe in rational expectations because we
cannot be more than 95% sure that another expectations mechanism is correct.
What is rational expectations
Economics is concerned with the actions of agents which, in turn, are determined by the
agents preferences and beliefs (and, if one allows a broader framework - emotions and
norms). Consumption, for example, depends the agents' beliefs about future income. Hence,
to predict consumption, or to evaluate the effects on consumption of changes in policy, we
must know how beliefs are formed. The great question is then: How do agents form their
Before we answer this question we may impose a few restrictions. First, is seems
unlikely that all the people can be fooled all the time. In other words, it seems wrong to
have a theory of expectations formation which implies that people make the same mistake
over and over again. If you have overestimated the growth in your real wage several years
in a row, you would probably decrease your estimate for real wage growth next year. At
least, this would be the rational thing to do since rationality implies adjusting your
beliefs according to evidence.
Second, we may argue that the mechanism for forming expectations should be efficient in
the sense that it should exploit all available evidence. This implies that it should not
be possible to arrive at a more correct expectation given the available information. Once
again we may justify this restriction by arguing that it would not be rational to ignore
valuable information when forming beliefs. We are usually best served by having correct
beliefs (not always since some lies may be necessary in order to avoid depression and
other undesirable consequence). Imagine you have mistaken beliefs about the probability of
a girl or a boy accepting your invitation to a date. This could cause some acute
embarrassment if you acted on these false beliefs and was rejected after asking the person
Based on these two restrictions, Muth (1961) proposed to make the subjective
expectations of agents in a model equal to the mathematical solution of the model. This
may sound convoluted, but it is simply to argue that the agents act as if they have
knowledge of the model before they form their expectations. This means that my expected
income is the same as the income predicted by the model - ignoring random fluctuations. We
can now replace an unknown variable - the expected income - with a known variable - the
income predicted by the model in question. In this way the model can be solved to give
The big question, of course, is whether models based on this procedure produces good
predictions about the real world. Before I discuss this, it is important to note that one
need not argue that agents actually go through the complicated functions of the model in
order to form their expectations. It is enough if they act as if they performed the
calculations. To use a simple example, we may use a complicated mathematical model to
predict the angle and strength of the shot of a pool player. This prediction can be
accurate even if the pool player does not use the model when he actually decides the angle
and strength of his shot.
Is it true?
a) Empirical arguments
There are a large number of problems associated with testing the rational expectations
approach and Sheffrin does not skip these. For example, to test for rational expectations
is always a joint test of the model employed and rational expectations. If your results do
not match data from the real world, you have two options. First, to say that the model is
wrong, and that we should still use the rational expectations approach. Second, to say
that the model is right, but that the result indicates that expectations are not rational.
There is no uniquely correct answer, though further testing may reveal one as more
probable than the other.
A more serious problem is to assume that the approach is correct as long as no other
hypothesis gives statistically significant results. This is a very weak test because
statistical convention has made it easy to maintain the null hypothesis. I found this to
be a major problem with Sheffrin's argument. He repeatedly reports that a test could
"not reject" the null hypothesis of rational expectations, but this is not a
very impressive or powerful result. (For some examples, see the following pages: 17, 21,
52-54, 142-3, 156). In traditional hypothesis testing the odds are stacked overwhelmingly
in favour of the null hypothesis. The result that the null hypothesis cannot be rejected
does not constitute convincing evidence in favour of a theory.
With these qualifications in mind, we may enter the field of empirical testing of the
rational expectations hypothesis. In order to be rational, Sheffrin argues that
expectations must be unbiased (no systematic mistakes), efficient (use all past
information about the variable), consistent (forecasts at different times should not
conflict) and the forecast-error must be unpredictable. He then surveys a large number of
articles employing the mentioned tests. These articles discuss the Livingstone data
(inflation expectations), interest-rate expectations data, sales-expectation data and
foreign-exchange-rate data. Sheffrin then concludes that "On the whole, survey data
do not support the rational expectations hypothesis" (p. 21).
Nevertheless, after concluding that the data doesn't support the hypothesis, Sheffrin
feels compelled to advance three arguments for disregarding the empirical tests (p. 21).
First, people may say one thing and do another - thus, surveys of opinions do not reveal
whether people actually behave rationally. Second, even if a survey shows that a majority
have non-rational expectations, we need only a few rational traders to make whole markets
rational. Third, rational expectations is an assumption - not an observable or testable
variable. Against these one might argue - first - that Sheffrin does not give us any
reasons to believe that people do not act on the reported beliefs. Sometimes people say
one thing and do another because they are embarrassed by revealing their true beliefs
(being racists, workers voting for the Tories in Britain etc.). However, there is no such
reason to hide your estimate of inflation. Second, many surveys do not test the opinions
of the agents, but whether the price of an asset follows a pattern which is
consistent with rational expectations. In this way they avoid the problem of confusing the
rationality of traders with the rationality of markets. As for the third argument, I see
no reason why we should not test the rational expectations approach even if the approach
is considered to be an assumption. Why not test assumptions? All tests are imperfect
(joint), but this does not constitute evidence against testing in general.
b) Theoretical arguments
There are a number of theoretical arguments for and against the rational expectations
approach. I shall consider four such arguments: Endless regression, reductio ad
absurdum, no other model give precise results, and the free rider problem.
One may try to justify the use of rational expectations by appealing to the standard
assumption of maximization of utility. Rational expectation, on this approach, becomes
nothing more than the application of the maximizing assumption in the field of
information: You collect information as long as the marginal benefits are higher than the
marginal costs. The problem is that it is impossible to know the marginal benefit of
information. One fact may radically change your beliefs (such as the appearance/loss of an
alibi for a person) and it is difficult (impossible?) to know how much the information is
worth before it is gathered. We might argue that we should establish higher order rules to
solve this problem: To find information on how much information we should gather. However,
this clearly leads to an endless regression - which need not converge to a limit - since
we must also gather information on how much information to gather on how much information
we should gather before we make a decision!
Sheffrin is aware of the above argument, as is evident from his comment that
"because knowledge of costs is so limited, it does not appear useful to base a theory
of rational behaviour solely on the benefit-cost principle of gathering information"
(p. 14). But, as far as I can see, Sheffrin does not provide an alternative basis for a
theoretical justification for rational expectations.
Maybe I am exaggerating the practical problems involved here? Although there are some
situations in which it is impossible to form rational expectations, this does not mean
that it is impossible to form a coarse estimate in many situations about the value and
cost of information. If you buy a second hand car, it is surely rational to make a
telephone to the national register for liabilities to see if the car is used as corallery
for a loan (at least in Norway you could end up paying the debt of the previous owner if
you do not do so). It then becomes an empirical question whether the number of situations
with radical uncertainty outnumber (in quality and quantity) the number of situations with
reasonably well known probabilities and payoffs.
Reductio ad absurdum
Sometimes rational expectations are justified by the argument that if expectations are not
rational, the dynamics of the system is such that an explosion will occur - the solutions
will become more and more extreme (A good example is the Cob-Web model). Now, since it is
difficult to believe in eternal explosions we should believe in rational expectations. At
least this leads to the stable solution. To quote Sheffrin again:"... in rational
expectations models the instability of the formal system is used to determine the actual
trajectories that the system will follow. We will assume that the system will
return to long-run equilibrium following any shock" (p. 70-71, italics as in the
original text). In short, consider a horse-rider who is sitting is his saddle. A saddle is
unstable in one direction (it is easy to slide from side to side), but stable in another
(it is hard to slide far backwards and forwards). Economic systems may be stable and
unstable in the same sense - an increase in a price may under some conditions lead to
another increase in the same price which in turn leads to an even bigger increase and so
on. Sheffrin's argument is that the rider - or the economy - will always tend toward the
stable path; to be in the saddle and not to fall off.
In what way is this assumption justified? First Sheffrin argues the assumption is
required in order to derive mathematically interesting answers. Second, the stable path is
often the utility-maximizing path - falling off the saddle is no way to maximize your
utility! I shall comment on the first argument below. I will only note that the argument
seems to ignore that collectives bodies are not rational in the same way as individuals.
As for the second argument it seems a bit curious to invoke the utility argument since
Sheffrin previously admitted that this was a weak argument (see the above quote from p.
More generally, I have problems with accepting arguments like "you should believe
theory X since if X does not apply the system may generate extreme solutions." First
of all, there is no law preventing extreme events from occurring. Second, other methods of
forming expectations may lead to stability (depending on the specification adaptive
expectations may lead to the stable path in a cob-web cycle). Third, there is not need for
the system to always end up in an extreme situation when expectations are irrational since
the system may be characterized by continuos and contradictory shocks. Thus, on its way to
one extreme, the system may be tilted in another direction by a second shock. This shock
may set the system on its course for another extreme, but a third shock may intervene to
prevent it reaching the extreme solution. It is a bit like a marble rolling on a big table
with people who continually raise and lower different ends of the table. Although there is
no stable point, it is possible that the marble will go on rolling for a long time -
forever is also possible - until it falls off. Hence, the fear of extreme solutions does
not lead me to accept the rational expectations thesis.
Nothing else produce usable results
As mentioned, Sheffrin sometimes justifies the rational expectations approach by arguing
that alternative methods does not yield useful results. For example, he writes "I am
not denying that economic systems can be unstable. I am, however, suggesting that
comparative statistic or dynamic exercises are not really meaningful or interesting with
unstable models" (p. 71). His discussion of Simon's more psychological approach to
expectations (bounded rationality) also illustrates how the desire for precise
mathematical solutions inspire the rejection of one theory (Simon) and the adoption of
The big problem, of course, is that a precise numerical solution is of little use if it
incorrect. There might be a trade-off between truth and precision, but the weighting must
surely be heavily skewed toward truth. To argue that we should use one theory
instead another because it gives us numerical results - although the other approach might
be more plausible - is sometimes valid, but not very convincing. To argue that one theory
is more true than another because it yields precise results is clearly false. If
reality is such that precise results are impossible, we might be better off simply
admitting this instead of trying to be hyperrational or rely on second-decimal arguments
(see the writings of Jon Elster for more on this).
One might also question whether the rational expectations approach gives the desired
precise results. The existence of multiple equilibria (see Sheffrin p.74) implies that
even with the assumption of rational expectations we are not guaranteed a unique and
precise solution to our model. Sheffrin also notes how rational expectations sometimes
leads to instability when combined with Keynesian models of the economy.
Lastly, I am also unsure about Sheffrin's claim that it is not meaningful or
interesting to examine non-stable systems mathematically. Since I only have limited
knowledge of the technical details, I shall refrain from sweeping denunciations. However,
I believe alternative methods of analyses (such as computer simulations) may yield both
interesting and equally reliable solutions even if the system examined is structurally
The free-rider problem
When determining how much to pay for a stock, it is rational to estimate the expected
value of this stock in the future. Even if we ignore the problem of endless regression and
radical uncertainty in finding this expected value, there is a problem of free-riding. If
all the other people who buy stocks are rational, then the stock price already reflects
all the relevant information and there is no need for me to incur the costs involved in
gathering information about the expected value of the stock. I may simply free-ride on the
information gathered by the other buyers which is reflected in the stock price. But, if I
can free-ride what prevents the other buyers from free-riding? As Sheffrin writes:
"If efficiency required that all available information be aggregated into prices,
then why would anyone bother to collect information to begin with?" (p. 100).
Luckily, there seems to be a solution to this problem. Grossman and Stiglitz (1980)
have argued that as long as prices "reflect the uncertain supply of the stock of the
risky asset" there is an incentive to collect some information. True, some of this
information is conveyed to the uninformed traders through the price of the asset, but the
information is not perfectly conveyed. An uninformed trader does not know whether a change
in prices is caused by a change in demand or supply. Since knowing this is valuable (we
get a more reliable estimate of the expected payoff), there is an incentive for some
traders to buy information. In equilibrium there will be some informed and some uninformed
traders. The informed earn higher returns, but they also have to pay for the costs of
Is it relevant?
If we assume it is true, then there is little doubt about the importance of thinking about
rational expectations. Sheffrin demonstrates this with admirable clarity by working
through a few instructive models. One example is the debate about policy ineffectiveness.
If people have rational expectations, then - the argument goes - the government cannot
affect the level of national output by fiscal or monetary policy. Sheffrin then shows how
this conclusion emerges in a short model.
But, Sheffrin is not content to merely show the conclusion. He goes on to demonstrate
how the conclusion depends on three factors. First, whether money is neutral or not. One
reason for believing that money is not neutral is that inflation will affect the relative
price between cash goods and credit goods, in which case policy still has a real effect.
Second, the specification of the aggregate supply cure is important in arriving at the
policy-ineffectiveness conclusion. Contracts may cause price-rigidities which means that
Lucas supply function is not correct. This, once again, gives policy a role to play since
the government may raise output by expansive policies without causing a great deal of
short run inflation (prices are fixed through contracts) or when the economy is in a
situation when relative prices must adjust (given asymmetric nominal stickiness - that
nominal prices are hard to adjust downwards). Third, the information-structure is
important. If governments have more information than agents, then policy may be effective.
All in all, the policy ineffectiveness proposition is driven by many factors, not only
rational expectations. This leads to the conclusion that rational-expectations are not
necessarily tied to conservative neo-classical economics. It is possible to have rational
expectations in an economy with sticky prices as well as the neo-classical economy of
quick price adjustments.
In the same structured way as he deals with the policy ineffectiveness debate, Sheffrin
also discusses some of the other major issues concerning the relevance of rational
expectations: Overshooting (in the housing and foreign-exchange market), business cycles
(and the somewhat implausible theory that slumps are really vacations), time
inconsistency, rules vs. discretion and the Lucas critique. Overall I felt the discussion
was very informative. It was clearly structured and the major positions were very well
summarised. Altogether they overwhelmingly demonstrate the importance of considering
rational expectations, given - of course, that the approach is valid. An approach may
yield very important implications, but this is of little interest if the approach itself
is based on false assumptions.
An interesting idea
Before concluding, I would like to point out one particularly interesting sub-chapter
titled "the micro-economics of rational expectations" (p. 101). One of the
themes of this chapter is an attack on conventional microeconomic theory since it
"does not take into account the potential gains from aggregating information"
(p. 102). The point is that according to conventional theory prices are functions of
preferences and the scarcity of resources. However, when uncertainty is introduced (about
resources and other variables), the market clearing prices in the conventional equilibrium
is itself a source of information for the agents in the economy. The aggregate prices give
you information about the expectations of the other agents. This implies that there is a
second equilibrium in which the agents also consider the information revealed by the
aggregate market prices (i.e. they update their beliefs once again). Yet, this second step
is an ignored topic in the classical literature. Lange and von Mises spent much time
considering the efficiency of the first equilibrium and whether it could be achieved and
improved by planning, however they did not take the second step to discuss the properties
of the second equilibrium.
It is important to go further into this because the second step may contain market
failures which create inefficiencies. Some research has been done by Grossman who first
considered the naive equilibrium to describe the equilibrium which exists when the
agents do not take into account that market prices reflect other agents' information. He
then used the term artificial economy to describe the solution in which each trader
access to all information. In his model Grossman then proved a strong welfare proposition
implying that there was no advantage to collecting information centrally i.e. there was no
scope for Pareto improvements in the equilibrium of the artificial economy. (This
corresponds to the standard conclusion about the welfare properties of the Walrasian
equilibrium or what we have called the naive equilibrium). Although I cannot claim to
fully understand all the details and implications of the above discussion, I do believe
Grossman points to an issue which has received little attention and which might be
important. In short, it deserves further thought.
If you want a panoramic overview of the literature surrounding rational expectations, then
Steven Sheffrin's book is just what you need. On the other hand, if you are interested in
a sustained argument for or against rational expectations, this book will disappoint you.
Comment from the author, S. Sheffrin
Thanks for letting me see your review. I will abstain (with one exception) from commenting
in that all the issues you raise are substantive points which need to be dealt with by a
thoughtful economist. However, as you can see from my book, I actually am very much in
favor of models with mixtures on rational and non-rational agents (eg. noise traders).
[Note for bibliographic reference: Melberg, Hans O. (1997), Why (dis)believe rational
expectations? A review of Sheffrin's Rational Expectations, http://www.oocities.com/hmelberg/papers/970307.htm]