American Economic Association

A Child's Guide to Rational Expectations

Author(s): Rodney Maddock and Michael Carter
Source: Journal of Economic Literature, Vol. 20, No. 1 (Mar., 1982), pp. 39-51
Published by: American Economic Association
Stable URL: https://www.jstor.org/stable/2724658
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 Journal of Economic Literature
Vol. XX (March 1982), pp. 39-51

A Child's Guide to
Rational Expectations

By

RODNEY MADDOCK AND MICHAEL CARTER

Research School of Social Sciences
Australian National University

DRAMATIS PERSONAE
(In order of speaking)

Ernie, first student, is something of a Keynesian.

Bert, second student, is more inclined to monetarism.

Scene i Prologue
Scene ii The Idea of Rational Expectations
Deriving the Impotence Results
Criticisms
Scene iii Testing
Significance
Conclusion
Appendix A Aggregate Supply
Appendix B Algebra of the Model
References

Scene i. Prologue Bert: Which?

Ernie: Somebody named Bennett McCallum
(Two students sharing coffee in the union of
was saying that rational expectations
an Australian university.)
proved that the government could not sta-
Ernie: Did you read that ridiculous article in bilize the economy. Hang on, I've got it
Challenge the other day? here: "An accurate understanding of how
expectations are formed leads to the con-
clusion that short-run stabilization policies
* Our thanks to Neville Cain for his inspiration are untenable." (McCallum, 1980, p. 37).
for this paper and to our colleagues at ANU, notably I don't know how they could develop theo-
Malcolm Gray, Adrian Pagan and Jim Trevithick,
ries like that. It's pretty obvious that gov-
for their comments. We are also grateful to Fred
Gruen and to an anonymous referee and the editor ernment policy does affect the economy
for their assistance. All faults, of course, remain ours. in the short run.

39

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 40 Journal of Economic Literature, Vol. XX (March 1982)

Bert: He didn't say they could not affect the all the people all the time. Therefore, sys-
economy in the short run or even in the tematic policy is ineffective.5
long run. The key word is stabilize.' Just Ernie: I'm not at all sure that the long-run
think about what's happened in the last Phillips curve is vertical.6 We used to have
few years-record inflation and record un- about one percent unemployment; now
employment. You don't call that stabiliza- we seem to be stuck at about eight per-
tion, do you? cent. How can you explain that with a ver-
Ernie: Well, maybe they've been stable at tical Phillips curve. "The Phillips curve is
high levels but I take your point. There vertical but moves around a lot"-hardly
does seem to have been some break- seems much of a theory.7 Even if it is verti-
down of the ways in which the govern- cal and we can't get away from it except
ment can influence the macroeconomy. by fooling people, clearly the government
Do these rational expectations blokes can fool people. Every time it changes pol-
think they have a model to explain stag- icy the people don't know about the new
flation? policy for a while so it takes time before
Bert: Yes, they do. It's caused by misguided they catch up.8
governments following Keynesian policies Bert: But that's just what rational expecta-
that haven't worked, don't work, and tions is all about! It suggests that people
won't work in the future.2 anticipate the effects of the new policy.
Ernie: I suppose they advocate doing nothing If that's true, then the policies won't cause
and letting the 'free market' do its worst. any increase in employment!
Great! They sound just like Friedman and Ernie: How on earth are people supposed to
all those old-fashioned monetarists. They anticipate the effects of policy? I just can't
have always said inflation was just a mone- see it. Have they all got econometric mod-
tary phenomenon and macro policy els under the sink?9
couldn't shift the economy to higher levels Bert: (Angrily) Now you're just being silly.
of employment. Have you read any of the basic litera-
Bert: Yes, that's right. Most economists now ture-Lucas, Sargent, Wallace, and so on?
agree that the long-run Phillips curve is Ernie: I've looked at some but it just seems
vertical.3 That means that there exists a unreal-too many equations. They never
natural rate of unemployment.4 Govern- define exactly how they think anybody
ment policy can bring about a departure forms these "rational expectations."
from that only in the short run and then Bert: Look, I've got to go to my macro lec-
only by fooling people. But you can't fool ture. How about we meet again tomorrow,

I Usually defined as minimization of the variance 5 This is Friedman's proposition that in the long
around some fixed macroeconomic objectives (Greg- run anticipated and actual economic values must be
ory Chow, 1970). equal so that policies that work through illusions,
2 There is a clear ideological component to much or systematically wrong anticipations, will be ineffec-
rational-expectations work and opponents will be tive in that long run.
tempted to dismiss the theory on ideological 6 Gordon (1976) considers a number of possibilities
grounds. Later we suggest that there are merits in mainly relying on different forms of sluggish price
the theory quite separate from its use to support adjustment.
particular propositions about the role of govern- 7 Robert Hall (1975) makes this criticism. As he
ment. interpreted the evidence, most of the variation in
3 See M. Friedman (1968) and Robert J. Gordon output came from changes in the natural rate, pro-
(1976) for views on this. Appendix A deals with the voking questions about the importance of a theory
issue in some more detail. which only explained deviations from the natural
4 "Natural" in the sense that everybody who wants rate. It would be a useful theory if it explained the
a job at the going wage has one. This definition de- movements in the rate itself.
nies the possibility of unemployment arising from 8John Taylor (1975) explores the possibilities for
a failure of effective demand and hence from the policy while people learn the new rule. Benjamin
"Keynesian" problem (Edmond Malinvaud, 1977). Friedman (1979) addresses the same question.
There is no necessary connection between verti- 9John Muth (1961, p. 317) in outlining what he
cal Phillips curves and a natural rate of employ- meant by rational expectations anticipated this criti-
ment. cism.

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 Maddock and Carter: Rational Expectations 41

and I'll introduce you to the magnificient processing of information and to the for-
world of rational expectations. Same time? mation of expectations."1
Ernie: Am I to infer that my utility function
Scene ii. A. The Idea and I sit down together and rationally de-
of Rational Expectations cide how much information I should ac-
quire in order to form the expectations
(In the same place, next day.)
that will help me maximize my utility? In-
Bert: Well, are you ready to try to under- credible!
stand what rational expectations is about? Bert: Yes, you can attack it that way if you
Ernie: Yes. Have you got it figured out yet? like, but that's a more general criticism
Bert: I've been thinking about it. Let's go of utility theory which we can argue about
through it systematically. First, we can talk some other time. All I'm saying here is
about just what rational expectations are. that if one considers economic agents to
Then we can look at the way the policy be rational maximizers, then it's
impotence result is derived. By then we consistent12 to consider information gath-
should have a pretty clear idea of what ering and expectation formation as deter-
this line of research is all about so we can mined by the same procedure.
try to figure out how it relates to the Phil- Ernie: O.K. So you'd insist upon a rational ex-
lips curve, monetarism, econometric mod- pectations postulate that private economic
els, and all that. O.K.? agents gather and use information effi-
Ernie: Alright. What's the definition of ra- ciently. That means you believe the mar-
tional expectations? What on earth might ginal costs of gathering and using informa-
irrational expectations be? tion are equated to their marginal benefits.
Bert: First things first. Let's start with famil- McCallum doesn't agree with you. He says:
iar ground. What would you say is the basic "Individual agents use all available and
behavioral assumption of economic behav- relevant information "13 and it seems to me
ior? that Sargent and Lucas say the same. It
Ernie: Utility maximization, I suppose. almost seems as if they think information
Bert: More or less. I would say that the basic is a free good.14
assumption about individual behavior is Bert: That's a good point. Many theorists
that economic agents do the best they can have ignored the costs of information used
with what they have. This principle forms in the formation of expectations. That is
the basis of consumption theory, produc- one of my criticisms of the literature. But
tion theory, human capital theory and so I think it is useful to distinguish between
on. rational expectations as a principle of in-
Ernie: So it's the basis of microeconomics.10 formational efficiency and rational expec-
But what's that got to do with expecta- tations as it appears in some of the macro-
tions? economic literature.'5
Bert: Everything. At its most fundamental, 11 This is not the approach usually adopted by ra-
rational expectations theorists argue that tional expectations theorists (fn. 15). It is, however,
the same principle should be applied to closer to the usual economic methodology and seems
preferable.
the formation of expectations. If you want
12 That is, consistent with the methodological ap-
a definition, how about: rational expecta- proach of explaining all behavior in terms of utility
tions is the application of the principle maximization.
of rational behavior to the acquisition and 13 McCallum (1980, p. 38). In fact, Ernie has quoted
McCallum out of context. He goes on to admit that
10 There is clearly some tension in macroeconom- information costs are neglected for simplicity.
ics between its empirical behavioral aspects (e.g., 14 Edgar Feige and Douglas Pierce (1976) consider
the consumption function) and its derivation of in- the implications of costly information for rational
sights from a microeconomic basis (e.g., permanent expectations.
income hypothesis). The micro foundations of macro- 15 The distinction seems important for clarifying
economics literature, for example Geoffrey Harcourt ideas within macroeconomics. The all-information
(1977) attempts to resolve this conflict but, so far, approach adopted by Sargent et al. should ideally
not very successfully. be given another name, for example "Muth expecta-

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 42 Journal of Economic Literature. Vol. XX (March 1982)

Ernie: The term 'rational' is quite confusing B. Deriving the Impotence Result
in the context and you are right that the
Bert: Without realizing it you've just made
distinction between the two things is im-
a very important distinction. The relation-
portant. But what difference does rational
ship between the level of employment and
expectations make to individuals? Can you
expectations is logically quite separate
give examples?
from beliefs about how expectations are
Bert: The example most often used in the lit-
formed. The conclusion that there is no
erature involves the allocation of time be-
scope for government policy-the impo-
tween labor and leisure.16 In deciding how
tence result-depends crucially upon im-
many hours to work this period, an individ-
posing a special assumption about expec-
ual must take account of expected future
tations-rational expectations-upon a
wages and not just the present wage. For
special type of macroeconomic model.
example, if you expect the real wage to
Ernie: Well I think I understand the meaning
be $10 per hour this week, and $1 next
of rational expectations. What types of
week, then it makes sense to work as much
macro models do rational expectations
as possible this week, and have some time
theorists use?
off next week. Therefore the number of
hours worked in any period, that is, the
Prices
labor supply, will depend not only on the Supply
current real wage but on expected future
real wages. A rational expectation of real
wages will take into account all available
information, including the effects of gov-
ernment policy.
Ernie: But my old man works 40 hours every
\ \Demando
Demand,
week-he doesn't have much choice.
Bert: But your old man's boss does. When he Yn Income = Output
is deciding whether to hire more people
or lay them off, he needs to take into ac- Diagram 1
count future prices and wages. His expec-
tations should be based on all the available Bert: (Drawing a diagram.) Most of them
information. This includes, among other work with the idea that the levels of out-
things, the impact of future government put and prices are determined by the in-
policy. tersection of an aggregate demand and ag-
Ernie: O.K. I see how the level of employment gregate supply function. The aggregate
might depend upon expectations and how supply curve is taken to be vertical, so that
'good' expectations are better than 'bad' output cannot deviate from Yn as a direct
ones. But I can't see why that means that result of any change in the level of de-
there is no room for government policy. mand. Thus government policies designed
to change the level of aggregate demand
are not likely to be effective. The level
tions," since the adjective "rational" is normally re- Yn is the output associated with equilib-
served in economics to describe the outcome of a
rium in the labor market at the natural
utility maximization process. J. J. Sijben writes:
"Muth's view implies that economic agents build up rate of unemployment so we can call Yn
their expectations as if they are fully informed of the natural rate of output or income for
the process which ultimately generates the real out- the economy.17
come of the variable concerned" (1980, p. 66).
Pushed further, McCallum follows the line that all
models are "unrealistic," which seems to lead him 17 Appendix A deals with the problems of the verti-
to the position that theories stand or fall on their cal aggregate supply curve in more detail. It should
predictions. be noted that the models are usually expressed in
16 Rational expectations in labor supply decisions logarithms so that the real debate concerns rates
have fairly obvious corollaries on capital investment of change rather than levels. The distinction is ne-
decisions (Robert Lucas, 1975, for example). glected here.

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 Maddock and Carter: Rational Expectations 43

Consider the possibility that the govern- taken expectations. Let's write down a
ment takes action that may, at first blush, simple model.
be supposed to increase output. For exam-
ple, let it act to increase nominal income (Bert's scribbling is attached as Appendix B.
and aggregate money demand. Money For those who like mathematical descriptions
wage rates will tend to rise, and if workers it should make the discussion clearer but is
regard this as equivalent to an increase not a necessary adjunct.)
in real wages, employment will increase
and output will temporarily rise to a level Ernie: That makes your position clearer. The
higher than Y.. But if production is carried actual aggregate supply function implies
on subject to diminishing returns to labor, that deviations of actual output from the
prices will rise relative to nominal wages, natural rate are directly proportional to
and real wages will fall. When workers re- deviations of actual prices from expected
alize this, employment will fall back to its prices. Since people with rational expecta-
original position, and output will return tions never make mistakes about policy
to Yn. At this point, nominal wage rates rules, policy will never fool them, and out-
and prices are higher (the nominal de- put will never deviate from its natural rate
mand curve crosses the vertical supply as a result of any policy rule.
curve at a higher level), but output and Bert: That's the idea but you've put it too
employment are back where they started. strongly. If government policies are ran-
Since the aggregate supply curve had not dom, they will be effective although not
shifted, the possibility of increasing em- necessarily desirable. It's the systematic
ployment and output arises only as long component of policy that the theory sug-
as people confuse nominal changes in gests will be ineffective.
wages (for example) with real changes. Ernie: I'm not too sure about the neutrality-
This means that government policy will of-money proposition19 generally but will
only increase the level of income in let it ride for now. You explain the rest
real terms if it is able to fool people into of the argument-then I'll put my objec-
confusing nominal changes with real tions one by one.
ones.18 Bert: Now the point of rational expectations
Ernie: That's ridiculous! The 'natural' rate of is that people won't be surprised by any
unemployment depends intimately upon systematic policy. Any government that
all sorts of government policies-for exam- relies upon a policy rule-one that has a
ple tax laws, minimum wage laws, immi- fixed growth of the money supply, or one
gration policy, school-leaving age, etc., etc. systematically related to income or unem-
Do you really mean that the government ployment-will never cause any deviation
can't change aggregate supply by increas- from the natural rate.20 A random policy
ing the investment allowance? Or by go- will affect real output. But any policy rule
ing to war, for that matter? that is systematically related to economic
Bert: You're right, you're right! I should have conditions, for example one designed with
been more careful. Clearly government stabilization in mind, will be perfectly an-
policy can alter the natural rate of unem- ticipated, and therefore have no effect on
ployment or, if you like, the position of output or employment. In other words, to
the aggregate curve. What I should have have real effects. monetary Dolicv must be
said is that the only way in which govern-
ment policy can bring about deviations
from the natural rate of unemployment 19 The idea that changes in money supply do not
influence people's preferred hours of work, portfolio
is by inducing private agents to have mis-
holdings, etc. Again, this is considered in Appendix
A.
"8As Thomas Sargent and Neil Wallace suggest 20 Sargent and Wallace (1976, pp. 177-78), put this
"it must somehow trick the public" (1976 p. 177). argument in almost the same form. Expectations can
The argument is more complex with capital in the be wrong but not systematically wrong (i.e., biased),
model as may be clear from Appendix A. hence there is no scope for systematic policy.

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 44 Journal of Economic Literature, Vol. XX (March 1982)

completely unpredictable. Any systematic relation.24 We tend to go through a series

policy will be impotent.21 of years in which unemployment is below
Ernie: Can we put it this way? Rational expec- the 'natural rate,' and then a series of years
tations are based on all available informa- in which it is above the 'natural rate.' It
tion. The available information set in- doesn't seem to be distributed very ran-
cludes the government policy rule. domly. Compare the sixties and seventies
Therefore, a rational expectation of in- in Australia-it's the old story of business
flation, for example, will include the an- cycle expansion and contraction.
ticipated effects of government policy so Bert: I can't deny the serial correlation in the
that the policy will have no effect on out- unemployment or income series. Most ra-
put.22 tional expectations models include lagged
Bert: Yes, that pretty well sums it up. income or lagged unemployment as expla-
natory variables in the supply function.25
C. Criticisms This does make the models fit the data
better, but there is no good theoretical
Ernie: Now that I think I understand what justification for it. Lucas is the only one I
you're on about, can I tell you what I think know who really addresses the issue.26 He
is wrong with the model? relies on the well-known 'fact' that all peo-
Bert: O.K. ple live on islands. At the end of each trad-
Ernie: First, I don't like your supply curve. ing period people choose a new island at
There are lots of criticisms one could random. Since they don't know the history
make, but the most important in the con- of their new island, they can't distinguish
text of the model is that you assume an immediately between real and nominal
extreme form of the neutrality of money.23 effects.27
Perfectly anticipated inflation has no real Ernie: These island models seem appropriate
effects in your model. That's clearly to a society in which the fastest form of
wrong. Buiter (1980) put the standard ar- communication is a floating coconut.
gument in terms of the portfolio readjust- Hasn't Lucas ever heard of radio and the
ments required because inflation changes telephone?28
the real rate of return on those financial Bert: I have to agree with you. I said that
assets which have a zero nominal return. the explanations for persistence weren't
Personally, I think the distortions intro-
duced by the progressive tax structure in 24 This was Hall's criticism (1975), and is also put
by Gordon to Sargent (1973, p. 478).
an inflationary situation are far more im-
25 Lucas (1973) introduced the lagged term with
portant empirically. a footnote explaining that not all deviation from the
Bert: Yes, but all models are approximations. natural rate of unemployment could be accounted
Ernie: True, but not all approximations are for by the error in expectations terms.
good approximations! Here's another 26 Lucas (1975) attempts a systematic explanation
for the serial correlation in terms of information lags.
problem. If expectations are rational, then
See Rodney Maddock (1979) for a discussion of the
expectation errors should be randomly dis- importance of persistence for the rational expecta-
tributed over time. A straightforward im- tion program.
plication of that for this model is that the 27 "The idea behind this island abstraction is not,
of course, to gain insight into maritime affairs, or
level of output (or unemployment) is un-
to comment on the aimlessness of life. It is intended
correlated over time. Yet everybody simply to capture in a tractable way the fact that
knows that the GNP and unemployment economic activity offers agents a succession of am-
series have a high degree of serial cor- biguous, unanticipated opportunities which cannot
be expected to stay fixed while more information
is collected. It seems safe and, for my purposes, sensi-
21 Gordon (1976) makes this clear. See especially ble to abstract here from the fact that in reality this
pp. 200-01. situation can be slightly mitigated by the purchase
22This follows the usual solution method followed of additional information" Lucas (1975, p. 1120).
by rational expectations models. See Lucas (1973) 28 Lucas does actually mention the problem in the
for an example. quotation in the previous footnote, but makes noth-
23 Some criticisms are discussed in Appendix A. ing of it.

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 Maddock and Carter: Rational Expectations 45

very convincing, especially when the gov- * . .actions based on inaccurate anticipations
ernment regularly publishes lots of statis- will not long survive experiences of a con-
trary character, so that the facts will soon
tics. The newspapers carry stock exchange
override anticipation except where they
prices every day. The information seems agree. [1930, p. 160].
to be essentially free.
Ernie: Granted there is a role for arbitrage.
There is another line of argument
But how do we know that expectations
though. If prices change suddenly, firms
of the experts will converge on the true
can increase their production less than
value? Give me any rational expectations
their sales by using up some of their inven-
model and I think I can show you a reason-
tories. If there is no price shock in the
able adjustment process that will not con-
next period production would then be
verge to the rational expectations equilib-
raised to build inventories back to their
rium.
original level. Thus there would be an in-
Bert: And I can probably show you one that
crease in production to meet the original
can. Unless the theorists specify an adjust-
stock and for as long thereafter as the re-
ment mechanism, we can't really argue
stocking took.
about this point. Rational expectations the-
Ernie: But that implies there should be a
orists haven't addressed this problem.31
strong relationship between inventory cy-
Ernie: That's a big gap in your theory. But let
cles and output cycles and that's not really
me read to you what Robert Shiller says:
true, is it?
Bert: Well, the relation is far from perfect. Even if a model does eventually converge
I was really just suggesting that in an econ- on a rational expectations equilibrium, it may
take such a long time to do so that, since
omy characterized by durable goods it
the structure of the economy changes occa-
shouldn't be too difficult to accept that ad- sionally, the economy is never close to a ra-
justments of various sorts will have effects tional expectations equilibrium. [1978, p. 39].
that persist.29 We really don't have a good
To recalculate a quarterly econometric
explanation for persistence (serial correl4-
model after a change in policy rule might
tion). I willingly concede that point.
take 20 quarters. To estimate the effect
What's next?
of policy based on the new estimates might
Ernie: O.K. Even if all that information is
take another 20 quarters. Thus, even if the
freely available, you assume that all the
process converges, each stage in the con-
agents know the correct model of the
vergence to the new equilibrium could
economy. How . . .
take five years-by which time we may
Bert: No, I don't. Well, not me really. I mean
all be dead!
that rational-expectations people don't
necessarily say that everybody knows the Bert: But if the Government's objective is to
correct model of the economy. They sug- stabilize the economy, then it wants to
gest that some arbitrage process takes
place whereby the people who have the
31 Shiller (1978, p. 38) focuses upon the issue of
correct model dominate the outcome.30 If convergence. There seem to be two separate issues
there are misapprehensions, then well- involved. Since rational expectations for this period
informed agents can make profits at the depend upon estimates about the future while the
future depends in part upon present expectations,
expense of the ill-informed. This will inevi-
there need be no unique rational expectation for
tably lead the system to converge to the the current period. In many models, methods of ad-
rational expectations equilibrium. As your justing expectations (i.e., forecasts) of the future will
old mate, John Maynard Keynes, said: either converge on a rational-expectations solution
or explode. The implicit argument of protagonists
29These issues are raised in a penetrating discus- seems to be that since we do not observe prices ex-
sion of the problem of persistence by Gordon (1981). ploding off to infinity we need only consider con-
30For example, Muth (1961) argued that econo- verging cases. This type of counter-factual reasoning
mists could sell the information profitably if expecta- is somewhat dubious. The dynamics of expectation
tions were not rational. Since he wrote, many have formation might still be explosive but some other
done so. This suggests that market forces would tend fact or-e.g., policy action-act to constrain the ex-
to drive decisions to those rationally based. plosive tendency.

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 46 Journal of Economic Literature, Vol. XX (March 1982)

make sure that private expectations are what they expect, and see if they are right?
rational, and hence it will inform the pub- Bert: Stephen Turnovsky (1970) and James
lic of any new policy rule.32 Pesando (1975) and a couple of other peo-
Ernie: That doesn't get you out of hot water. ple have done that, but the results have
First, the learning problem doesn't con- been inconclusive. Economists tradition-
cern the policy rule alone. Agents also ally don't like surveys, anyway.
have to learn the structure of economy, Ernie: Well, how have rational expectations
which is subject to change. Econometric protagonists tried to test the theory?
modellers don't have an outstanding rec- Bert: Basically they have taken two different
ord of success, do they? Second, why do approaches. Have a look at the supply
you assume that the goverment's objective function again. The natural rate hypothe-
is to stabilize the economy? It seems to sis will only allow non-random deviations
me that the government's real objective if there are expectations errors of some
is to remain in power-you know, the po- sort. Under the rational expectations hy-
litical business cycle idea.33 And if that is pothesis there are no expectations errors-
their objective it may be in their interest or at most, only random ones. Thus, devia-
to hide information and fool the public. tions from the natural rate of output must
If that is the case the voters can hardly be random.36 In particular, deviations can-
be expected to believe the signals the gov- not be systematically related to any other
ernment is sending out and the whole explanatory variable, for example the
macroeconomic process degenerates into (lagged) money supply or the wage rate.
a guessing game. And so the first type of test is essentially
Bert: But you must agree that most macro- to see whether deviations from the natural
economics does assume the objective of rate are systematically related to any other
stabilization. This literature falls into that variables. This test has been applied in a
tradition which is concerned with govern- number of different ways especially by
ment policy rules designed to achieve Sargent (1973; 1976). In those papers the
macroeconomic stabilization.34 joint hypothesis-natural rate and rational
Ernie: Let's go and get a beer.35 expectations-was rejected in a number
of cases, jointly rejected because they
Scene iii. (In the union bar) were jointly tested. With slightly different
A. Testing specifications, they weren't. Sargent con-
Bert: Now the testing is a bit tricky. It's a cludes that rational expectations is 'not ob-
pretty young research program and there scenely at variance with the data.'37
are no well-accepted testing procedures Ernie: Remarkable resilience, eh!
as yet. The principal difficulty is that we Bert: Yes, what's more, his next paper was
are really testing a joint hypothesis-the entitled 'The Observational Equivalence
economic model and the expectations of Natural and Unnatural Rate Theories
mechanism. That makes it difficult to de- of Macroeconomics.'38 This initiated the
cide just where the responsibility for fail- second approach to testing rational expec-
ures of tests really lie. tations. It was based on the idea that what
Ernie: But why can't you just test the expecta- rational expectations models add, com-
tions mechanism directly? Ask people pared with other models, is that price ex-

32Sargent and Wallace (1976, pp. 181-83) argue 36Actually, some allowance in the tests is made
this point. for persistence by the inclusion of lagged values of
33The nature of the problem when the govern- the dependent variable.
ment's objectives vary over time does not seem to 37The theory suggests that no extra information
would significantly contribute to the prediction. The
have been well explored. Clearly, rational expecta-
evidence would thus appear to falsify the theory.
tions forces economists to think more about the pre-
cise nature of learning. Sargent (1976), instead, went on to try an alternative
type of test. See especially p. 233.
34 Following the tradition of Dutch economists Jan
Tinbergen (1952) and Henri Theil (1958). 38Sargent (1976) and Sargent and Wallace (1975)
35 Following a sound Australian tradition. start to develop this idea.

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 Maddock and Carter: Rational Expectations 47

pectations take into account the policy of a complex world. Of course, the test
rule the government is using. If that rule is a bit tricky. It's not really clear to me
does not change, ordinary models and ra- that that's the way to estimate the govern-
tional expectations models will fit any data ment policy rule and then, even if it is,
set equally well, though probably with dif- there are probably other non-rational ex-
ferent parameters. What it means is that pectations mechanisms which would sug-
you can only distinguish between rational gest a change in the econometric structure
expectations macro models and ordinary as a result of a change in policy rule.
ones if the policy rule has changed.39 It There's no real alternative hypothesis in-
seems a reasonable idea to me. volved in the test!
Ernie: Maybe. Bert: Everyone agrees it's not a very strong
Bert: Well, anyway, it gave Sargent and Salih test; it's titled 'A Little Bit of Evidence
Neftci (1978) an idea for a new type of . . . ' but it is suggestive and does focus
test. First, they estimated the govern- upon the relation between expectations
ment's policy rule by regressing the and the policy rule and not upon the natu-
money supply on past levels of income. ral rate. It gets away from the dogmatic
They then analysed the results to see if form of the natural rate, impotence of pol-
there had been any significant changes in icy area, and focuses upon the positive
the relationship, that is, to see if the policy contribution of the rational expectations
rule had changed.40 They found changes idea.
in 1929 and 1964. They then looked at
some ordinary macroeconomic models to B. Significance
see whether the parameters had changed
Ernie: O.K., we've covered the model and the
at about the same time that the policy rule
evidence, such as it is. What's all the fuss
changed. In each case they found some
about?
evidence that it had.4'
Bert: Well, it really nails the Phillips curve.
Ernie: Well, that seems like a reasonable sort
Much post-war stabilization policy has
of approach. Really it depends on the ra-
been based on the idea that there is a
tional expectations idea-that people
trade-off between unemployment and in-
change their behavior as policy changes-
flation that the government can exploit by
rather than on the natural rate proposi-
influencing aggregate demand-the so-
tion. I'm inclined to agree that people take
called Phillips curve. Friedman largely un-
into account what the government is try-
dermined that with the natural rate idea.
ing to do when they plan for the future
He said that policy only worked by fooling
but the extreme form of the natural rate
people and that in the long-run they could
of unemployment is an over-simplification
not be fooled. This still left the way open
for effective short-run policy. If people
39 Since expectations are usually unobservable have rational expectations they won't be
they are eliminated from econometric model to be fooled. If people have rational expecta-
estimated by introducing an equation about their
tions they won't be fooled by systematic
relation to known variables. The parameters of this
equation then become embedded in the actual re- policy even in the short run so there is
duced form equations which are estimated. An no scope for short-run policy either. This
"equation" for rational expectations incorporates the explains why the Phillips curve became
parameters of the policy rule being used by the gov- unstable the moment policy makers tried
ernment. Under the assumption of rational expecta-
to exploit it.
tions these parameters of the policy rule become
embedded in the reduced form (i.e., estimating) Ernie: But the explanation depends really
equations of the economy. Thus they suggest that heavily, as you've already agreed, upon
structure of the economy, as measured by usual the particular macroeconomic model you
econometric models, will appear to change when-
have set up.42 The monetarists have
ever the policy rule changes.
40 Using Ml there was a policy change, but with
M2 none appeared to have taken place. 42 Alan Preston and Adrian Pagan (Forthcoming,
41 The tests were non-parametric. Ch. 10) explore the way in which the impotence

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 48 Journal of Economic Literature, Vol. XX (March 1982)

grabbed this idea43 to support their tradi- output in anticipation of those effects
tional position that active government pol- rather than waiting for the rise in demand
icy is not desirable.44 It's largely been their to be obvious in the market. In that case,
baby until now. The reason is not hard far from policy being impotent, rational
to see. The impotence result strongly sup- expectations may make policy more effec-
ports their ideological position that the tive.
government should keep its hands off the This example, by the way, illustrates the
economy.45 fact that most of the rational expectations
Bert: That's rather harsh. Monetarists are no literature has a particular economic model
more ideological than other economists. built in, one in which all markets clear
What would be your 'un-ideological' view instantaneously; unemployment is, there-
of rational expectations? fore, voluntary, hence 'natural'; and
Ernie: I've been wondering how a future his- money is necessarily neutral. But if that
torian of thought might assess it. I think model is not applicable, policy need not
rational expectations theory will be seen be impotent, and, as said, rational expec-
as a very important development in eco- tations may make it more rapidly effec-
nomics, but not because of the impotence tive.
result. Rational expectations are important What's more rational expectations can
in any situation in which market behavior be applied in microeconomic situations.46
is influenced by expectations. Take the Cobweb models of dynamic behavior in
case of an aggregate demand deficiency commodity markets depend upon 'irra-
in a Keynesian model. The usual argument tionality of expectations'-the idea that
is that monetary expansion will work next year's prices will be the same as this
through affecting interest rates so that year's or even a simple extrapolation of
gradually the economy shifts to a higher it. Clearly, producers can do better than
output level. With rational expectations that, and if they have rational expectations
the shift to the new level would be ex- the market is likely to approach its equilib-
tremely rapid. If businessmen understand rium quite quickly.
the economic implications of expansionary Bert: You're right! The idea can be applied
government policy, they can expand their in a wide variety of models but what about
your general conclusions about policy for-
mation?
result depends on particular specifications of the Ernie: Yes, I agree that there are important
macroeconomic model being considered. They de-
implications for policy design. Private eco-
velop a more general model that includes the usual
rational expectations models as particular cases.
nomic agents are intelligent decision-mak-
43 Lucas and Leonard A. Rapping used adaptive ers and can be expected to take the effects
expectations (1969), then rational distributed lag ex- of government policy changes into ac-
pectations (1969) before Lucas first introduced ra- count in deciding their behavior. This
tional expectations (1972). Where adaptive expecta-
means that the policy-maker must antici-
tions assumed that people just simply adapted to past
errors, rational distributed lag expectations were the pate the effect of policy on private expec-
very best econometrically predicted estimates of tations and the consequent changes in be-
prices derived from analysis of all past price informa- havior. In practical terms it means that
tion.
we need to know a lot more about the
44 Any stable understandable rule would have no
effect if people were exactly able to predict it. By
availability and use of information by pri-
that test a "discretionary" rule and a fixed money vate decision-makers.47 Thus, the focus of
growth rate rule would be equally impotent. If sto- the theory of policy should be on expecta-
chastic effects of discretionary rules are allowed for
however, these cannot be predicted and would intro-
duce fluctations into the system. See Sargent and 46The seminal article by Muth (1961) deals with
Wallace (1976) for a discussion of the issues. microeconomic market situations.
45 McCallum's (1980) popularization of their posi- 47Sargent and Wallace (1975, p. 251) provide a
tion carries the inference that the results are quite start in this direction by modelling a case where
robust, but that does not appear to be the case. See government has an information advantage over pri-
Preston and Pagan (Forthcoming). vate actors.

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 Maddock and Carter: Rational Expectations 49

tions and information and on their role The rational expectations hypothesis, in
in determining behavior. itself, should not be provocative to econo-
Bert: I think you can go further. People used mists. It merely brings expectations within
to think that the only reason stabilization the scope of individual maximizing behav-
policy didn't work well was that policy- ior. Expectations used to be handled
makers didn't have enough knowledge within economic models on an ad hoc ba-
about the structure of the economy. Ra- sis. Rational expectations provides a way
tional expectations has taught us that the of incorporating expectations which is con-
problem may not be just one of the abso- sistent with the orthodox economic theori-
lute knowledge of the authorities but zing.
rather of how much more or less they The development of rational expecta-
know than the public does-a problem of tions theory will make a more significant
relative knowledge. If this is true, the contribution to economics in the impetus
problem will always be with us. it gives to research on the vital areas of
learning and expectations formation. It
C. Conclusion brings to the fore questions about the
availability and use of information. Instead
Ernie: Well, I started off inclined towards Gor-
of being the finale of the monetarist's case
don's view that rational expectations is an
against policy intervention, it should be
example of a recent development in eco-
seen as the prologue for a revitalized the-
nomics "in which theory proceeds with
ory of expectations, information and pol-
impeccable logic from unrealistic assump-
icy.
tions to conclusions that contradict the his-
torical record" (1976, p. 5). But now I see Bert: I guess you're right. Let's go and get
that that's a bit too harsh. another beer.
Most of the research on rational expecta-
tions has exhibited great technical compe-
APPENDIX A: Aggregate Supply
tence, 'impeccable logic,' and considera-
ble ingenuity. This has contributed in no The underlying inspiration for rational ex-
small measure to its apparent success, and pectations macro models is derived from the
to the confusion and uncertainty which ra- notion of general equilibrium. With price flexi-
tional expectations have aroused in the bility, for given endowments and skills, a condi-
rest of the economics profession. The fun- tion of general equilibrium requires equilib-
damental simplicity of the ideas involved rium in the labor markets. In such a world all
has become obscured by overly rigorous unemployment is voluntary, everybody who
development, and especially by the un- wants a job has one. Every individual has his
convincing resort to extraneous construc- labor hours and assets allocated according to
tions, such as the 'islands' mentioned some personal optimum. The remaining unem-
above. ployment can be termed the "natural" rate
Undoubtedly, it is the impotence of pol- of unemployment and the level of output
icy results that has aroused most attention. termed the "natural" level of output.
Yet these results depend very heavily on Abstracting from inter-industry shifts in pro-
a particular type of macroeconomic model duction, the only way output can change is
usually embodying a strong form of the through a change in employment. To increase
natural rate hypothesis. If you start with or decrease the level of output government
'classical' models in which policy can have policy must alter the equilibrium in the labor
no real effects, it is hardly surprising that markets. But if the natural rate of unemploy-
you get results in which policy is impotent. ment represents an optimal position for pri-
Because of this the novelty of rational ex- vate actors, how can government policy affect
pectations has become bundled up with it?
tired and worn notions of the way in which The models rational expectations theorists
the world works. It is vitally important to usually work with suggest that this is possible
unbundle these ideas. only if the government is able to fool people.

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50 Journal of Economic Literature, Vol. XX (March 1982)

If people confuse nominal wage changes for Equating demand and supply, we obtain the
real ones, they might reallocate their portfolios following reduced form equation:
and their hours of work, and thus increase out-
put. While allowing for this possibility the mod- Pt = a + b (apt + c [4]
els suggest that such a change would not be
desirable for the worker (representing a sub- Now, by the rational expectations assumption
optimal decision) and would be avoided if they (eqn. 3),
had rational expectations. They suggest that
the labor supply decision is made in real terms pt* = E[ptjIt-1]
so that labor market equilibrium is indepen-
dent of prices which, in turn, is taken to imply using (4) = E[ (apt*+ext- y--u)]
1
that output is independent of prices. This re-
sult is presented in a vertical aggregate supply
curve. = a + b (aEp* + cExt - E-- Eu
Alternative macro-economic theories sug-
gest that the optimal allocation decisions of pri- But Ept* = pt*, Ey= y EutO=
vate actors will be affected by changes in
prices, but not just because people are fooled. so Pt+b(aPt* + cExtY-) [5]
If this were true, increases in aggregate de-
mand could increase output and employment Subtracting [5] from [4]
even with rational expectations. One argu-
1
ment for the proposition suggests that people
Pt -Pt* = a+b [c(xt -Ext) -Ut] [6]
don't hold money in their asset portfolios sim-
ply for transaction purposes. If prices go up, Substituting [6] in equation [1]
the desirability of holding such money goes a
down, changing people's private allocation de- Yt Y = a + b [c(xt-Ext)-ut] + ut
cisions, and perhaps the rate of capital forma- a+ b
tion or number of hours worked. Thus it might
=acb (Xt -Ext) + b [7]
a +b a+ b Ut
be said that the rational expectations models
assume that the only motive for holding money
That is, the deviation of output fro
is the transactions motive.
ral' level y-depends only on the unsystematic
component of government policy (x - Ext). To
APPENDIX B: Algebra of the Model see this, assume that the government uses the
following policy rule:
Supply: yt- -= a(pt-pt*) + ut [1]
xt= kxt-1 + lyt-, + mpt-i - nPt-2 + vt [8]
Demand: Yt = -bpt + eXt [2] where vt is a random variable, Evt= 0.

Expectations: Pt* = E[ptlIt-1] [3] Then,

Ext = kxt_- + lyt-, + mpt-i - nPt-2 [9]
where Yt= income
Subtracting [9] from [8]
y= income level corresponding
Xt- Ext = vt
to the natural rate of unem-
ployment Putting this in [7]
Pt= prices
Pt*= price expectations - ac + b
xt= government policy instru-
Yt Y a+ b a+ b`
ment, e.g., money supply 1
It-, = all information available at = a+ b (acvt + but)
time t- 1
ut = random error term; Eut = 0 Deviations of Yt from - are thus entirely ran-
E = expectations operator. dom. This implies that systematic government

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 Maddock and Carter: Rational Expectations 51

policy is impotent (in this model), since the J Polit. Econ., Sept./Oct. 1969b, 77(5), pp. 721-
systematic component of any policy will be in- 54.
MADDOCK, RODNEY. Rational expectations, political
corporated in Ext, and therefore be cancelled
business cycles and the course of macroeconomic
out in forming xt - Ext. theory. Unpublished Ph.D. Thesis. Duke Univer-
sity, 1979.
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