A Childs Guide to Rational Expectations 1982

8/11/2019 A Childs Guide to Rational Expectations 1982

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American Economic Association

A Child's Guide to Rational ExpectationsAuthor(s): Rodney Maddock and Michael CarterSource: Journal of Economic Literature, Vol. 20, No. 1 (Mar., 1982), pp. 39-51Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/2724658 .Accessed: 25/06/2013 16:54

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Journal of Economic LiteratureVol. XX (March 1982), pp. 39-51

C h i ld s G u id e t

at ional xpectations

By

RODNEY MADDOCK AND MICHAEL CARTERResearch 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 PrologueScene ii The Idea of Rational Expectations

Deriving the Impotence ResultsCriticisms

Scene iii TestingSignificanceConclusion

Appendix A Aggregate SupplyAppendix B Algebra of the ModelReferences

Scene i. Prologue

(Two students sharing coffee in the union ofan Australian university.)

Ernie: Did you read that ridiculous article inChallenge the other day?

Bert: Which?

Ernie: Somebody named Bennett McCallumwas saying that rational expectationsproved that the government could not sta-bilize the economy. Hang on, I've got ithere: "An accurate understanding of howexpectations are formed leads to the con-clusion that short-run stabilization policiesare untenable." (McCallum, 1980, p. 37).I don't know how they could develop theo-ries like that. It's pretty obvious that gov-ernment policy does affect the economyin the short run.

* Our thanks to Neville Cain for his inspirationfor this paper and to our colleagues at ANU, notablyMalcolm Gray, Adrian Pagan and Jim Trevithick,for their comments. We are also grateful to FredGruen and to an anonymous referee and the editorfor their assistance. All faults, of course, remain ours.

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

Bert: He didn't say they could not affect theeconomy in the short run or even in thelong run. The key word is stabilize.' Just

think about what's happened in the lastfew years-record inflation and record un-employment. You don't call that stabiliza-tion, do you?

Ernie: Well, maybe they've been stable athigh levels but I take your point. Theredoes seem to have been some break-down of the ways in which the govern-ment can influence the macroeconomy.Do these rational expectations blokesthink they have a model to explain stag-flation?

Bert: Yes, they do. It's caused by misguidedgovernments following Keynesian policiesthat haven't worked, don't work, andwon't work in the future.2

Ernie: I suppose they advocate doing nothingand letting the 'free market' do its worst.Great They sound just like Friedman andall those old-fashioned monetarists. Theyhave always said inflation was just a mone-tary phenomenon and macro policycouldn't shift the economy to higher levelsof employment.

Bert: Yes, that's right. Most economists nowagree that the long-run Phillips curve isvertical.3 That means that there exists anatural rate of unemployment.4 Govern-ment policy can bring about a departurefrom that only in the short run and thenonly by fooling people. But you can't fool

all the people all the time. Therefore, sys-tematic policy is ineffective.5

Ernie: I'm not at all sure that the long-run

Phillips curve is vertical.6 We used to haveabout one percent unemployment; nowwe seem to be stuck at about eight per-cent. How can you explain that with a ver-tical Phillips curve. "The Phillips curve isvertical but moves around a lot"-hardlyseems much of a theory.7 Even if it is verti-cal and we can't get away from it exceptby fooling people, clearly the governmentcan fool people. Every time it changes pol-icy the people don't know about the newpolicy for a while so it takes time before

they catch up.8Bert: But that's just what rational expecta-

tions is all about It suggests that peopleanticipate the effects of the new policy.If that's true, then the policies won't causeany increase in employment

Ernie: How on earth are people supposed toanticipate the effects of policy? I just can'tsee it. Have they all got econometric mod-els under the sink?9

Bert: (Angrily) Now you're just being silly.Have you read any of the basic litera-

ture-Lucas, Sargent, Wallace, and so on?Ernie: I've looked at some but it just seems

unreal-too many equations. They neverdefine exactly how they think anybodyforms these "rational expectations."

Bert: Look, I've got to go to my macro lec-ture. How about we meet again tomorrow,

I Usually defined as minimization of the variancearound some fixed macroeconomic objectives (Greg-ory Chow, 1970).

2 There is a clear ideological component to much

rational-expectations work and opponents will betempted to dismiss the theory on ideologicalgrounds. Later we suggest that there are merits inthe theory quite separate from its use to supportparticular propositions about the role of govern-ment.

3 See M. Friedman (1968) and Robert J. Gordon(1976) for views on this. Appendix A deals with theissue in some more detail.

4 "Natural" in the sense that everybody who wantsa job at the going wage has one. This definition de-nies the possibility of unemployment arising froma failure of effective demand and hence from the"Keynesian" problem (Edmond Malinvaud, 1977).There is no necessary connection between verti-cal Phillips curves and a natural rate of employ-ment.

5 This is Friedman's proposition that in the longrun anticipated and actual economic values must beequal so that policies that work through illusions,or systematically wrong anticipations, will be ineffec-

tive in that long run.6 Gordon (1976) considers a number of possibilitiesmainly relying on different forms of sluggish priceadjustment.

7 Robert Hall (1975) makes this criticism. As heinterpreted the evidence, most of the variation inoutput came from changes in the natural rate, pro-voking questions about the importance of a theorywhich only explained deviations from the naturalrate. It would be a useful theory if it explained themovements in the rate itself.

8John Taylor (1975) explores the possibilities forpolicy while people learn the new rule. BenjaminFriedman (1979) addresses the same question.

9John Muth (1961, p. 317) in outlining what hemeant by rational expectations anticipated this criti-cism.



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Maddock and Carter: Rational Expectations 41

and I'll introduce you to the magnificientworld of rational expectations. Same time?

Scene ii. A. The Ideaof Rational Expectations

(In the same place, next day.)

Bert: Well, are you ready to try to under-stand what rational expectations is about?

Ernie: Yes. Have you got it figured out yet?Bert: I've been thinking about it. Let's go

through it systematically. First, we can talkabout just what rational expectations are.Then we can look at the way the policyimpotence result is derived. By then we

should have a pretty clear idea of whatthis line of research is all about so we cantry to figure out how it relates to the Phil-lips curve, monetarism, econometric mod-els, and all that. O.K.?

Ernie: Alright. What's the definition of ra-tional expectations? What on earth mightirrational expectations be?

Bert: First things first. Let's start with famil-iar ground. What would you say is the basicbehavioral assumption of economic behav-ior?

Ernie: Utility maximization, I suppose.Bert: More or less. I would say that the basic

assumption about individual behavior isthat economic agents do the best they canwith what they have. This principle formsthe basis of consumption theory, produc-tion theory, human capital theory and soon.

Ernie: So it's the basis of microeconomics.10But what's that got to do with expecta-tions?

Bert: Everything. At its most fundamental,rational expectations theorists argue thatthe same principle should be applied tothe formation of expectations. If you wanta definition, how about: rational expecta-tions is the application of the principleof rational behavior to the acquisition and

processing of information and to the for-mation of expectations."1

Ernie: Am I to infer that my utility functionand I sit down together and rationally de-cide how much information I should ac-quire in order to form the expectationsthat will help me maximize my utility? In-credible

Bert: Yes, you can attack it that way if youlike, but that's a more general criticismof utility theory which we can argue aboutsome other time. All I'm saying here isthat if one considers economic agents tobe rational maximizers, then it'sconsistent12 o consider information gath-

ering and expectation formation as deter-mined by the same procedure.Ernie: O.K. So you'd insist upon a rational ex-

pectations postulate that private economicagents gather and use information effi-ciently. That means you believe the mar-ginal costs of gathering and using informa-tion are equated to their marginal benefits.McCallum doesn't agree with you. He says:"Individual agents use all available andrelevant information "13 and it seems to methat Sargent and Lucas say the same. It

almost seems as if they think informationis a free good.14Bert: That's a good point. Many theorists

have ignored the costs of information usedin the formation of expectations. That isone of my criticisms of the literature. ButI think it is useful to distinguish betweenrational expectations as a principle of in-formational efficiency and rational expec-tations as it appears in some of the macro-economic literature.'5

10There is clearly some tension in macroeconom-ics between its empirical behavioral aspects (e.g.,the consumption function) and its derivation of in-sights from a microeconomic basis (e.g., permanentincome hypothesis). The micro foundations of macro-economics literature, or example Geoffrey Harcourt(1977) attempts to resolve this conflict but, so far,not very successfully.

11This is not the approach usually adopted by ra-tional expectations theorists (fn. 15). It is, however,closer to the usual economic methodology and seemspreferable.

12 That is, consistent with the methodological ap-proach of explaining all behavior in terms of utilitymaximization.

13 McCallum 1980, p. 38). In fact, Ernie has quotedMcCallum out of context. He goes on to admit thatinformation costs are neglected for simplicity.

14 Edgar Feige and Douglas Pierce (1976) considerthe implications of costly information for rationalexpectations.

15 The distinction seems important for clarifyingideas within macroeconomics. The all-informationapproach adopted by Sargent et al. should ideallybe 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 confusingin the context and you are right that thedistinction between the two things is im-

portant. But what difference does rationalexpectations make to individuals? Can yougive examples?

Bert: The example most often used in the lit-erature involves the allocation of time be-tween labor and leisure.16 In deciding howmany hours to work this period, an individ-ual must take account of expected futurewages and not just the present wage. Forexample, if you expect the real wage tobe $10 per hour this week, and $1 nextweek, then it makes sense to work as much

as possible this week, and have some timeoff next week. Therefore the number ofhours worked in any period, that is, thelabor supply, will depend not only on thecurrent real wage but on expected futurereal wages. A rational expectation of realwages will take into account all availableinformation, including the effects of gov-ernment policy.

Ernie: But my old man works 40 hours everyweek-he doesn't have much choice.

Bert: But your old man's boss does. When he

is deciding whether to hire more peopleor lay them off, he needs to take into ac-count future prices and wages. His expec-tations should be based on all the availableinformation. This includes, among otherthings, the impact of future governmentpolicy.

Ernie: O.K. I see how the level of employmentmight depend upon expectations and how'good' expectations are better than 'bad'ones. But I can't see why that means thatthere is no room for government policy.

B. Deriving the Impotence Result

Bert: Without realizing it you've just madea very important distinction. The relation-ship between the level of employment andexpectations is logically quite separatefrom beliefs about how expectations areformed. The conclusion that there is noscope for government policy-the impo-tence result-depends crucially upon im-posing a special assumption about expec-tations-rational expectations-upon aspecial type of macroeconomic model.

Ernie: Well I think I understand the meaningof rational expectations. What types ofmacro models do rational expectationstheorists use?

Prices Supply

\ \ Demand,Demando

Yn Income = Output

Diagram 1

Bert: (Drawing a diagram.) Most of themwork with the idea that the levels of out-put and prices are determined by the in-tersection of an aggregate demand and ag-gregate supply function. The aggregatesupply curve is taken to be vertical, so thatoutput cannot deviate from Ynas a directresult of any change in the level of de-mand. Thus government policies designedto change the level of aggregate demandare not likely to be effective. The levelYn s the output associated with equilib-rium in the labor market at the naturalrate of unemployment so we can call Ynthe natural rate of output or income forthe economy.17

tions," since the adjective "rational" s normally re-served in economics to describe the outcome of autility maximization process. J. J. Sijben writes:"Muth's view implies that economic agents build uptheir expectations as if they are fully informed ofthe process which ultimately generates the real out-come of the variable concerned" (1980, p. 66).Pushed further, McCallum follows the line that allmodels are "unrealistic," which seems to lead himto the position that theories stand or fall on theirpredictions.

16 Rational expectations in labor supply decisionshave fairly obvious corollaries on capital investmentdecisions (Robert Lucas, 1975, for example).

17 Appendix A deals with the problems of the verti-cal aggregate supply curve in more detail. It shouldbe noted that the models are usually expressed inlogarithms so that the real debate concerns rates

of change rather than levels. The distinction is ne-glected here.



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Consider the possibility that the govern-ment takes action that may, at first blush,be supposed to increase output. For exam-ple, let it act to increase nominal incomeand aggregate money demand. Moneywage rates will tend to rise, and if workersregard this as equivalent to an increasein real wages, employment will increaseand output will temporarily rise to a levelhigher than Y.. But if production is carriedon subject to diminishing returns to labor,prices will rise relative to nominal wages,and real wages will fall. When workers re-alize this, employment will fall back to itsoriginal position, and output will return

to Yn. At this point, nominal wage ratesand prices are higher (the nominal de-mand curve crosses the vertical supplycurve at a higher level), but output andemployment are back where they started.Since the aggregate supply curve had notshifted, the possibility of increasing em-ployment and output arises only as longas people confuse nominal changes inwages (for example) with real changes.This means that government policy willonly increase the level of income in

real terms if it is able to fool people intoconfusing nominal changes with realones.18

Ernie: That's ridiculous The 'natural' rate ofunemployment depends intimately uponall sorts of government policies-for exam-ple tax laws, minimum wage laws, immi-gration policy, school-leaving age, etc., etc.Do you really mean that the governmentcan't change aggregate supply by increas-ing the investment allowance? Or by go-ing to war, for that matter?

Bert: You're right, you're right I should havebeen more careful. Clearly governmentpolicy can alter the natural rate of unem-ployment or, if you like, the position ofthe aggregate curve. What I should havesaid is that the only way in which govern-ment policy can bring about deviationsfrom the natural rate of unemploymentis by inducing private agents to have mis-

taken expectations. Let's write down asimple model.

(Bert's scribbling is attached as Appendix B.For those who like mathematical descriptionsit should make the discussion clearer but isnot a necessary adjunct.)

Ernie: That makes your position clearer. Theactual aggregate supply function impliesthat deviations of actual output from thenatural rate are directly proportional todeviations of actual prices from expectedprices. Since people with rational expecta-tions never make mistakes about policy

rules, policy will never fool them, and out-put will never deviate from its natural rateas a result of any policy rule.

Bert: That's the idea but you've put it toostrongly. If government policies are ran-dom, they will be effective although notnecessarily desirable. It's the systematiccomponent of policy that the theory sug-gests will be ineffective.

Ernie: I'm not too sure about the neutrality-of-money proposition19 generally but willlet it ride for now. You explain the rest

of the argument-then I'll put my objec-tions one by one.

Bert: Now the point of rational expectationsis that people won't be surprised by anysystematic policy. Any government thatrelies upon a policy rule-one that has afixed growth of the money supply, or onesystematically related to income or unem-ployment-will never cause any deviationfrom the natural rate.20 A random policywill affect real output. But any policy rulethat is systematically related to economic

conditions, for example one designed withstabilization in mind, will be perfectly an-ticipated, and therefore have no effect onoutput or employment. In other words, tohave real effects. monetary Dolicv must be

"8As Thomas Sargent and Neil Wallace suggest"it must somehow trick the public" (1976 p. 177).The argument is more complex with capital in themodel as may be clear from Appendix A.

19The idea that changes in money supply do notinfluence people's preferred hours of work, portfolioholdings, etc. Again, this is considered in AppendixA.

20 Sargent and Wallace (1976, pp. 177-78), put thisargument n almost the same form. Expectations canbe wrong but not systematically wrong (i.e., biased),hence there is no scope for systematic policy.



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completely unpredictable. Any systematicpolicy will be impotent.21

Ernie: Can we put it this way? Rational expec-tations are based on all available informa-tion. The available information set in-cludes the government policy rule.Therefore, a rational expectation of in-flation, for example, will include the an-ticipated effects of government policy sothat the policy will have no effect on out-put.22

Bert: Yes, that pretty well sums it up.

C. Criticisms

Ernie: Now that I think I understand whatyou're on about, can I tell you what I thinkis wrong with the model?

Bert: O.K.Ernie: First, I don't like your supply curve.

There are lots of criticisms one couldmake, but the most important in the con-text of the model is that you assume anextreme form of the neutrality of money.23Perfectly anticipated inflation has no realeffects in your model. That's clearlywrong. Buiter (1980) put the standard ar-

gument in terms of the portfolio readjust-ments required because inflation changesthe real rate of return on those financialassets which have a zero nominal return.Personally, I think the distortions intro-duced by the progressive tax structure inan inflationary situation are far more im-portant empirically.

Bert: Yes, but all models are approximations.Ernie: True, but not all approximations are

good approximations Here's anotherproblem. If expectations are rational, thenexpectation errors should be randomly dis-tributed over time. A straightforward im-plication of that for this model is that thelevel of output (or unemployment) is un-correlated over time. Yet everybodyknows that the GNP and unemploymentseries have a high degree of serial cor-

relation.24 We tend to go through a seriesof years in which unemployment is belowthe 'natural rate,' and then a series of years

in which it is above the 'natural rate.' Itdoesn't seem to be distributed very ran-domly. Compare the sixties and seventiesin Australia-it's the old story of businesscycle expansion and contraction.

Bert: I can't deny the serial correlation n theunemployment or income series. Most ra-tional expectations models include laggedincome or lagged unemployment as expla-natory variables in the supply function.25This does make the models fit the databetter, but there is no good theoretical

justification for it. Lucas is the only one Iknow who really addresses the issue.26Herelies on the well-known 'fact' that all peo-ple live on islands. At the end of each trad-ing period people choose a new island atrandom. Since they don't know the historyof their new island, they can't distinguishimmediately between real and nominaleffects.27

Ernie: These island models seem appropriateto a society in which the fastest form ofcommunication is a floating coconut.

Hasn't Lucas ever heard of radio and thetelephone?28

Bert: I have to agree with you. I said thatthe explanations for persistence weren't

21 Gordon (1976) makes this clear. See especiallypp. 200-01.

22This follows the usual solution method followedby rational expectations models. See Lucas (1973)

for an example.23 Some criticisms are discussed in Appendix A.

24 This was Hall's criticism (1975), and is also putby Gordon to Sargent (1973, p. 478).

25 Lucas (1973) introduced the lagged term witha footnote explaining that not all deviation from thenatural rate of unemployment could be accountedfor by the error in expectations terms.

26 Lucas (1975) attempts a systematic explanationfor the serial correlation n terms of information ags.See Rodney Maddock (1979) for a discussion of theimportance of persistence for the rational expecta-tion program.

27 "The idea behind this island abstraction s not,of course, to gain insight into maritime affairs, orto comment on the aimlessness of life. It is intendedsimply to capture in a tractable way the fact thateconomic activity offers agents a succession of am-biguous, unanticipated opportunities which cannotbe expected to stay fixed while more informationis collected. It seems safe and, for my purposes, sensi-ble to abstract here from the fact that in reality thissituation can be slightly mitigated by the purchaseof additional nformation" Lucas (1975, p. 1120).

28Lucas does actually mention the problem in the

quotation in the previous footnote, but makes noth-ing of it.



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very convincing, especially when the gov-ernment regularly publishes lots of statis-tics. The newspapers carry stock exchangeprices every day. The information seemsto be essentially free.

There is another line of argumentthough. If prices change suddenly, firmscan increase their production less thantheir sales by using up some of their inven-tories. If there is no price shock in thenext period production would then beraised to build inventories back to theiroriginal level. Thus there would be an in-crease in production to meet the originalstock and for as long thereafter as the re-

stocking took.Ernie: But that implies there should be astrong relationship between inventory cy-cles and output cycles and that's not reallytrue, is it?

Bert: Well, the relation is far from perfect.I was really just suggesting that in an econ-omy characterized by durable goods itshouldn't be too difficult to accept that ad-justments of various sorts will have effectsthat persist.29 We really don't have a goodexplanation for persistence (serial correl4-

tion). I willingly concede that point.What's next?Ernie: O.K. Even if all that information is

freely available, you assume that all theagents know the correct model of theeconomy. How . . .

Bert: No, I don't. Well, not me really. I meanthat rational-expectations people don'tnecessarily say that everybody knows thecorrect model of the economy. They sug-gest that some arbitrage process takesplace whereby the people who have thecorrect model dominate the outcome.30 fthere are misapprehensions, then well-informed agents can make profits at theexpense of the ill-informed. This will inevi-tably lead the system to converge to therational expectations equilibrium. As yourold mate, John Maynard Keynes, said:

* . .actions based on inaccurate anticipationswill not long survive experiences of a con-trary character, so that the facts will soonoverride anticipation except where they

agree. [1930, p. 160].Ernie: Granted there is a role for arbitrage.

But how do we know that expectationsof the experts will converge on the truevalue? Give me any rational expectationsmodel and I think I can show you a reason-able adjustment process that will not con-verge to the rational expectations equilib-rium.

Bert: And I can probably show you one thatcan. Unless the theorists specify an adjust-ment mechanism, we can't really argueabout this point. Rational expectations the-orists haven't addressed this problem.31

Ernie: That's a big gap in your theory. But letme read to you what Robert Shiller says:

Even if a model does eventually convergeon a rational expectations equilibrium, t maytake such a long time to do so that, sincethe structure of the economy changes occa-sionally, the economy is never close to a ra-tional expectations equilibrium. 1978, p. 39].

To recalculate a quarterly econometricmodel after a change in policy rule mighttake 20 quarters. To estimate the effectof policy based on the new estimates mighttake another 20 quarters. Thus, even if theprocess converges, each stage in the con-vergence to the new equilibrium couldtake five years-by which time we mayall be dead

Bert: But if the Government's objective is tostabilize the economy, then it wants to

29These issues are raised in a penetrating discus-sion of the problem of persistence by Gordon (1981).

30For example, Muth (1961) argued that econo-mists could sell the information profitably f expecta-tions were not rational. Since he wrote, many havedone so. This suggests that market forces would tendto drive decisions to those rationally based.

31Shiller (1978, p. 38) focuses upon the issue ofconvergence. There seem to be two separate issuesinvolved. Since rational expectations for this perioddepend upon estimates about the future while thefuture depends in part upon present expectations,there need be no unique rational expectation forthe current period. In many models, methods of ad-justing expectations (i.e., forecasts) of the future willeither converge on a rational-expectations olutionor explode. The implicit argument of protagonistsseems to be that since we do not observe prices ex-ploding off to infinity we need only consider con-verging cases. This type of counter-factual easoningis somewhat dubious. The dynamics of expectationformation might still be explosive but some otherfact or-e.g., policy action-act to constrain the ex-plosive tendency.



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make sure that private expectations arerational, and hence it will inform the pub-lic of any new policy rule.32

Ernie: That doesn't get you out of hot water.First, the learning problem doesn't con-cern the policy rule alone. Agents alsohave to learn the structure of economy,which is subject to change. Econometricmodellers don't have an outstanding rec-ord of success, do they? Second, why doyou assume that the goverment's objectiveis to stabilize the economy? It seems tome that the government's real objectiveis to remain in power-you know, the po-litical business cycle idea.33 And if that is

their objective it may be in their interestto hide information and fool the public.If that is the case the voters can hardlybe expected to believe the signals the gov-ernment is sending out and the wholemacroeconomic process degenerates intoa guessing game.

Bert: But you must agree that most macro-economics does assume the objective ofstabilization. This literature falls into thattradition which is concerned with govern-ment policy rules designed to achieve

macroeconomic stabilization.34Ernie: Let's go and get a beer.35

Scene iii. (In the union bar)A. Testing

Bert: Now the testing is a bit tricky. It's apretty young research program and thereare no well-accepted testing proceduresas yet. The principal difficulty is that weare really testing a joint hypothesis-theeconomic model and the expectationsmechanism. That makes it difficult to de-cide just where the responsibility for fail-ures of tests really lie.

Ernie: But why can't you just test the expecta-tions mechanism directly? Ask people

what they expect, and see if they are right?Bert: Stephen Turnovsky (1970) and James

Pesando (1975) and a couple of other peo-

ple have done that, but the results havebeen inconclusive. Economists tradition-ally don't like surveys, anyway.

Ernie: Well, how have rational expectationsprotagonists tried to test the theory?

Bert: Basically they have taken two differentapproaches. Have a look at the supplyfunction again. The natural rate hypothe-sis will only allow non-random deviationsif there are expectations errors of somesort. Under the rational expectations hy-pothesis there are no expectations errors-

or at most, only random ones. Thus, devia-tions from the natural rate of output mustbe random.36 n particular, deviations can-not be systematically related to any otherexplanatory variable, for example the(lagged) money supply or the wage rate.And so the first type of test is essentiallyto see whether deviations from the naturalrate are systematically related to any othervariables. This test has been applied in anumber of different ways especially bySargent (1973; 1976). In those papers the

joint hypothesis-natural rate and rationalexpectations-was rejected in a numberof cases, jointly rejected because theywere jointly tested. With slightly differentspecifications, they weren't. Sargent con-cludes that rational expectations is 'not ob-scenely at variance with the data.'37

Ernie: Remarkable resilience, ehBert: Yes, what's more, his next paper was

entitled 'The Observational Equivalenceof Natural and Unnatural Rate Theoriesof Macroeconomics.'38 This initiated thesecond approach to testing rational expec-tations. It was based on the idea that whatrational expectations models add, com-pared with other models, is that price ex-

32Sargent and Wallace (1976, pp. 181-83) arguethis point.

33The nature of the problem when the govern-ment's objectives vary over time does not seem tohave been well explored. Clearly, rational expecta-tions forces economists to think more about the pre-cise nature of learning.

34 Following the tradition of Dutch economists Jan

Tinbergen (1952) and Henri Theil (1958).35 Following a sound Australian tradition.

36Actually, some allowance in the tests is madefor persistence by the inclusion of lagged values ofthe dependent variable.

37The theory suggests that no extra informationwould significantly contribute to the prediction. Theevidence would thus appear to falsify the theory.Sargent (1976), nstead, went on to try an alternativetype of test. See especially p. 233.

38Sargent (1976) and Sargent and Wallace (1975)start to develop this idea.



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pectations take into account the policyrule the government is using. If that ruledoes not change, ordinary models and ra-tional expectations models will fit any dataset equally well, though probably with dif-ferent parameters. What it means is thatyou can only distinguish between rationalexpectations macro models and ordinaryones if the policy rule has changed.39 Itseems a reasonable idea to me.

Ernie: Maybe.Bert: Well, anyway, it gave Sargent and Salih

Neftci (1978) an idea for a new type oftest. First, they estimated the govern-ment's policy rule by regressing the

money supply on past levels of income.They then analysed the results to see ifthere had been any significant changes inthe relationship, hat is, to see if the policyrule had changed.40 They found changesin 1929 and 1964. They then looked atsome ordinary macroeconomic models tosee whether the parameters had changedat about the same time that the policy rulechanged. In each case they found someevidence that it had.4'

Ernie: Well, that seems like a reasonable sort

of approach. Really it depends on the ra-tional expectations idea-that peoplechange their behavior as policy changes-rather than on the natural rate proposi-tion. I'm inclined to agree that people takeinto account what the government is try-ing to do when they plan for the futurebut the extreme form of the natural rateof unemployment is an over-simplification

of a complex world. Of course, the testis a bit tricky. It's not really clear to methat that's the way to estimate the govern-ment policy rule and then, even if it is,there are probably other non-rational ex-pectations mechanisms which would sug-gest a change in the econometric structureas a result of a change in policy rule.There's no real alternative hypothesis in-volved in the test

Bert: Everyone agrees it's not a very strongtest; it's titled 'A Little Bit of Evidence. . . ' but it is suggestive and does focusupon the relation between expectationsand the policy rule and not upon the natu-

ral rate. It gets away from the dogmaticform of the natural rate, impotence of pol-icy area, and focuses upon the positivecontribution of the rational expectationsidea.

B. Significance

Ernie: O.K., we've covered the model and theevidence, such as it is. What's all the fussabout?

Bert: Well, it really nails the Phillips curve.Much post-war stabilization policy hasbeen based on the idea that there is atrade-off between unemployment and in-flation that the government can exploit byinfluencing aggregate demand-the so-called Phillips curve. Friedman largely un-dermined that with the natural rate idea.He said that policy only worked by foolingpeople and that in the long-run they couldnot be fooled. This still left the way openfor effective short-run policy. If peoplehave rational expectations they won't be

fooled. If people have rational expecta-tions they won't be fooled by systematicpolicy even in the short run so there isno scope for short-run policy either. Thisexplains why the Phillips curve becameunstable the moment policy makers triedto exploit it.

Ernie: But the explanation depends reallyheavily, as you've already agreed, uponthe particular macroeconomic model youhave set up.42 The monetarists have

39Since expectations are usually unobservablethey are eliminated from econometric model to beestimated by introducing an equation about theirrelation to known variables. The parameters of thisequation then become embedded in the actual re-duced form equations which are estimated. An"equation" or rational expectations ncorporates heparameters of the policy rule being used by the gov-ernment. Under the assumption of rational expecta-tions these parameters of the policy rule becomeembedded in the reduced form (i.e., estimating)equations of the economy. Thus they suggest thatstructure of the economy, as measured by usualeconometric models, will appear to change when-ever the policy rule changes.

40 Using Ml there was a policy change, but withM2 none appeared to have taken place.41 The tests were non-parametric.

42 Alan Preston and Adrian Pagan (Forthcoming,Ch. 10) explore the way in which the impotence



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grabbed this idea43 o support their tradi-tional position that active government pol-icy is not desirable.44 t's largely been their

baby until now. The reason is not hardto see. The impotence result strongly sup-ports their ideological position that thegovernment should keep its hands off theeconomy.45

Bert: That's rather harsh. Monetarists are nomore ideological than other economists.What would be your 'un-ideological' viewof rational expectations?

Ernie: I've been wondering how a future his-torian of thought might assess it. I thinkrational expectations theory will be seen

as a very important development in eco-nomics, but not because of the impotenceresult. Rational expectations are importantin any situation in which market behavioris influenced by expectations. Take thecase of an aggregate demand deficiencyin a Keynesian model. The usual argumentis that monetary expansion will workthrough affecting interest rates so thatgradually the economy shifts to a higheroutput level. With rational expectationsthe shift to the new level would be ex-

tremely rapid. If businessmen understandthe economic implications of expansionarygovernment policy, they can expand their

output in anticipation of those effectsrather than waiting for the rise in demandto be obvious in the market. In that case,

far from policy being impotent, rationalexpectations may make policy more effec-tive.

This example, by the way, illustrates hefact that most of the rational expectationsliterature has a particular economic modelbuilt in, one in which all markets clearinstantaneously; unemployment is, there-fore, voluntary, hence 'natural'; andmoney is necessarily neutral. But if thatmodel is not applicable, policy need notbe impotent, and, as said, rational expec-

tations may make it more rapidly effec-tive.What's more rational expectations can

be applied in microeconomic situations.46Cobweb models of dynamic behavior incommodity markets depend upon 'irra-tionality of expectations'-the idea thatnext year's prices will be the same as thisyear's or even a simple extrapolation ofit. Clearly, producers can do better thanthat, and if they have rational expectationsthe market is likely to approach ts equilib-

rium quite quickly.Bert: You're right The idea can be appliedin a wide variety of models but what aboutyour general conclusions about policy for-mation?

Ernie: Yes, I agree that there are importantimplications for policy design. Private eco-nomic agents are intelligent decision-mak-ers and can be expected to take the effectsof government policy changes into ac-count in deciding their behavior. Thismeans that the policy-maker must antici-pate the effect of policy on private expec-tations and the consequent changes in be-havior. In practical terms it means thatwe need to know a lot more about theavailability and use of information by pri-vate decision-makers.47 hus, the focus ofthe theory of policy should be on expecta-

result depends on particular specifications of themacroeconomic model being considered. They de-velop a more general model that includes the usualrational expectations models as particular cases.

43 Lucas and Leonard A. Rapping used adaptiveexpectations (1969), then rational distributed ag ex-pectations (1969) before Lucas first introduced ra-tional expectations (1972). Where adaptive expecta-

tions assumed that people just simply adapted to pasterrors, rational distributed ag expectations were thevery best econometrically predicted estimates ofprices derived from analysis of all past price informa-tion.

44 Any stable understandable rule would have noeffect if people were exactly able to predict it. Bythat test a "discretionary" ule and a fixed moneygrowth rate rule would be equally impotent. If sto-chastic effects of discretionary rules are allowed forhowever, these cannot be predicted and would intro-duce fluctations into the system. See Sargent andWallace (1976) for a discussion of the issues.

45 McCallum's 1980) popularization of their posi-tion carries the inference that the results are quiterobust, but that does not appear to be the case. SeePreston and Pagan (Forthcoming).

46The seminal article by Muth (1961) deals withmicroeconomic market situations.

47Sargent and Wallace (1975, p. 251) provide astart in this direction by modelling a case where

government has an information advantage over pri-vate actors.



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tions and information and on their rolein determining behavior.

Bert: I think you can go further. People usedto think

that the only reason stabilizationpolicy didn't work well was that policy-makers didn't have enough knowledgeabout the structure of the economy. Ra-tional expectations has taught us that theproblem may not be just one of the abso-lute knowledge of the authorities butrather of how much more or less theyknow than the public does-a problem ofrelative knowledge. If this is true, theproblem will always be with us.

C. ConclusionErnie: Well, I started off inclined towards Gor-

don's view that rational expectations is anexample of a recent development in eco-nomics "in which theory proceeds withimpeccable logic from unrealistic assump-tions to conclusions that contradict the his-torical record" (1976, p. 5). But now I seethat that's a bit too harsh.

Most of the research on rational expecta-tions has exhibited great technical compe-tence, 'impeccable logic,' and considera-ble ingenuity. This has contributed in nosmall measure to its apparent success, andto the confusion and uncertainty which ra-tional expectations have aroused in therest of the economics profession. The fun-damental simplicity of the ideas involvedhas become obscured by overly rigorousdevelopment, and especially by the un-convincing resort to extraneous construc-tions, such as the 'islands' mentionedabove.

Undoubtedly, it is the impotence of pol-icy results that has aroused most attention.Yet these results depend very heavily ona particular ype of macroeconomic modelusually embodying a strong form of thenatural rate hypothesis. If you start with'classical' models in which policy can haveno real effects, it is hardly surprising thatyou get results n which policy is impotent.Because of this the novelty of rational ex-pectations has become bundled up withtired and worn notions of the way in which

the world works. It is vitally important tounbundle these ideas.

The rational expectations hypothesis, initself, should not be provocative to econo-mists. It merely brings expectations withinthe scope of individual maximizing behav-ior. Expectations used to be handledwithin economic models on an ad hoc ba-sis. Rational expectations provides a wayof incorporating expectations which is con-sistent with the orthodox economic theori-zing.

The development of rational expecta-tions theory will make a more significantcontribution to economics in the impetusit gives to research on the vital areas oflearning and expectations formation. It

brings to the fore questions about theavailability and use of information. Insteadof being the finale of the monetarist's caseagainst policy intervention, it should beseen as the prologue for a revitalized the-ory of expectations, information and pol-icy.

Bert: I guess you're right. Let's go and getanother beer.

APPENDIX A: Aggregate Supply

The underlying inspiration for rational ex-pectations macro models is derived from thenotion of general equilibrium. With price flexi-bility, for given endowments and skills, a condi-tion of general equilibrium requires equilib-rium in the labor markets. In such a world allunemployment is voluntary, everybody whowants a job has one. Every individual has hislabor hours and assets allocated according tosome personal optimum. The remaining unem-ployment can be termed the "natural" rateof unemployment and the level of outputtermed the "natural" level of output.

Abstracting from inter-industry shifts in pro-duction, the only way output can change isthrough a change in employment. To increaseor decrease the level of output governmentpolicy must alter the equilibrium in the labormarkets. But if the natural rate of unemploy-ment represents an optimal position for pri-vate actors, how can government policy affectit?

The models rational expectations theorists

usually work with suggest that this is possibleonly if the government is able to fool people.



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If people confuse nominal wage changes forreal ones, they might reallocate their portfoliosand their hours of work, and thus increase out-

put. While allowing for this possibility the mod-els suggest that such a change would not bedesirable for the worker (representing a sub-optimal decision) and would be avoided if theyhad rational expectations. They suggest thatthe labor supply decision is made in real termsso that labor market equilibrium is indepen-dent of prices which, in turn, is taken to implythat output is independent of prices. This re-sult is presented in a vertical aggregate supplycurve.

Alternative macro-economic theories sug-

gest that the optimal allocation decisions of pri-vate actors will be affected by changes inprices, but not just because people are fooled.If this were true, increases in aggregate de-mand could increase output and employmenteven with rational expectations. One argu-ment for the proposition suggests that peopledon't hold money in their asset portfolios sim-ply for transaction purposes. If prices go up,the desirability of holding such money goesdown, changing people's private allocation de-cisions, and perhaps the rate of capital forma-

tion or number of hours worked. Thus it mightbe said that the rational expectations modelsassume that the only motive for holding moneyis the transactions motive.

APPENDIX B: Algebra of the Model

Supply: yt- -= a(pt-pt*) + ut [1]

Demand: Yt= -bpt + eXt [2]

Expectations: Pt* E[ptlIt-1] [3]

where Yt= income

y= income level correspondingto the natural rate of unem-ployment

Pt= pricesPt*= price expectationsxt= government policy instru-

ment, e.g., money supplyIt-, = all information available at

time t- 1

ut = random error term; Eut = 0E = expectations operator.

Equating demand and supply, we obtain thefollowing reduced form equation:

Pt = a + b (apt + c [4]

Now, by the rational expectations assumption(eqn. 3),

pt* E[ptjIt-1]

1sing (4) = E[ (apt*+ext- y--u)]

= a + b (aEp*+ cExt E-- Eud)

But Ept* pt*, y= y EutO=so Pt+b(aPt* +cExtY-) [5]

Subtracting [5] from [4]

1Pt -Pt* = a+b [c(xt -Ext) -Ut] [6]

Substituting [6] in equation [1]a

Yt Y = a + b [c(xt-Ext)-ut] + uta+ b

=acb (Xt Ext) + b [7]a +b a+ b Ut

That is, the deviation of output from the 'natu-ral' level y-depends only on the unsystematiccomponent of government policy (x - Ext). Tosee this, assume that the government uses thefollowing policy rule:

xt= kxt-1+ lyt-, + mpt-i - nPt-2 + vt [8]where vt is a random variable, Evt= 0.

Then,

Ext = kxt_- + lyt-, + mpt-i - nPt-2 [9]Subtracting [9] from [8]

Xt- Ext = vt

Putting this in [7]

- ac + bYt Y a+ b a+ b`

1= a+ b (acvt + but)

Deviations of Yt rom-are thus entirely ran-dom. This implies that systematic government



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A Childs Guide to Rational Expectations 1982

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