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: http://www.jstor.org/stable/2724658 Accessed: 20-03-2015 00:44 UTC

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This content downloaded from 208.138.56.79 on Fri, 20 Mar 2015 00:44:00 UTC All use subject to JSTOR Terms and Conditions 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

DRAMATISPERSONAE (In order of speaking)

Ernie, first student, is something of a Keynesian. Bert, second student, is more inclined to .

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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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 (, 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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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 consistent12to 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 marginalbenefits. Bert: First things first. Let's start with famil- McCallumdoesn'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, 11This 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 the formation of expectations. If you want preferable. 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 McCallumout of context. He goes on to admit that 10There 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 foundationsof macro- 15 The distinction seems important for clarifying economics literature,for example GeoffreyHarcourt 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 "Muthexpecta-

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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 \ Demand, week-he doesn't have much choice. Demando 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 Ynas 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- Ynis 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'sview 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 corollarieson capital investment of change rather than levels. The distinction is ne- decisions (Robert Lucas, 1975, for example). glected here.

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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 19 from the natural rate of unemployment 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 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. Expectationscan The argument is more complex with capital in the be wrong but not systematicallywrong (i.e., biased), model as may be clear from Appendix A. hence there is no scope for systematic policy.

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completely unpredictable. Any systematic relation.24We 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 'naturalrate,' 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 correlationin 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.26He 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 an inflationary situation are far more im- by Gordon to Sargent (1973, p. 478). 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 correlationin terms of informationlags. 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 abstractionis not, level of output (or unemployment) is un- of course, to gain insight into maritime affairs, or 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 abstracthere 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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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 the will converge on the true can increase their production less than of experts their sales by using up some of their inven- value? Give me any rational expectations I I can show you a reason- tories. If there is no price shock in the model and think that will not con- next period production would then be able adjustment process raised to build inventories back to their verge to the rational expectations equilib- original level. Thus there would be an in- rium. And I can show you one that crease in production to meet the original Bert: probably an stock and for as long thereafter as the re- can. Unless the theorists specify adjust- mechanism, we can't really argue stocking took. ment the- Ernie: But that implies there should be a about this point. Rational expectations strong relationship between inventory cy- orists haven't addressed this problem.31 Ernie: That's a big gap in your theory. But let cles and output cycles and that's not really what Robert Shiller says: true, is it? me read to you Bert: Well, the relation is far from perfect. Even if a model does eventually converge I was reallyjust suggesting that in an econ- on a rationalexpectations equilibrium,it may omy characterized by durable goods it take such a long time to do so that, since the structure of the economy changes occa- shouldn't be too difficultto 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]. have a that persist.29We really don't good To recalculate a quarterly econometric explanation for persistence (serial correl4- model after a change in policy rule might I that point. tion). willingly concede 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.30If 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 expense of the ill-informed.This will inevi- future depends in part upon present expectations, 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-expectationssolution 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-factualreasoning mists could sell the informationprofitably 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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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.33And 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.36In 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 systematicallyrelated 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.'38This 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 have been well explored. Clearly, rational expecta- would significantlycontribute to the prediction. The tions forces economists to think more about the pre- evidence would thus appear to falsify the theory. cise nature of learning. Sargent (1976), instead, went on to try an alternative 34 Following the tradition of Dutch economists Jan type of test. See especially p. 233. 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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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.39It 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.40They 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 has of approach. Really it depends on the ra- Much post-war stabilization policy tional expectations idea-that people been based on the idea that there is a in- change their behavior as policy changes- trade-off between unemployment and rather than on the natural rate proposi- flation that the government can exploit by tion. I'm inclined to agree that people take influencing aggregate demand-the so- into account what the government is try- called Phillips curve. Friedman largely un- ing to do when they plan for the future dermined that with the natural rate idea. but the extreme form of the natural rate He said that policy only worked by fooling of unemployment is an over-simplification people and that in the long-run they could not be fooled. This still left the way open for effective short-run policy. If people 39Since 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 rationalexpectations incorporatesthe explains why the Phillips curve became parametersof the policy rule being used by the gov- unstable the moment policy makers tried ernment. Under the assumptionof rational expecta- tions these parameters of the policy rule become to exploit it. 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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grabbed this idea43to 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.44It'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, illustratesthe economy.45 fact that most of the rational expectations Bert: That's rather harsh. Monetaristsare no literature has a particulareconomic 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. Rationalexpectations 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 Keynesianmodel. 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- implicationsfor 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- tions assumedthat people just simply adapted to past means that the policy-maker must antici- 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 analysisof all past price informa- havior. In practical terms it means that tion. we need to know a lot more about the 44 Any stable understandablerule 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.47Thus, the focus of growth rate rule would be equally impotent. If sto- the theory of policy should be on expecta- chastic effects of discretionaryrules 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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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 Ernie: Well, I started off inclined towards Gor- availability and use of information. Instead don's view that rational expectations is an of being the finale of the monetarist's case example of a recent development in eco- against policy intervention, it should be nomics "in which theory proceeds with seen as the prologue for a revitalized the- impeccable logic from unrealistic assump- ory of expectations, information and pol- tions to conclusions that contradict the his- icy. 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 rationalexpecta- tions has exhibited great technical compe- APPENDIXA: 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 particulartype 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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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)] that output is independent of prices. This re- 1 sult is presented in a vertical aggregate supply = curve. a + b (aEp*+ cExt- E-- Eud) 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] be said that the rational expectations models a +b a+ b Ut assume that the only motive for holding money of from the 'natu- is the transactions motive. That is, the deviation output ral' level y-depends only on the unsystematic component of government policy (x - Ext).To APPENDIXB: 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 - ac + b Pt*= price expectations Yt Y xt= government policy instru- 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 Ytfrom are thus entirely ran- E = expectations operator. dom. This implies that systematic government

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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. REFERENCES MALINVAUD, EDMOND. The theory of unemploy- BUITER, WILLEM. "The Macroeconomicsof Dr. Pan- ment reconsidered. New York: Wiley. Oxford: gloss: A Critical Survey of the New ClassicalMac- Blackwell, 1977. roeconomics,"Econ. J, March 1980, 90(1),pp. 34- MCCALLUM,BENNETT T. "The Significance of Ra- 50. tional ExpectationsTheory," Challenge.Jan./Feb. CHow, GREGORY. "Optimal Stochastic Control of 1980, pp. 37-43. Linear Economic Systems," J Money, Credit, MUTH,JOHN. "Rational Expectations and the Theory Banking, Aug. 1970, 2(3), pp. 291-302. of Price Movements," Econometrica, July 1961, DECANIO, STEPHEN. "Rational Expectations and 29(3), pp. 315-35. Learning from Experience," Quart.J. Econ., 1979, NEFTCI, SALIH AND SARGENT, THOMAS. "A Little 93(1), pp. 47-57. Bit of Evidence on the Natural Rate Hypothesis FEIGE, EDGAR AND PEARCE, DOUGLAS. "Eco- from the U.S.," J Monet. Econ., 1978, 4(1), pp. nomically Rational Price Expectations," I. Polit. 315-19. Econ., 1976, 84(3), pp. 499-522. PESANDO, JAMES. "A Note on the Rationalityof the FRIEDMAN, BENJAMIN. "Optimal Expectations and Livingston Price Expectations," J. Polit. Econ., the Extreme InformationAssumptions of 'Rational Aug. 1975, 83(4), pp. 849-58. Expectations'Macromodels," J Monet. Econ., Jan. PRESTON, ALAN AND PAGAN, ADRIAN. The theory 1979, 5(1), pp. 23-41. of economic policy: Statics and dynamics. New FRIEDMAN, MILTON. "The Role of MonetaryPolicy," York: Cambridge University Press, forthcoming. Amer. Econ. Rev., March 1968, 58(1), pp. 1-17. SARGENT, THOMAS. "RationalExpectations, the Real GORDON, ROBERT A. "Rigor and Relevance in a Rate of Interest, and the Natural Rate of Unem- Changing InstitutionalSetting," Amer. Econ. Rev., ployment," BrookingsPap. Econ. Act., 1973, 2, pp. 1976, 66(1), pp. 1-14. 429-72. GORDON, ROBERT J. "Recent Developments in the . "A Classical Macroeconomic Model for the Theory of Inflationand Unemployment," J Monet. ,"J. Polit. Econ., April 1976a, 84(2), Econ., April 1976, 2(2), pp. 185-220. pp. 207-37. . "Output Fluctuationsand GradualPrice Ad- _ . "The Observational Equivalence of Natural justment," J Econ. Lit., June 1981, pp. 493-530. and UnnaturalRate Theories of Macroeconomics," HALL, ROBERT E. "The Rigidity of Wages and the I. Polit. Econ., June 1976b, 84(3), pp. 631-40. Persistence of Unemployment," Brookings Pap. AND WALLACE, NEIL. "'Rational' Expecta- Econ. Act., 1975, 2, pp. 301-49. tions, the Optimal Monetary Instrument and the HARCOURT, GEOFFREY, ed. The microeconomic Optimal Money Supply Rule,"J Polit. Econ., 1975, foundations of macroeconomics.London: Macmil- 83(2), pp. 241-55. lan, 1977. . "Rational Expectations and the Theory of KEYNES, JOHN. A treatise on money. Vols I and II. Economic Policy," J Monet. Econ., April 1976, New York:Harcourt Brace, 1930. 2(2), pp. 169-83. LUCAS, ROBERT E., JR. "Testing the Natural Rate SHILLER, ROBERT J. "RationalExpectations and the Hypothesis,"in Theeconometrics of price determi- Dynamic Structure of MacroeconomicModels: A nation, Conference. Edited by OTTo ECKSTEIN. Critical Review," J Monet. Econ., Jan. 1978, 4(1), Washington, D.C.: Federal Reserve Board, 1972, pp. 1-44. pp. 50-59. SIJBEN, J. J. Rational expectationsand monetarypol- . "Some International Evidence on Output- icy. Alphen aan den Rijn,The Netherlands:Sijthoff InflationTradeoffs," Amer. Econ. Rev.,June 1973, and Noordhoff, 1980. 63(3), pp. 326-34. TAYLOR, JOHN. "MonetaryPolicy during the Transi- . "An Equilibrium Model of the Business Cy- tion to RationalExpectations," J. Polit. Econ., 1975, cle," J Polit. Econ., Dec. 1975, 83(6), pp. 1113- 83(5), pp. 1009-21. 44. THEIL, HENRI. Economicforecasts and policy. Am- . "Econometric Policy Evaluation: A Cri- sterdam: North-Holland, 1958. tique," J Monet. Econ., Supplementary Series TINBERGEN, JAN. On the theory of economic policy. 1976, 1, pp. 19-46. Amsterdam:North-Holland, 1952. LUCAS, ROBERT E., JR. AND RAPPING, LEONARD A. TURNOVSKY, STEPHEN J. "Empirical Evidence on "Price Expectations and the Phillips Curve," the Formation of Price Expectations," J. Amer. Amer. Econ. Rev., June 1969a, 59(3), pp. 342-50. Statist. Assoc., Dec. 1970, 65(332), pp. 1441- . "Real Wages, Employment and Inflation," 54.

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