Almost two months ago I wrote a provocatively titled post about rational expectations, in which I argued against the idea that it is useful to make the rational-expectations assumption in developing a theory of business cycles. The title of the post was probably what led to the start of a thread about my post on the econjobrumors blog, the tenor of which can be divined from the contribution of one commenter: “Who on earth is Glasner?” But, aside from the attention I received on econjobrumors, I also elicited a response from Scott Sumner

David Glasner has a post criticizing the rational expectations modeling assumption in economics:

What this means is that expectations can be rational only when everyone has identical expectations. If people have divergent expectations, then the expectations of at least some people will necessarily be disappointed — the expectations of both people with differing expectations cannot be simultaneously realized — and those individuals whose expectations have been disappointed will have to revise their plans. But that means that the expectations of those people who were correct were also not rational, because the prices that they expected were not equilibrium prices. So unless all agents have the same expectations about the future, the expectations of no one are rational. Rational expectations are a fixed point, and that fixed point cannot be attained unless everyone shares those expectations.

Beyond that little problem, Mason raises the further problem that, in a rational-expectations equilibrium, it makes no sense to speak of a shock, because the only possible meaning of “shock” in the context of a full intertemporal (aka rational-expectations) equilibrium is a failure of expectations to be realized. But if expectations are not realized, expectations were not rational.

I see two mistakes here. Not everyone must have identical expectations in a world of rational expectations. Now it’s true that there are ratex models where people are simply assumed to have identical expectations, such as representative agent models, but that modeling assumption has nothing to do with rational expectations, per se.

In fact, the rational expectations hypothesis suggests that people form optimal forecasts based on all publicly available information. One of the most famous rational expectations models was Robert Lucas’s model of monetary misperceptions, where people observed local conditions before national data was available. In that model, each agent sees different local prices, and thus forms different expectations about aggregate demand at the national level.

It is true that not all expectations must be identical in a world of rational expectations. The question is whether those expectations are compatible with the equilibrium of the model in which those expectations are embedded. If any of those expectations are incompatible with the equilibrium of the model, then, if agents’ decision are based on their expectations, the model will not arrive at an equilibrium solution. Lucas’s monetary misperception model was a clever effort to tweak the rational-expectations assumption just enough to allow for a temporary disequilibrium. But the attempt was a failure, because Lucas could only generate a one-period deviation from equilibrium, which was too little for the model to pose as a plausible account of a business cycle. That provided Kydland and Prescott the idea to discard Lucas’s monetary misperceptions idea and write their paper on real business cycles without adulterating the rational expectations assumption.

Here’s what Muth said about the rational expectations assumption in the paper in which he introduced “rational expectations” as a modeling strategy.

In order to explain these phenomena, I should like to suggest that expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory. At the risk of confusing this purely descriptive hypothesis with a pronouncement as to what firms ought to do, we call such expectations “rational.”

The hypothesis can be rephrased a little more precisely as follows: that expectations of firms (or, more generally, the subjective probability distribution of outcomes) tend to be distributed, for the same information set, about the prediction of the theory (or the “objective” probability distributions of outcomes).

The hypothesis asserts three things: (1) Information is scarce, and the economic system generally does not waste it. (2) The way expectations are formed depends specifically on the structure of the relevant system describing the economy. (3) A “public prediction,” in the sense of Grunberg and Modigliani, will have no substantial effect on the operation of the economic system (unless it is based on inside information).

It does not assert that the scratch work of entrepreneurs resembles the system of equations in any way; nor does it state that predictions of entrepreneurs are perfect or that their expectations are all the same. For purposes of analysis, we shall use a specialized form of the hypothesis. In particular, we assume: 1. The random disturbances are normally distributed. 2. Certainty equivalents exist for the variables to be predicted. 3. The equations of the system, including the expectations formulas, are linear. These assumptions are not quite so strong as may appear at first because any one of them virtually implies the other two.

It seems to me that Muth was confused about what the rational-expectations assumption entails. He asserts that the expectations of entrepreneurs — and presumably that applies to other economic agents as well insofar as their decisions are influenced by their expectations of the future – should be assumed to be exactly what the relevant economic model predicts the expected outcomes to be. If so, I don’t see how it can be maintained that expectations could diverge from each other. If what entrepreneurs produce next period depends on the price they expect next period, then how is it possible that the total supply produced next period is independent of the distribution of expectations as long as the errors are normally distributed and the mean of the distribution corresponds to the equilibrium of the model? This could only be true if the output produced by each entrepreneur was a linear function of the expected price and all entrepreneurs had identical marginal costs or if the distribution of marginal costs was uncorrelated with the distribution of expectations. The linearity assumption is hardly compelling unless you assume that the system is in equilibrium and all changes are small. But making that assumption is just another form of question begging.

It’s also wrong to say:

But if expectations are not realized, expectations were not rational.

Scott is right. What I said was wrong. What I ought to have said is: “But if expectations (being divergent) **could not have been** realized, those expectations were not rational.”

Suppose I am watching the game of roulette. I form the expectation that the ball will not land on one of the two green squares. Now suppose it does. Was my expectation rational? I’d say yes—there was only a 2/38 chance of the ball landing on a green square. It’s true that I lacked perfect foresight, but my expectation was rational, given what I knew at the time.

I don’t think that Scott’s response is compelling, because you can’t judge the rationality of an expectation in isolation, it has to be judged in a broader context. If you are forming your expectation about where the ball will fall in a game of roulette, the rationality of that expectation can only be evaluated in the context of how much you should be willing to bet that the ball will fall on one of the two green squares and that requires knowledge of what the payoff would be if the ball did fall on one of those two squares. And that would mean that someone else is involved in the game and would be taking an opposite position. The rationality of expectations could only be judged in the context of what everyone participating in the game was expecting and what the payoffs and penalties were for each participant.

In 2006, it might have been rational to forecast that housing prices would not crash. If you lived in many countries, your forecast would have been correct. If you happened to live in Ireland or the US, your forecast would have been incorrect. But it might well have been a rational forecast in

all countries.

The rationality of a forecast can’t be assessed in isolation. A forecast is rational if it is consistent with other forecasts, so that it, along with the other forecasts, could potentially be realized. As a commenter on Scott’s blog observed, a rational expectation is an expectation that, at the time the forecast is made, is consistent with the relevant model. The forecast of housing prices may turn out to be incorrect, but the forecast might still have been rational when it was made if the forecast of prices was consistent with what the relevant model would have predicted. The failure of the forecast to be realized could mean either that forecast was not consistent with the model, or that between the time of the forecast and the time of its realization, new information, not available at the time of the forecast, came to light and changed the the prediction of the relevant model.

The need for context in assessing the rationality of expectations was wonderfully described by Thomas Schelling in his classic analysis of cooperative games.

One may or may not agree with any particular hypothesis as to how a bargainer’s expectations are formed either in the bargaining process or before it and either by the bargaining itself or by other forces. But it does seem clear that the outcome of a bargaining process is to be described most immediately, most straightforwardly, and most empirically, in terms of some phenomenon of stable and convergent expectations. Whether one agrees explicitly to a bargain, or agrees tacitly, or accepts by default, he must if he has his wits about him, expect that he could do no better and recognize that the other party must reciprocate the feeling. Thus, the fact of an outcome, which is simply a coordinated choice, should be analytically characterized by the notion of convergent expectations.

The intuitive formulation, or even a careful formulation in psychological terms, of what it is that a rational player expects in relation to another rational player in the “pure” bargaining game, poses a problem in sheer scientific description. Both players, being rational, must recognize that the only kind of “rational” expectation they can have is a fully shared expectation of an

outcome. It is not quite accurate – as a description of a psychological phenomenon – to say that one expects the second to concede something; the second’s readiness to concede or to accept is only an expression of what he expects the first to accept or to concede, which in turn is what he expects the first to expect the second to expect the first to expect, and so on. To avoid an “ad infinitum” in the description process, we have to say that both sense a shared expectation of an outcome; one’s expectation is a belief that both identify the outcome as being indicated by the situation, hence as virtually inevitable. Both players, in effect, accept a common authority – the power of the game to dictate its own solution through their intellectual capacity to perceive it – and what they “expect” is that they both perceive the same solution.Viewed in this way, the intellectual process of arriving at “rational expectations” in the full-communication “pure” bargaining game is virtually identical with the intellectual process of arriving at a coordinated choice in the tacit game. The actual solutions might be different because the game contexts might be different, with different suggestive details; but the intellectual nature of the two solutions seems virtually identical since both depend on an agreement that is reached by tacit consent. This is true because the explicit agreement that is reached in the full communication game corresponds to the a prioir expectations that were reached (or in theory could have been reached) jointly but independently by the two players before the bargaining started. And it is a tacit “agreement” in the sense that both can hold confident rational expectation only if both are aware that both accept the indicated solution in advance as

theoutcome that they both know they both expect.

So I agree that rational expectations can simply mean that agents are forming expectations about the future incorporating as best as they can all the knowledge available to them. This is a weak common sense interpretation of rational expectations that I think is what Scott Sumner has in mind when he uses the term “rational expectations.” But in the context of formal modelling, rational expectations has a more restrictive meaning, which is that given all the information available, the expectations of all agents in the model must correspond to what the model itself predicts given that information. Even though Muth himself and others have tried to avoid the inference that all agents must have expectations that match the solution of the model, given the information underlying the model, the assumptions under which agents could hold divergent expectations are, in their own way, just as restrictive as the assumption that agents hold convergent expectations.

In a way, the disconnect between a common-sense understanding of what “rational expectations” means and what “rational expectations” means in the context of formal macroeconomic models is analogous to the disconnect between what “competition” means in normal discourse and what “competition” (and especially “perfect competition”) means in the context of formal microeconomic models. Much of the rivalrous behavior between competitors that we think of as being essential aspects of competition and the competitive process is simply ruled out by the formal assumption of perfect competition.

On the roulette ball issue scott is showing an example of the ergodic fallacy of the resolution of the St Petersberg paradox in probability. He assumes that the agent has a correct prior based on past rolls of the wheel, wheras in economics you only have the time average of past rolls. See ole Peters writings on this issue – demolishes concept of utility. https://publishing.aip.org/publishing/journal-highlights/exploring-gambles-reveals-foundational-difficulty-behind-economic

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If equilibrium is incompatible with the original information set upon which the expectations were built we have learning and a revision of the information set or the rules used to form expectations based on that information set but with learning expectations are “less rational” and open the possibility to endless disequilibria and cycles

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“….the expectations of all agents in the model must correspond to what the model itself predicts given that information.”

Does this mean that all economic agent must know how the model is constructed and how it derives predictions?

And isn’t there the prior consideration of whether the model’s predictions are based on the expectations of economic agent’s? Does the model assume that economic agents know what the outcome of the model will be?

Isn’t this all entirely circular?

For the model to make predictions the model has to incorporate the expectations of all economic agents but the expectations of all economic agents are based on the predictions of the model.

How can there be any determinable equilibrium position is such circumstances?

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Very clear indeed. So, there is a circular argument (as says Henry) in the rational expectation, in the sense that the equilibrium of the model is determined before all agents have formed their expectation just to reach the end of the model. Any loose in this closed circle needs to incorporate an ad hoc hypotesis -The agent capacity to converge to a new equilibrium, because the previous one is not more possible to reach. The new equilibrium is perhaps without full employment – if that thing can existed in RE models.

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Andrew, Thanks for the link to the Peters and Gell-Mann paper which I will try to read. Sounds fascinating.

Jose, I’m not sure what it means to say that equilibrium is incompatible with the original information set. For any information set, there should be some equilibrium that would correspond to it,but that doesn’t mean that the expectations formed by the agents will be compatible with that equilibrium. The point of rational expectations is that that there is a set of equilibrium expectations and that the set of equilibrium-compatible expectations is what is meant by “rational expectations.” The mistake that is so commonly made is to assume that just because individuals are acting rationally that there is any actual mechanism that ensures that the set of rational expectations is actually realized. Nor is it clear that nearly rational expectations are good enough.

Henry, People only know what they know. A model of rational people has to have the property that if people expect the equilibrium state of the model to be achieved, i.e., there expectation of the relevant variables in the model correspond to the equilibrium values of the model, then the model will generate the equilibrium outcome. If that condition is not satisfied, then there is something wrong with the model. What happens when the agents don’t expect the equilibrium values of the variables in the model, is something that has to be worked out within the model. The model doesn’t tell you what people expect, it just says that there is a set of equilibrium expectations for the model, i.e, the set of expectation that, if agents form those expectations, leads to the equilibrium outcome

Miguel, If people don’t have equilibrium expectations, the model will generally fail to achieve an optimal result, presumably output will be less than full employment, though sometimes, there can be “overfull” employment, e.g, in the early stages of an inflationary boom..

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” The model doesn’t tell you what people expect, it just says that there is a set of equilibrium expectations for the model,…….”

Agents’ expectations govern their behaviour.

Agents’ behaviour govern the outcomes of a model.

For a model to make predictions about its outcomes it must make predictions about agents’ behaviour.

To make predictions about agents’ behaviour a model has to make predictions about agents’ expectations.

The argument is immediately circular.

Under those circumstances how can there be a set of equilibrium conditions?

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The equilibrium expectations are the set of expectations that turn out to be self-fulfilling. Not all conceivable expectations have that property. The model can’t predict what actual expectations will be unless there is an explicit theory of expectation formation, but the model can identify which expectations are equilibrium (or “rational”) expectations.

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I should have added one final statement:

Agents’ expectations govern their behaviour.

Agents’ behaviour govern the outcomes of a model.

For a model to make predictions about its outcomes it must make predictions about agents’ behaviour.

To make predictions about agents’ behaviour a model has to make predictions about agents’ expectations.

But agents’ expectations are given by the model’s outcomes.

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“The model can’t predict what actual expectations will be unless there is an explicit theory of expectation formation…”

Then that’s the end of it. If there is no such theory, how can a model make predictions?

“…but the model can identify which expectations are equilibrium (or “rational”) expectations.”

How?

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There are many theories of expectation formation, none of them is particularly good. Sometimes, assuming rational expectations is actually not a bad assumption, e.g., for markets dominated by very knowledgeable specialists. It is a horrible assumption to make to try and understand how economies operate in times of distress and upheaval. If the model makes enough assumptions so that equilibrium can be found, then you just assume that expected prices are equilibrium prices. That’s not hard to do, if you make enough assumptions, but it doesn’t help you understand how an actual economy, as opposed to the model economy, actually works.

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Equilibrium expectations are given by the outcomes of the model. What we are really interested in is how the model works when it is not in equilibrium, and whether it can come closer to equilibrium instead of moving further away form equilibrium.

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David,

We not discussing how a real world economy works.

We are discussing the REH, which is an abstraction.

The REH says agents expect the outcome of the model to be the outcome of the model.

However, as I have argued above, the outcome of the model depends on the expectations of the agents.

And this model economy we are discussing set the theoretical/academic agenda for 40 years and I am arguing, rightly or wrongly, that it is based on a circular argument, where outcomes cannot be specified.

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“…whether it can come closer to equilibrium instead of moving further away form equilibrium.”

OK. But how is this equilibrium defined?

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It is not circular because not all possible expectations have the property that if those are the expectations that are held by agents in the model that the expectations will be realized. Expectations formed at random or by some other arbitrary rule for expectation formation will not have that very special property of b

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“…if those are the expectations that are held by agents in the model that the expectations will be realized.”

How do we know that any set of expectations can be realized, other than by assumption, in which case we can assume anything we want and start a new theoretical revolution, presuming enough people are suckered in.

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Sorry, Henry, but that’s not the way the game is played. In a general equilibrium model, each agent is optimizing based on actual and expected prices. So a general equilibrium has the property that, given actual and expected prices, each agent is doing as well as he can, given the vector of actual and expected prices he is confronting or expecting. So if all agents have price expectations that are equilibrium price expectations, then their optimal plans will be simultaneously realized because every plan, being an optimal plan will be executed if price expectations are fulfilled. The equilibrium set of expected prices is what mathematicians call a fixed point; an equilibrium set of prices and price expectations has the property of being a fixed point. A non-equilibrium set of price expectations is not a fixed point, so it doesn’t reproduce itself. Now the mathematicians might be wrong, but I wouldn’t bet on that being the case. And if they aren’t wrong, the argument you are trying to make simply doesn’t work. The assumption of equilibrium is not arbitrary it is extremely demanding and restrictive. It’s too demanding and too restrictive, and that’s why it doesn’t work as an empirical theory, which is why I think rational expectations is not a good modeling strategy for macroeconomics.

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“… if price expectations are fulfilled”

There’s the rub..”if”.

This rests on an assumption.

The New Classical revolution was essentially foundered on this assumption along with arguing that the macromodels of the 1960s were ineffective (using as evidence the stagflation of the early 1970s – which can be explained in other ways I would argue – macromodels weren’t running policy, politics was).

“And if they aren’t wrong…”

Arrow Debreu GE theory was considered unassailable until the 1970s at which time the uniqueness of the equilibrium point was questioned.

“The assumption of equilibrium is not arbitrary it is extremely demanding and restrictive…”

It may be extremely demanding and restrictive but it is arbitrary, is it not, as probably most assumptions are?

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Here’s another way of looking at the situation.

In pure classical/neoclassical theory, three assumptions, among others are made:

1. agents have perfect rationality (essentially more is preferred to less).

2. agents have perfect knowledge.

3. agents have perfect foresight (could probably include this one in two).

From these assumptions, it can be logically concluded that markets will clear and that there will be a determinate equilibrium point. The equilibrium point does not exit by assumption but because of assumptions.

Now of course, these assumptions suffer from the criticism that they are totally unrealistic and hence that the classical/neoclassical model is totally unrealistic.

Along comes Robert Lucas and in an attempt to make the classical/neoclassical model more realistic he dispenses with the above three assumptions and replaces them with “rational expectations”.

But now equilibrium cannot be said to be determinate as a logical consequence of the starting premises of the revised model, it has to be assumed.

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“The equilibrium point does not exit by assumption but because of assumptions.”

‘exit” in the sentence should be “exist”.

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Henry, Agents are assumed to have a complete and consistent preference ordering over all possible choices. I don’t know what the adjective “perfect” means in that context. I don’t know what “perfect knowledge” means. Agents are assumed to know all prices at which they could make transactions. There is no assumption of perfect foresight, though this is sometimes inaccurately asserted. Your expectations of the future can be correct without having the give of prophecy. These assumptions, by the way, are not sufficient to establish that markets will clear. They will only clear in the event that expectations are correct. Clearing markets and correct expectations by all agents are essentially synonymous. Everyone acknowledges that the assumptions are unrealistic, but unrealistic assumptions may not render a model empirically useless. Whether it is empirically useless will depend on how skillful the theorist/practitioner is in knowing or guessing how to relax the assumptions in a theoretically and empirically fruitful way. You said:

“But now equilibrium cannot be said to be determinate as a logical consequence of the starting premises of the revised model, it has to be assumed.”

That’s exactly right. And Hayek said precisely that in his 1937 paper “Economics and Knowledge.” It’s a pity Lucas either never read it or never understood it. But you state the conclusion as if it were somehow problematic. What do you find problematic about it?

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” I don’t know what “perfect knowledge” means. Agents are assumed to know all prices at which they could make transactions.”

I would say these two statements are compatible and effectively equivalent.

When I was taught micro over 40 years ago, there was no mention of expectations. It was perfect foresight/knowledge. As far as I am concerned, expectations don’t appear in the classical model’s specifications, they are not necessary if there is perfect knowledge. In the neoclassical model, perfect knowledge was replaced by tatonnement – an auctioneer was required to settle equilibrium prices. (So I should not have included neoclassical theory in my explanation above.)

“What do you find problematic about it?”

It weakens the foundation on which REH is constructed, particularly as I would argue and you disagree with, that if there was no assumption to that affect, the hypothesis would be reduced to a circular argument .

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Since I don’t know what “perfect knowledge” means I am not going to argue that it is not equivalent to knowing all prices at which transactions could be made. However, when I referred to knowing all prices at which transactions could be made I meant only prices for current transactions not future transactions when there is not a full array of current markets for all future exchanges. So perfect knowledge cannot be the same thing as perfect foresight. If expectations were not mentioned when you were taught micro 40 years, that was a significant gap in your education. You are free to characterize the “classical model” however you wish to, but expectations have been part of economic theorizing for a very long time. Assuming perfect knowledge does solve a lot of problems, but the principle of Occam’s Razor encourages us to be parsimonious in our assumptions, and perfect knowledge — whatever you may want it to mean — seems like a rather extravagant assumption. All that Arrow and Debreu proved — and they never claimed to have proved anything more — is that an economy satisfying certain assumptions about individual preferences and production technology would have at least one — and possibly more than one — set of equilibrium prices with the property that, if all agents were given the opportunity to trade at those prices, all trades would be executed as planned and all agents would be optimizing given their wealth and knowledge endowments, and skills. They did not claim that the existence of an equilibrium meant that the economy would actually attain that equilibrium.

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“Since I don’t know what “perfect knowledge” means …”

Think what it would mean to have perfect knowledge – the present, past and future would known as one. That is why perfect knowledge is the same as perfect foresight. There would be no need for futures markets. Futures market arise because of uncertainty. With perfect knowledge there would be no uncertainty. Each good, asset would be priced on the basis of no uncertainty. Equilibrium would be fixed, stable and immutable. Isn’t that what pure classical theory says? In this pure, perfect world expectations are not necessary – everything there is to know is known.

Relax any of the assumptions and you step out of a classical world into a Keynesian world. (You’ll cane me on that one for sure. 🙂 )

” If expectations were not mentioned when you were taught micro 40 years, that was a significant gap in your education. ”

In macro yes, micro no.

“They did not claim that the existence of an equilibrium meant that the economy would actually attain that equilibrium.”

I’m pretty much gobsmacked at this statement. So what is the point of GE theory? Equilibrium is central to GE theory. There is no path to equilibrium. It is instantaneous. It is given by the assumptions of the theory.

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As serendipity would have it, in working on other things yesterday, I came across a paper, in my collection, by Oskar Morgenstern, “Perfect Foresight and Economic Equilibrium” (1935 I think). It’s fairly dense.

I don’t think he would be very happy with my use of the assumption above.

The first thing he does is outline where in the then existing literature on general equilibrium theory there is use of the perfect foresight assumption.

However, he then proceeds to (attempt to, in my view) demolish the need for the assumption.

He discusses various paradoxes which he says the assumption gives rise to. However, I think he misses the point of foresight being perfect.

He goes on to argue that economic agents would have to have a perfect understanding of economic theory. I would argue that is not necessary. Economic agents do what they do, their behaviour given by the assumptions not by understanding economic theory (unlike in the case of the rational expectations model, where agents would require a perfect understanding of the economic model).

He introduces expectations – again he misses the point of perfect knowledge.

He introduces monopoly behaviour – he is way off beam here having departed from the theory of perfect competition, to where the assumption solely applies.

He raises Walrasian tatonnement. Again the perfect foresight assumption is not meant to apply.

Towards the end of the paper he says, (pulling the rug entirely from underneath his own argument):

“If, however, it is meant that the theory of equilibrium describes only an absolutely static situation, then, one can, of course, establish perfect foresight, for nothing can be changed ex definitione, since everything is given as static and unchangeable.”

Precisely, that is what the pure theory of perfect competition says. Most of his paper has him wandering off into the real world.

And I would argue that any excursion from the state of perfect competition lands you in a Keynesian world, i.e., the REAL world.

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