Rational Expectations and Reality

Last week, while I was going over the history of macroeconomic thought in class, I briefly discussed the concept of Rational Expectations and the place it occupied in the development of modern macroeconomics.  In truth, I don’t spend a lot of time talking formally about rational expectations because it is simply part of the standard backdrop.  That is to say, rational expectations (RE) models are not contentious anymore.  This was not always the case.  When rational expectations models were being developed in the 1960’s and early 1970’s it was a very foreign concept and was met with skepticism by mainstream macroeconomists.  Today, rational expectations are the norm and are rarely discussed as a controversial part of the field.  Outside of the economics profession, the idea that people possess something called rational expectations in the real world is often assumed to be wholly unrealistic and prima facie evidence that economic reasoning is useless and out of touch.

I’m going to use this post to discuss the meaning of rational expectations because (1) I think it is one of the most commonly misunderstood aspects of macroeconomics and (2) for the most part, rational expectations is essentially true in the real world – that is to say, most people actually have rational expectations.

The notion of rational expectations that I prefer (what I might call the weak-form of RE) goes something like this:  People have rational expectations if their beliefs are consistent with the world they live in.

People hold lots of beliefs and these anticipations and expectations constantly influence their choices.  For example, the exact time you leave for work in the morning might be influenced by your beliefs about when traffic is particularly heavy.  When you leave might also depend on your beliefs about when the parking garage at work fills up.  Your choice of restaurants might be influenced by how busy you think the restaurant will be, and so forth.  The RE hypothesis says that these beliefs are consistent with the real world.  If you think that your parking garage fills up by 8:45 am then you should not observe that the garage typically has empty spaces at 9:00.  This is not to say that RE implies that your beliefs are perfectly correct.  Expectational errors (or forecast errors) are perfectly consistent with the rational expectations hypothesis.  For instance, if I roll two 6-sided dice, you will guess that the most likely number to get is 7.  You will usually be wrong of course, but you won’t be systematically biased in your beliefs.  It’s easy to find economic examples of RE as well.  For example, if I tell you the economy is experiencing high unemployment and low inflation then you might guess that the Fed is more likely to cut the Federal funds rate rather than to raise it (assuming we aren’t at the zero lower bound of course).  Again, the bond market traders could be surprised, but they shouldn’t be systematically surprised.

For this definition of rational expectations (the weak-form of RE), there is no need for individuals to understand why they observe the patterns they observe.  They don’t need to know the model.

The examples I chose above are all cases in which RE works well.  In these cases, RE is clearly the correct way to understand people’s actual beliefs and behavior based on those beliefs.  Part of the reason these situations work well is that people have lots of experience with these situations.  Everyone knows how to play the morning commuting game.  Everyone knows how to play the restaurant game and so forth.  We have repeated exposure to these situations and so beliefs which don’t fit with the real world will be punished and inevitably people will adopt “correct” beliefs.  (It will take only a few days when you can’t find parking at 8:55 am before you revise your anticipations.)

Of course, there are situations when the rational expectations hypothesis is much less likely to hold.  For example, we only play the marriage game one (or two or three) times.  Hopefully we will only play the retirement game once.  In these cases, we can’t rely on experience to discipline our beliefs and guarantee that our expectations will be rational.  This doesn’t necessarily mean that RE isn’t a good assumption.  We can still learn from the experiences of others; we can ask our friends or relatives what their experiences were like, and so forth.

The reason that RE is so common in macroeconomics is twofold.  First, because much of macroeconomics concerns behavior which unfolds over time, anticipations and expectations inevitably influence current choices.  As a result, macroeconomists have to make some assumption about where these beliefs come from.  Second, while many situations might not be natural settings to trust a RE solution, RE is often a good benchmark.

One area in macroeconomics in which RE solutions are used often but in which we have good reason not to trust the solution concerns one-time unanticipated events.  An investment tax subsidy should of course encourage investment but it should also influence the long-term payoff to capital.  Forming expectations about this payoff requires investors to form accurate beliefs which extend far into the future.  This seems like a hopeless case.  The common solution (and the one I would use) is to invoke RE.  This is convenient because it allows me to “fill in the blanks” and attach beliefs to future events but I’ll be the first to admit that this is a bit of a stretch.  An even more difficult case might concern a policy for which we have little basis for comparison at all.  The rapid extension of loan guarantees to financial intermediaries during the crisis surely had important effects on the market and surely behavior was conditioned to some extent by beliefs.  I doubt these beliefs were anything resembling rational expectations though.  My suspicion is that situations like this create confusion on the part of market participants.  Unfortunately we don’t really have a good theory of confusion yet.

At its core, the rational expectations hypothesis says that your beliefs are not really your own.  Your seemingly subjective and personal beliefs are influenced by the world you live in.  In econ-lingo, your beliefs are endogenous.

Let me make one final comment.  RE doesn’t really say anything directly about where your beliefs come from or how they are built up over time.  If you move to a new city, you will gradually learn about the local commuting patterns and as you do so, your beliefs will converge to RE beliefs and your commuting choices will become more and more refined.  Technically, RE assumes that the people in the model economy already have rational expectations.  That is, RE doesn’t incorporate learning.  Of course we have the ability to include learning but it is not too common in most models.  There is of course the important issue of whether learning will actually lead to a RE equilibria.  Usually it will – among the many important papers in one by Kalai and Lehrer (1993) which says that eventually RE will emerge provided that peoples’ initial beliefs possess a “grain of truth.”

(OK, I’m going to stop here, if I’m not careful I will go into full blown geek-out mode … )

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16 thoughts on “Rational Expectations and Reality

  1. Thank you Dr. House. I’m an undergraduate student in economics at Oregon State, and I’ve heard of RE in passing, but never really knew what it was or knew of a good intro of the concept. I feel like I understand the concept much better now and I’ve filed this post away to refer back to as I continue through my degree program!

  2. Hey!

    I used to attend your undergrad macro class long, long ago.

    Anyway, I’m a bit disturbed when you wrote Rational Expectation doesn’t incorporate learning. I’ve always thought RE was RE because people learn. Without learning, wouldn’t that leave RE into just Adaptive Expectation, ie expectation will systematically lag behind reality exactly because people don’t learn or update their belief enough in the way an RE agent would?

  3. I think the problem that people (implicitly) have with RE is actually something slightly different. It is not the “rationality” that people have a problem with, but the assumption of oracular knowledge. Take your example of high unemployment/low inflation: ask most people on the street and my guess is you’re going to get fairly random answers. But if you tell them: don’t worry! When faced with these situations, people will rationally assume the Fed will do X and behave accordingly! Well, they’re going to squint at you funny. I think that’s what they really have a problem with.

    I mean, I understand why this ‘works’ on a macro level. But I don’t think it’s the strict idea of rational expectations as you lay them out that people have a problem with per se.

    (Or, as we usually point out in neuroscience, everything is optimal as long as you can figure out what you want to optimize.)

    • This is why Muth, the founder of RE, thought the model best applied to well-defined micro markets and not to the macro economy where any one model is a very crude attempt at understanding an unimaginably complicated environment.

      Fact is RE is the foundation of finance and all micro models but only academics use it for macro.

      So Muth was right but the macro ideologues got the Nobel prize.

  4. (Sorry this comment went a little off from what your post is arguing)

    I’m always confused by the use of “rational.” It seems like an almost useless term.

    How can my beliefs be irrational? At any moment, If I prefer A to B and B to C, I must prefer A to C. If I prefer C to A, it must be because something else has changed (probably the time), so the old rankings are different. Irrationality, the way that economists generally define it, is a logical impossibility.

    Now, “rational” is not a strong claim. Any beliefs are rational, but that does not tell us much. It certainly does not allow for predictions. So economists put other restrictions on beliefs, u'(.)>0, u”(.)<0, u(t)=B*u(t+1), etc. that allow for clear predictions with a single optimization point.

    If I am correct, "rational expectations" come from applying u(t)=B*u(t+1) for all t. If this does not hold in reality, does that mean that people are irrational? or maybe B is not a constant but something more complex? Prospect theory has shown that static utility functions are not simple increasing functions with decreasing slope. We can call that a break of "rationality," but it doesn't seem like it should be.

  5. Rational expectations is a self-disconfirming theory. Like old-time religion, it is an illusion in the Freudian sense and only by chance consistent with the world.

    So let’s forget aabout the kindergarten stories about commuters and look at the experimental data, which OVERWHELMINGLY FALSIFIES rational expectations.

    The economy is intriguing. The schoolmen who pretend to study it are merely boring.

  6. After practicing law for over 30 years, it is very evident to me that people do not make rational decisions in most of the important decisions they make in life.

    We have a whole industry, the advertising industry, which is based on manipulating people’s decisions, and in many cases duping people into making bad decisions. The advertiser wants to convince you that buying a new Voltron automobile will make you rich, good looking and happy. Or you will become a movie star if you smoke cigarettes.

    I have seen many people buy automobiles they cannot afford, and try to keep it in bankruptcy, when it is perfectly obvious to everyone involved that they cannot afford the car. The car salesman, in particular, knows that the customer will not be able to make the required payments on the car, knowing that this will lead to default, repossession and a huge deficiency judgment against the purchaser.

    If you ask the average person on the street whether they want $100 today, or $120 a year from now, most will tell you to give them the $100 now, even though waiting for $120 a year from now is the more rational decision in most cases.

    As far as marriage, it is pretty obvious to me that most people get married for stupid reasons which have more to do with how our prehistoric brains function than based on rational considerations. People also get divorced for equally stupid reasons. There really is no decision more important in one’s life than whom one marries, and this decision is almost totally irrational..

    Sometimes there is no choice at all. For example if one has a medical emergency, the ambulance will go to the nearest hospital. There is no calculation as to the cost benefits of one hospital over another when one is having a heart attack.

    Recently we have seen fraud on an industrial scale where mortgage backed securities were sold as AAA securities, when, in fact, they were junk. Yet, even highly sophisticated investors purchased these securities because it was the safe decision to make at the time.

  7. People (on average) have some economically relevant types of expectations regarding repeated that don’t converge to observed probabilities — at least within any observable period.

    A major example is anticipation of “loss” — for example car accidents, airplane accidents, etc. Car rental companies make money by selling insurance at the counter, because people consistently over-estimate the probability and cost to them of potential accidents. Even though people frequently rent cars, know others who do, etc. the rental car companies can continue to make money this way.

    Similarly appliance vendors sell extended warranties at a profit due to consistent over-estimation of the risk of loss by customers.

    Since anticipation of loss is a factor in nearly all economic transactions it is a big elephant in the rational expectations room. I believe it applies to a lot of business decision making as well as consumer decision making — since after all both kinds are done mostly by humans. I suppose it might contribute to a lot of “irrational” economic behavior such as wage and price stickiness, slow adoption of “rationalized” methods, etc.

  8. “Rational expectations” is an expression that is here to stay. “Model-consistent expectations” would probably have been better and more informative. It is not an indication of the knowledge of the agent but rather of the ignorance (and humility ?) of the modeler.

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  11. In enjoyed the post and continue to try to learn why people like the RE ideas so much.
    But I did want to make some comments on one point:

    You wrote:
    “There is of course the important issue of whether learning will actually lead to a RE equilibria. Usually it will – among the many important papers in one by Kalai and Lehrer (1993) which says that eventually RE will emerge provided that peoples’ initial beliefs possess a “grain of truth.” ”

    I’m not reassured! Having looked at that paper, it seems to require that the people playing the games considered have no limits to their power to reason strategically about the infinite future, and that they play the same simple game repeatedly forever (the game never changes), and that they’re safe in assuming that everyone always makes their decisions independently, among other things. IN THIS CASE, learning leads to rational expectations. This looks like a mathematical situation concocted just to get this result, and in no way resembles any situation likely to be encountered in the real economic world.

    A recent review of the learning literature (http://www.suomenpankki.fi/en/julkaisut/tutkimukset/keskustelualoitteet/Documents/BoF_DP_1108.pdf) found that learning converges to rational expectations, but ONLY IF one makes the amazing assumption that agents in the model ALREADY KNOW the exact equations of motion for the economy and only have to learn a few parameters. Again, hardly reassuring.

    More interesting and relevant to the real world are some recent experiments (http://dare.uva.nl/document/460200) in which people try to learn in a simple economy where they DO NOT know the equations of motion. What they do in fact is to use heuristic strategies, and they often switch from one strategy to another. The worst hypothesis (among several tested) to account for their behavior was rational expectations. In many cases the economy didn’t settle into an equilibrium at all. This does look more like the real world. I’d say time to ditch the rational expectations idea.

    • Hi Mark,

      The experimental forecasting performance in the paper you linked to is interested but it is fairly disconnected from the situations people actually find themselves in. I would encourage you to consider a real-world example that you confront. There are many situations in which expectations influence our behavior. For example, I sometimes play poker with friends. I’m not very good and I’m pretty sure my expectations are not perfectly rational the way a model would presuppose. That said, I would guess that my subjective assessments of the probabilities of winning hands is fairly close to the actual probabilities (and for good poker players they will be remarkably close). Do you have an example from your own experience in which you think that your expectations are not rational?

      About the Kalai Lehrer paper, it’s true that it is fairly demanding mathematically and they are confining their attention to players who use Bayesian updated to revise their beliefs. At the same time, the paper is analyzing a very complex situation in which people play a repeated game with strategic interaction. In the real world, we often don’t face this situation. Take my poker example for instance. I’m a novice and so I sit down and start learning about how the other people play. Now of course, as I learn, the strategies of the other players will change. The KL paper says that if I do Bayesian updating and they do Bayesian updating then in the end we will be playing a Nash Equilibrium (we will be in a RE equilibrium). In the real world however, the other players won’t change their behavior that much when I show up. Instead, they just keep on playing the strategies that they think work well. I learn and eventually I will have Rational Expectations. In my opinion, this type of simple observational learning (where my learning doesn’t have very strong feedback effects on the world) is typical of most of the environments we find ourselves in out there in the real world.

  12. Hi Chris,

    Thanks for your thoughtful response. I thought I had signed up to be notified of any follow up comments, but somehow that didn’t happen…

    Anyway, my clearest example of having non-rational expectations is in regard to the Cleveland Browns. Every year I am convinced that THIS YEAR they will be greatly improved. I really do come to believe this and see compelling evidence for it. Then the season starts….

    But, more seriously, I would think that the study I mentioned by Assenza and colleagues does represent, to a decent approximation, the situation faced by people and businesses in a real economy, where they must try to form sensible predictions of what will happen with inflation, output, etc., whether or not they have a very good picture of what drives those things (which may often be other peoples’ expectations of the same things). This is precisely the setting (as I understand it) where the RE idea is most relevant to macro, and here (in the experiments I mentioned) you have real people in this situation not acting on rational expectations. That seems very relevant to me. Acting on heuristics, trying to learn, sometimes succeeding and sometimes not; that seems more in keeping with reality.

    On the more general point, my belief that people do not generally have rational expectations does NOT mean that I think they have totally irrational expectations. I think most people learn fairly well and have plausibly realistic expectations, at least in relatively simple situations, much of the time. At other times, and not infrequently, I think people have almost no idea what to expect, don’t even have a clear picture of the kinds of things that could happen, and form their expectations mostly by looking to see what other people expect. This happens especially when new things come into being, like new technologies, or powerful recent trends that make the world seem very different. The most recent housing bubble was a good example of that. I think there was a powerful component of social influence in that episode, people buying because they saw others buying and profiting and they didn’t want to be left out (of course there were many other factors). A friend of mine bought 3 houses because, in his words, “housing prices never go down.” He heard that somewhere and the recent evidence was enough to convince him. I don’t think there’s anything very rational about this; it’s an effect of social psychology.

    I understand your point about how, for many of the situations we face, our actions do not change the world around us, which remains fixed. What I do is almost certainly not going to change the laws, for example. But I would think that, in economics, where one often thinks about firms in interaction with other firms, there is a very complicated situation of co-evolution of strategies, learning and adjustment to what others do. In this kind of setting, I find other studies (such as http://arxiv.org/PS_cache/arxiv/pdf/1109/1109.4250v1.pdf) much more persuasive and likely to reflect what actually happens, which is ongoing chaos rather than convergence to any equilibrium. From that paper, just to give an idea of what it is about:

    “Here we show that if the players use a standard approach to learning, for complicated games there is a large parameter regime in which one should expect complex dynamics. By this we mean that the players never converge to a fixed strategy. Instead their strategies continually vary as each player responds to past conditions and attempts to do better than the other players. The trajectories in the strategy space display high-dimensional chaos, suggesting that for most intents and purposes the behavior is essentially random, and the future evolution is inherently unpredictable.”

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