Rational vs adaptive expectations: a false dichotomy

Arnold Kling has posted another good installment of his Macro Doubtbook. But it contains what I think is a false dichotomy between adaptive (habit) and rational (model-based) expectations. Since Arnold is not alone in thinking this way, I thought I would do a short post to explain why I think it's wrong.

I'm just old enough (55) to remember what macroeconomics was like before rational expectations. We used adaptive expectations (a.k.a. error-learning). So if we were talking about people's expectations of some variable X, we wrote down an equation like X(t)e - X(t-1)e = B[X(t-1) - X(t-1)e], 0<B<1. Intuitively, if X came in above what people had previously expected by (say) one unit, they adjust their expectation for the next period up by (say) half a unit (for B=0.5). We built that equation into our model, and off we went, and gave policy advice.

We recognised two problems:

1. What was B? We thought of B as some sort of psychological parameter. We figured it had to be somewhere between 0 and 1, but where exactly? This was clearly an empirical question, but perhaps we could estimate B by estimating the whole model? Or from surveys? In any case, the qualitative predictions of the model could still be useful, even if we couldn't get exact numbers.

2. What was X? For example, if we were talking about inflationary expectations (we usually were) should X be the price level, or the rate of inflation? You get very different predictions from the model depending on which you choose. I don't remember an answer to this question. I'm not even sure if we all realised it was a problem.

Rational expectations answered both those questions at once.

If people were living in a world where the price level followed a random walk, for example, so that P(t)=P(t-1)+u(t), where the error term u(t) is mean zero and serially uncorrelated, then X should be P, and B should be 1. Expected inflation should always be zero on such a world; people should always expect that next year's price level would be the same as this year's.

But if people were living in a world where the price level was white noise, so that P(t)=Pbar+u(t), then X should be P, and B should be 0. The expected price level should be the constant Pbar and never change.

And if people were living in a world where the rate of inflation were a random walk, then X should be inflation, not the price level, and B should be 1.

And so on.

Interpreted in this light, rational expectations is not an alternative to adaptive expectations. Instead, rational expectations answered two questions that adaptive expectations left unanswered. Rational expectations did not contradict adaptive expectations, it just specified more precisely how expectations should adapt. People could still base their expectations on habit, without having a clue about the underlying macroeconomic model that was determining inflation. It was just that their habits had to make sense in their world.

People's habits for forming expectations have to be consistent with their world. And if the world in question is an artificial world, created by an economic model, that means the artificial people living in that artificial world would have to have expectations consistent with that artificial world and therefore consistent with the model that created that world. That's what rational or model-consistent expectations implies. It doesn't mean that that people understand the model, the true model, or even have any model at all. They've noticed a certain repeated pattern in the price level, and expect that same pattern to continue. They needn't have a clue about why that pattern exists, or what determines the price level. It could all be magic, as far as they are concerned.

And if we change the world people live in (whether it's a real or artificial world), by changing policy, then people's habits will change too. Eventually.

That's where the real dichotomy comes. There's the comparative statics question, where we traverse across possible worlds, each with its own different policy, and its own history of policy. Each possible world will have its own habits consistent with that world and its history. And there's the dynamic question, where we change from one policy to another in real time, so present and future policy is different from what it would be, but history is the same.

How long does it take people's habits to change when the policy regime changes in real time? How long will it take before habits are consistent with the new world? And will it indeed ever happen, if changing habits themselves change the world?

That's the real dichotomy. Habits never change, vs habits instantly change to be consistent with the new world. And most reasonable economists would want to go somewhere in between those two extremes. If you expect the new habits to change instantly, and be consistent with the new world, then people really would have to understand the true model, or listen to someone who did.

Update: Arnold responds, and it's a good response. His main point is that the way expectations respond in local markets may be very different to the way expectations respond in national markets. I think it's a good point. My guess is that the underlying reason may have something to do with the number of traders, and the liquidity of the goods traded.

Comments

[Luis H Arroyo]

Very good, Nick. Tahnks. You've taken me a complex that I had acquired with the damn RE.

[westslope]

Both approaches are "model-based".

'Habit' suggests rules of thumb behaviour. That strikes me as a misleading way of portraying adaptive expectations. I suppose that RE hypothesis typically implies instant decision-making and the AE hypothesis implies slower changes or some inertia in behaviour.

Would you describe Bayesian 'learning' or updating as leading to 'habits' or 'rules of thumb'? It can, but not necessarily.

I agree that both AE and RE information processing assumptions are very similar. If I follow your argument, the AE hypothesis can be thought of as a special limiting case of the broader RE hypothesis.

Talk of 'habits' makes me think of self-enforcing social conventions and norms. Robert Sugden and other scholars of social conventions argue that models of conventions should incorporate inductive inferences. Sugden argues against a priori methods of popular non-cooperative game theory to study conventions. The favourite theoretical tools of enquiry are coordination models, and evolutionary stable strategies.

If rule of thumb behaviour is deemed important in order to understand macroeconomic policy, then I suspect that there are much better ways of getting at it than through the a simple AE hypothesis.

[Nick Rowe]

Luis: Thanks!

westslope: I like the term "rules of thumb". I prefer it to "habits", but Arnold used "habits", and I think of them as roughly equivalent.

" If I follow your argument, the AE hypothesis can be thought of as a special limiting case of the broader RE hypothesis." I think it's the other way round. RE is more like a special case of AE, except that which particular special case of AE we should chose depends on whichever special case happens to be consistent with the world we are talking about. Though in another sense you are right. In AE, you base your expectation of X only on your previous expectation of X and on the last observed value of X. You ignore any other information. That's normally not rational, except in special cases.

I think that Bayesian learning, where you are learning about a moving variable, would look very much like a special case of AE. (Bayesian learning is rational, of course.

The tricky distinction to make is between: using an observed historical pattern in the data to forecast the next data point; and learning a new pattern when the pattern changes. The most extreme versions of RE must assume we can learn a new pattern instantly (even before we have enough data points to reveal what the pattern is). Of course, if the pattern never changes, we never face this problem.

And the philosophical problem: when is a new pattern really new, and when is is just the rolling out of a grander meta-pattern? (I ducked that one in this post).

Interesting point about Robert Sugden. I haven't been following the literature on social conventions. The evolutionary approach you describe him as approving strikes me as sensible too. But occasionally, we do stop and think about the a priori: "Can I really trust him? Would it be in his interest to do X if he expects others to do Y if he does X, and they....etc."

[Min]

Thanks, Nick. Interesting and informative. :)

Nick Rowe: "Interpreted in this light, rational expectations is not an alternative to adaptive expectations. Instead, rational expectations answered two questions that adaptive expectations left unanswered."

Well, as you explain it, it seems to me that, by providing those answers, rational expectations is less empirical than adaptive expectations, perhaps to the vanishing point. (Or perhaps rational expectations is simply more falsifiable. If so, it has been falsified, right? ;))

[westslope]

Nick: I suspect that we delegate much of our economic decision-making to 'habits' or rules of thumb. (Note how the '60s counter-culture in North America never advocated driving on the left hand side of the road?) I reckon that confirmatory bias plays a significant role in resource allocation decisions, and that a little stubborn disbelief is not necessarily irrational or sub-optimal.

In the perfect foresight version of RE, past data are irrelevant. In the 'best use of available, costly information' RE hypothesis version, sunk information costs could generate inertia and resistance to change.

[Adam P]

I don't think your characterization of rational expectations is right here Nick. RE came started appearing around the same time as the Lucas critique and I sort of thought that the Lucas critique was somewhat instrumental in it gaining wide acceptance.

The critque though was about how people respond to changes in their economic environment and here you can't say that the rational expectations did not contradict adaptive expectations.

To take one of your examples, suppose P = Pbar + e, e iid with mean zero. Suppose the reason for this is that the economy is on a firm gold standard with no fractional backing, transactions are actually made usiing gold coins. You get B = 0.

Now suppose that, because of the need to finance a war, the government confiscates all the gold and gives the citizens notes in exchange. Each note promises the return of the gold after the war. But suppose everyone recognizes that the only reason for replacing the gold with the notes is to print more notes than you can really pay back with the gold.

So, what happens to the price level? Under adaptive expectations nothing happens to the price level. Though inflation comes later due to aggregate demand being above potential output. Under rational expectations the price level begins rising immediately. Of coures, in real life neither is exactly right but rational expectations people did lots of studies when first arguing for the assumption that showed that in examples like this rational expectations was the better approximation to reality.

And of course there is the critique itself. In this example under adaptive expectations the government earns lots of revenue from the printing of additional money, in rational expectations they don't. Again, the ratex people had lots of studies showing that in extreme examples the rational expectations assumption looked better.

[Adam P]

Nick, just to clarify my example, the last paragraph is really where the action is at. The price level response might appear to fall under the "Habits never change, vs habits instantly change" dichotomy. The output response does not.

In effect rational expectations says that habits change before we even see any more data. Under extreme ratex and no pricing frictions prices change before the government spends the new money, no seignorage is earned. I don't see you get that from changing the value of B or X, even instantly. As Sargent always says, it's the cross-equation restrictions that are important.

[Adam P]

Sorry, one more clarification. The point in the examples is that ratex goes beyond just changing B to match changes in money growth behaviour. Under rational expectations people understand what it is the government is trying to do, they know it wants to essentially extract a tax. Thus they anticipate that the government will increase money growth in response to higher inflation and so they try to stay ahead of the government, that's why you get something like hyper-inflation.

So, it's not just that B changes, even quickly, it's that the value of B takes into account expectations of where you'll want to B to be in the future.

However, now that I think of it in this way isn't the real difference simply the endogeneity of B under ratex. Wouldn't a guy like Sargent say that once you allow B to change endongenously to changing economic conditions then it's already not adaptive expectations anymore?

[Luis H Arroyo]

"That's the real dichotomy. Habits never change, vs habits instantly change to be consistent with the new world. And most reasonable economists would want to go somewhere in between those two extremes. If you expect the new habits to change instantly, and be consistent with the new world, then people really would have to understand the true model, or listen to someone who did."

So,Perhaps the important thing is the regularity of behavior, and the change to a different pattern of regularity.

Now, is only rational to think that if the Central Bank increases M0, the only rational reaction is expected to increase inflation? I suppose in the current conditions, rational agents will see an increased demand ... rather than an immediate increase in inflation.

[TNB]

How do the media play into this?

If one group call them "Fox News Watchers" are being bombarded with images of imminent economic doom while another group, call them "MSNBC Watchers", are receiving constant economic cheerleading, the groups would have radically different expectations. I guess one would expect this to balance across the whole population but it may not as one media source may have more power. It seems to me carpet bombing of distorted information by the mass media may render Rational Expectations meaningless.

Expectations are whatever the most powerful media player says they are regardless of economic conditions or policy.

[Adam P]

"Now, is only rational to think that if the Central Bank increases M0, the only rational reaction is expected to increase inflation?"

in an economy with rational expectations and without frictions in the price or wage setting process then the answer is yes. In fact it has to be since the economy is always at full-employment. In this case money is neutral, it has no real effects.

[Luis H Arroyo]

TNB, Interesting question. Rationality does not imply that the model is true - as Nick said. Therefore, the media can impose their "models."

AdamP, I can not see that. In fact, I believe that under certain conditions the monetary policy has real effects, either upward or downward.

[Adam P]

yes under certain conditions monetary policy has real effects, under others it doesn't.

[Nick Rowe]

Min: RE is generally more falsifiable than AE, since it places more restrictions on how the parameters must match the data, while AE lets B be whatever it needs be to match the data. In particular, RE says that the agent's forecast errors must be uncorrelated with anything in the agent's information set. That's very falsifiable, at least in principle. Usually though we don't test hypotheses about expectations directly (unless we have survey data telling us directly what people expect); we test a joint hypothesis of FE plus some economic theory about how people behave. For example, we can test the joint hypothesis of RE plus the Permanent Income Hypothesis. And if it fails the test, we can't tell whether it's RE, PIH, or both, that is false.

westslope: I agree that we use rules of thumb a lot. For one thing, it's just too much work to process data, never mind collect it. RE ignores that information-processing cost, and I think that's its biggest reason for failure, when it does fail.

I see perfect foresight as very different from RE. We nearly always have limited information, so will nearly always make forecast errors, even under RE. All RE says is that those forecast errors should themselves be unforecastable, given available information.

Adam: AFAIK, RE came into macro with Lucas' 72 paper, Expectations and the Neutrality of Money. But I agree that Lucas 75, the Lucas Critique, is probably much more influential in spreading RE. (It was easier to understand, and more general in its implications.)

But I remember reading Lucas on RE somewhere (can't remember where) interpreting RE in a very similar manner to me. Saying that it did not imply an immediate jump to people forming expectations consistent with the new policy regime. Only that we couldn't expect the rules of thumb ("decision rules") to stay stable when the policy regime changed. And this was one of his arguments for rules vs discretion. Under discretion, with no stable policy regime, economists didn't have any chance of predicting people's behaviour, just because those rules of thumb would be changing at an unknown speed in an unknown way. We might be able to predict how the economy would operate under stable policy rules, but not otherwise.

In other words, Lucas' own interpretation of RE was much more moderate and reasonable than many "Lucasians".

For the rest of your comments, I tend to agree. Yes, if we interpret AE as "B does not change when the policy regime changes" (and that indeed was something we didn't think about with AE), then RE contradicts AE. I expect my point is that the relation between AE and RE is not as simple as two alternative contradictory hypotheses. It's more complex than that. And in particular, RE (under a reasonable interpretation) *is* compatible with people using habits, or rules of thumb, and not having a model or understanding how the economy works.

[Nick Rowe]

TNB: when the economy keeps on doing the same thing, following the same patterns, even if it's stochastic (random), then it's relatively easy to say what is and is not a rational expectation. And it's also easy for agents to follow simple rules of thumb that let them forecast as well as they possibly can, even if they don't understand how the economy works.

It's when something genuinely new happens that it gets harder, both to forecast rationally, and to say whether people have rational expectations. Different economic forecasters can have different forecasters, based on different models. (Just the same as Fox news vs MSNBC.)

(There is also a game-theoretic literature arguing that rational people who can communicate and take bets could never "Agree to Disagree". But I don't understand that literature too well.)

[Adam P]

Nick, yeah I think you're right about Lucas. His version of rational expectations was much more moderate and realistic than what came later.

After all, Lucas explicitly separated rationalality of expectations from the assumption of full information for everone. His explanation of the empirical Phillips curve was based on the idea that people saw increased demand for their output but didn't know whether it was due just to an increase in the money supply or shift in demand towards their good. Nowadays most people who invoke rational expectations think that it involves assuming everyone has full-information, which is where the money neutrality results come from.

But I'm pretty sure the whole point of the critique, in the context of this post, would basically be the statement that "you've been assuming B won't change but it will", so it must be that AE was generally interpreted as B being fixed exongenously.

[westslope]

"But occasionally, we do stop and think about the a priori: "Can I really trust him? Would it be in his interest to do X if he expects others to do Y if he does X, and they....etc." " -NR

Nick: That is precisely the 'trust dilemma' that stag-hunt or assurance coordination games try to capture. Bagging an adult red deer requires team work to be successful. Killing a hare is easy to do as a lone hunter. The temptation is to defect for the sure thing. FWIW, I think I see the potential for motivating time inconsistency or dynamic inconsistency policy problems as a stag-hunt coordination game. Clearly, one way of solving the stag-hunt coordination challenge is for the hunters to make binding commitments so when the time comes, hunters ignore the siren call of the hares. Excuse the mixed metaphors.

'Cheap talk' in theoretical models and 'credible assignments' in the form of authoritative statements in experiments help players coordinate on the socially optimal outcome in stag-hunt type settings. Not familiar with the communicate-bet literature.

[dlr]

It seems like you framed this in a way the defines AE away. Even though Kling's post is about habits, I think it seems too narrow to focus on habits as the key dichotomy.

You say RE can been seen as AE with a specific description of how expectations should adapt. But I don't think AE merely says that expectations should be affected somehow by something. I see it as saying expectations should adapt based on the combination of a particular set of inputs and an exogenous weighting heuristic. Maybe there is latitude in choosing the particular input X in a particular model or defining the heuristic B, but if you widen that latitude too much then AE seems to lose all meaning. If anything can be used as an input (maybe X is not just the price level or inflation but every knowable piece of information in the world) and B can be a recursive and endogenous information process then all you have left is the E. Adaptive would be left to mean only "any combination of any information in any way" which isn't really saying much of anything about how expectations are formed.

RE says that however expectations adapt, it must be in a consistent way, whether that is according to a particular data set and an exogenous heuristic or not. That seems contradictory to a meaningfully defined AE, the same way a theory the says stock prices are exclusively determined by some rule of thumb weighting between past and present earnings or dividends or stock price or cash flows is contradictory to EMH. We could expand the former pricing theory to include past and future anything combined in any matter whatever, but then what is the theory exactly?

I think that a meaningfully defined AE means that habits can create unique, inconsistent outcomes whereas under RE habits may exist but only subject to consistency. But I agree that neither necessarily implies a particular level of habit-ness or behavioral stickiness. Yet I still don't think your dichotomy between unchanged habits and instantly changing habits are best described as the real dichotomy, because that still ignores the consistency constraint. The extent to which habits shift instantly can be affected by consistency, as can which information is used to form expectations and other features (besides stickiness of habits) about how it is used.

[Nick Rowe]

Adam and dlr: my trouble is, I tend to agree with a lot of what you both are saying.

Let me list some distinctions:

1. Agents follow rules of thumb vs agents understand the true model.
2. Those rules of thumb are/are not consistent with the world.
3. Those rules of thumb do/do not change when the world changes.
4. Those rules of thumb change slowly/quickly when the world changes.

I expect we could say that trying to collapse those 4 questions into one simple AE/RE dichotomy is a mistake.

My main point in this post was that the AE/RE distinction was not the same as distinction 1. Plus, that distinction 2 (which implies 3) is the more important one.

Your comments are helping bring this out.

[Luis H Arroyo]

I always thought Lucas was a little freaky. Until, in 2009, he defended the QE Bernanke. This article has reconciled me with him. And Nick & Co. has clarified many things for me.
I've never fully known him. Could someone point out to his most significant papers? (not very much math, please)

[Adam P]

I'm not sure how to this fits in here but there is a slightly deeper point lurking here. When Nick says:

"If people were living in a world where the price level followed a random walk, for example, so that P(t)=P(t-1)+u(t), where the error term u(t) is mean zero and serially uncorrelated, then X should be P, and B should be 1."

he's leaving out half the story. It's not just that P(t)=P(t-1)+u(t) implies X=P and B=1, it's just as much that X=P and B=1 implies P(t)=P(t-1)+u(t). Equilibrium price level dynamics and expectations are both jointly determined endogenously under rational expectations. Is the same true of AE?

[Nick Rowe]

Adam: It's true, I am leaving out half the story (in most cases). I thought about including it, but decided it would only complicate the issue. (I alluded to it in my comment above when I raised the question of whether expectations would converge to rational).

In most models, the way people form expectations will affect the thing they are forming expectations about. That's almost always true in macro, if the thing is inflation. If you change the parameter B in AE, that will change the process actually generating P. Simple example: if B=0, then the Expectations Augmented Aggregate Supply Curve (the SRAS) will not shift, when last year's AD shifts; but if B=1, the EAS curve will shift. And the process determining P will depend both on how the AD shifts and on how the EAS shifts.

RE models solve for both simultaneously. Usually using the Method of Undetermined Coefficients. We "guess" that the actual process determining P takes the form P(t)=BP(t-1)+u(t), for example, then assume that people form their expectations according to the rule of thumb P(t)e=BP(t-1), then plug that into the model, solve for P(t) as a function of P(t-1) to check our guess is right, and solve for B at the same time.

George Soros calls this "reflexivity", and seems to think he discovered it. But macroeconomists have known about this since the 1970's.

Luis: Lucas' most influential papers. From my vague memory:

Lucas and Rapping 1968, in the Phelps volume. An early model of the SRAS curve, pre-RE. Don't bother with this one. It was influential, but wrong. He forgets the interest rate.

Lucas 1972, Expectations and the Neutrality of Money. Most influential. Laid out a macro model with full microfoundations, flexible prices and RE, where suppliers had imperfect information and so could not distinguish a nominal shock from a real shock. So unanticipated nominal shocks had real effects, because suppliers thought it might be real. Set a new methodological standard for macro, of what it means to model something properly. Introduced RE into macro. The foundation paper for New Classical macro. (Is also badly flawed because the model does not contain an interest rate; money is the only asset.) Too mathy for easy reading.

Lucas 1975. The lucas critique. A must-read. No math. "If we change policy the world will change, and people's rules of thumb will also change, which changes the world again. If we ignore that second effect we will not properly understand the effects of policy. That's why we need theory, so we can really understand everything, not just blindly run regressions."

Lucas 198? When he switched to growth theory. "All my previous work has been on business cycle theory. And I've just realised that it's all nearly irrelevant. A rich country in a recession is still much richer than a poor country in a boom. And booms and recessions mostly cancel out anyhow. Forget that trivial business cycle stuff, and let's switch to understanding growth".

Those are my picks. The lucas/Stokey stuff never impressed me much.

[Mike Moffatt]

"The lucas/Stokey stuff never impressed me much."

Wow. This could make a top ten list of "statements that will get you thrown out of Rochester".

I'd love to hear why!

[Nick Rowe]

Mike: Not that I'm an expert. I skimmed Lucas/Stokey.

Lucas 72 is technically impressive. Solving an RE model from preferences and technology with signal processing is hard.

But it's a lot more than just technically impressive:

1. It set a new standard for what it means to have a macro model.

2. It explained (or, at least, gave an explanation, right or wrong) the business cycle.

3. That explanation was new (OK, the seeds were in the Phelps volume).

4. It created the seeds of a new understanding of what we might mean by "policy" (distinguishing between the policy action and the policy regime).

5. It contained the seeds of the Lucas critique; it showed that policy might appear to be effective even when it wasn't.

6. It had policy implications.

7. It explained (at least, provided an explanation of) a load of other facts, like shifting slope and intercepts of Phillips Curves.

In sum, it changed the way we think about a lot of stuff.

Lucas/Stokey is technically impressive. Very. But what more?

[Nick Rowe]

8. It changed the way we think about what "equilibrium" means.

[Luis H Arroyo]

Wow! thanks very much!!!

[edeast]

Mike and if you could define recursive utility for me that would be great. I use recursion in programming, but not sure how it's used in econ.