Monday, October 03, 2016

Hunting the Rational Expectations whale

1. Why is Rational Expectations still around, anyway? 

Rational Expectations is (are?) one of the key features of almost every macro model in existence today, and has been for decades. Why? One reason is that it's easy to work with, mathematically - just stick an "E" in front of things, and voila, that's what the agents in your model believe! Another reason is that RE is appealing to folks who think that the government shouldn't be able to trick people consistently. A third reason is that there's just no obvious alternative way of modeling expectations. Classic alternatives like adaptive expectations are rigid, simplistic, and just generally very weak. And more sophisticated alternatives, besides being unwieldy to model, also tend to be hyper-specific - if there are actually a number of different ways that RE fails, each of these models will only catch one of them.

But the real reason is that it's hard to test people's expectations directly. Instead, what macroeconomists do is to just throw the expectations assumption into the model along with a million other things like Euler equations, transversality conditions, industry structure, etc., and then test the model against macro facts. If the model fails to match enough macro facts, or the "right" macro facts, to garner interest, the problem is assumed not to lie with the expectations, but with some other assumption of the model. So RE survives. In Lakatos' jargon, it's part of the "hard core" of modern macro.

2. Observing expectations directly

But in recent years, a few brave souls have started to hunt the great Rational Expectations whale. These intrepid hunters are doing the simple and obvious thing that economists previously didn't dare to do: Just ask people what they expect.

Duh, right? Actually, tons of people have collected and analyzed survey measures of expectations. But there's a reason macroeconomists haven't relied on these surveys much in the past (and it's not just fear of getting yelled at by Bob Lucas). First of all, it's not clear that people's stated expectations have anything to do with their functional expectations. I might say that I think inflation is going to rise, and I might even feel deep in my bones that this is truthy, but does that mean I'm buying TIPS and shorting Treasuries? Not recently, it doesn't. What we care about isn't what people "believe", whatever that means, but what they act as if they believe

So the RE-hunters have to take an extra step - they have to show that stated expectations explain actual behavior. And explaining actual behavior requires assumptions, about all the other stuff that might be affecting behavior. And unless you want to be a "heterodox" person shouting in the wilderness, those assumptions are going to have to come from currently respected theory. So that's what the RE-hunters are now doing - showing that stated expectations, e.g. from surveys, explain behavior well when you stick them into popular theories.

3. The RE-hunters

One of the RE-hunters is Andrei Shleifer, who along with coauthors like Robin Greenwood, Yueran Ma and Nicola Gennaioli has started working with survey expectations in finance. Finance is relatively easy to work with because a lot of the popular models are partial equilibrium. Examples of Shleifer's work include this paper on investor expectations and this paper on CFO surveys and investment. He's also made a general equilibrium asset-pricing model, along with some other co-authors, using extrapolative expectations (which surveys seem to show some evidence for). 

In macro it's a bit harder, since most top people now agree that you need general equilibrium for anything important. So the burden of proof is on the RE-hunters - they have to show that an alternative model of expectations, together with some other fairly standard model elements, can explain macro facts in a general equilibrium type model.

One of the most popular non-RE models is the "sticky information" model of Mankiw and Reis, which says that people update their information with a time lag. Along with Justin Wolfers, Mankiw and Reis showed over a decade ago that survey expectations line up with this model in many ways (though as the comments at the bottom of the paper show, they had difficulty persuading certain folks).

Another popular model is Chris Sims' "rational inattention" model. This says that people only get imperfect information because it's costly to filter out noise. Mike Woodford has also worked with models like this.

4. Coibion and Gorodnichenko

Now there is a powerful new team hunting the Rational Expectations whale: Olivier Coibion and Yuriy Gorodnichenko. In 2012, they showed that survey expectations of macreconomic stuff match many of the predictions of sticky information and noisy information models, using a method that's largely agnostic between the two. In other words, they show that stated expectations look like real expectations no matter which of the two models you believe in.

Then in 2015, Coibion and Gorodnichenko came out with a new paper out that's even more general. Their old approach required them to specify the shocks in the economy, but they figured out a way to avoid having to do this. It's really neat. 

Here's the idea. Forecasters make forecasts of things many years in the future. I might forecast the 2020 inflation rate in 2015. But they also update their forecasts - in 2016 I'll make another forecast of 2020 inflation. In general the 2016 forecast will be different from the 2015 forecast. Under RE, the differerence - called the "forecast update" - should have no relation to the eventual forecast miss. In other words, under RE, if my 2015 forecast for 2020 inflation is 2.5% and my 2016 forecast is 2%, that shouldn't mean that my 2016 forecast is more likely to overshoot than undershoot.

But it does. That's what Coibion and Gorodnichenko show. Forecast updates predict forecast misses. That's consistent with a model where information is "sticky" and one where it's "noisy".

That's the paper's central insight, but it has lots more in it than that. The authors test whether the result could come from forecasters intentionally "smoothing" their forecasts, i.e. giving intentionally stale forecasts in order to cater to some clients. But they don't find evidence for this. 

They also find that the degree of "noisiness" or "stickiness" of information varies depending on what's happening in the economy. After big shocks like 9/11, the amount of apparent stickiness/noisiness goes down. But in the Great Moderation, it went up. So when macroeconomic stuff is more important, people either pay more attention, or spend more effort making accurate projections, or whatever. That reassuring.

So Coibion and Gorodnichenko's new method shows that professional forecasts behave like true expectations for a very wide class of models. Not for all models, obviously, but for two of the mainstream alternatives to RE. And this is independent of all kinds of other things, like consumption behavior, industrial structure, or the nature of the shocks that drive the economy. In other words, it's getting harder and harder to dismiss direct measurements of expectations - maybe you really just can ask people what they believe, and get a useful result!

5. So what?

Interesting note: There are both "behavioral" and "non-behavioral" explanations for this failure of Rational Expectations. Information could be "sticky" or "noisy" because information is costly to acquire and process, or because people are just slow to believe or accept new information. (I call this "Smith's Principle": Any behavioral explanation will have an observationally equivalent explanation based on information structure and/or costs. I can name stuff after myself because this is my blog, hehehe. And because I'm too lazy to find out if anyone else has made this claim.) As the authors point out, it's perfectly possible that a bunch of individually rational but information-constrained agents can produce an aggregate forecast that does not take into account all of the available information in the economy:
This predictability of the average forecast error across agents from forecast revisions is an emergent property in both models, i.e. a property which arises only from the aggregation process and not at the individual level. 
Nice to see economists using the term "emergent property"! In other words, it's perfectly possible to have rational agents without Rational Expectations.

But anyway, if you believe this result, it means two things: 1. that forecasts are good measures of expectations, and that 2. sticky/noisy information should be a much more standard feature of macro models. If on the other hand you disbelieve the result, you must believe that A) forecasts don't represent true expectations, and B) sticky/noisy information models aren't good models, and also C) forecasts fail to reveal true expectations in precisely a way that makes it look like sticky/noisy information models are good!

Now, RE defenders may shrug and say "So what? No one expects RE to be exactly right, it's just a useful approximation." But as Coibion and Gorodnichenko point out, that's not true in this case. Sticky/noisy information models differ in very important ways from RE models. Ways that are very important for policymaking. In other words, by linking their test of RE to a model that we already know has economically significant implications, Coibion and Gorodnichenko's claimed failure of RE must be economically significant too. This isn't just a wrinkle on a largely successful theory; it's a claim that the theory fails in big, critical ways.

Nothing is for certain, especially in macro, but this is another harpoon tossed into the side of the Rational Expectations hypothesis.

(No whales were harmed in the making of this blog post. Noahpinion condemns the practice of whaling, and also believes that whale meat tastes like stale hamachi.)


  1. "But in recent years, a few brave souls have started to hunt the great Rational Expectations whale."

    In recent years? Economists have been collecting "direct" evidence of price expectations for over 50 years. Muth actually cites surveys that been conducted by Modigliani and others in his original 1961 article.

    I know the narrative is supposed to be that economists like Muth applied rational expectations without concern for its empirical validity. But, the truth is, the main reason Muth proposed rational expectations was because static and adaptive expectations suffered from empirical failings that had been noted as early as Coase and Fowler (1935). Namely, that they did a very poor job of explaining the length of hog cycle.

    1. Yep, surveys are very old. Didn't want to imply otherwise. What's new is macroeconomists taking them seriously as measures of true expectations.

      I don't think the narrative is about Muth...I think the narrative is that Lucas took Muth's idea and applied it to macro without much concern for empirical validity in that domain.

  2. Well, while farmers were outsmarting the hog cycle (even though cattle cycles certainly still exist and corn-hog cycles did up until not too long ago), there has been plenty of evidence against ratex for a long time. It has just been ignored, even though some of it has involved marcoreconomics, especially in forex markets, with much of that involving surveys of expectations, and also involving it being clear that the only way forex data could be consistent with ratex was to assume extreme volatilities of risk premia and other wild stuff. Some of this lit goes back to the 80s, with some showing needing highly volative risk premia coming from people like Hansen and Hodrick in 1983 and Fama in 1984. The definitive stuff drawing on surveys was done by Froot and Frankel in 1989, with the following quote pretty much summarinzing it:

    "We cannot reject the hypothesis that all of the bias is attributable to these systematic expectational errors, and none to time-varying risk premia" (p. 159. QJE, vol. 104).

    There have been quite a few other tests of ratex based on various methods and approaches, with very few supporting it. A study long viewed as essentially definitive, except of course by the macro ratex gang who simply ignored it was Michael C. Lovell, 1986, AER, "Tests of the Rational Expectations Hypothesis." Only ignorant fools have believed in ratex over the last 30 years, although, as you noted, Noah, many of these people are willing to accept that it is not quite right, but just say it is too useful to give up.

    I welcoms this newer research, which seems to doing useful work on these issues of sticky versus noisy information models. But nobody should be going around claiming that this is what has finally shown the problems with ratex.

    Oh, and as for your "Smith Effect," well, George Stigler was making this argument back in the 1960s and 1970s, and reaffirmed at as the proper Chicago response to Simon's bounded rationality, which, of course, Muth was trying to respond to as well. You should be careful about dissing Muth when you try to rename the "Stigler Effect" after yourself (although I grant nobody has called it that, but he beat you to the punch by more than a half century, sorry).

    Barkley Rosser

  3. Anonymous5:08 PM

    The smell of a dead rotting corpse is not appealing, to say the least, but in this case, the smell of the dead rotting corpse of the REH is.

  4. It’s in the hard core, stupid
    Comment on Noah Smith on ‘Hunting the Rational Expectations whale’

    It is long known that economists violate well-defined scientific standards: “In economics we should strive to proceed, wherever we can, exactly according to the standards of the other, more advanced, sciences, where it is not possible, once an issue has been decided, to continue to write about it as if nothing had happened.” (Morgenstern, 1941, p. 369)

    A case in point is rational expectations. Strictly speaking, the concept is already dead since Walras: “Walras approached Poincaré for his approval. ... But Poincaré was devoutly committed to applied mathematics and did not fail to notice that utility is a nonmeasurable magnitude. ... He also wondered about the premises of Walras’s mathematics: It might be reasonable, as a first approximation, to regard men as completely self-interested, but the assumption of perfect foreknowledge ‘perhaps requires a certain reserve’.” (Porter, 1994, p. 154)

    This was a polite thumb down but Walras did not get the point and neither did those who came after him. Not only this: “So RE survives. In Lakatos’ jargon, it’s part of the ‘hard core’ of modern macro.”

    And this proves the utter scientific incompetence of economists. While it is, of course, legitimate to fool around with hypotheses in the analytical superstructure, it is NOT legitimate for the adherents of a research program to change the hard core. Methodology tells us that it is the hard core which DEFINES the paradigm. A change of the hard core amounts to the abolition of the paradigm. This is allowed, of course, but for the proponents of a paradigm it is equivalent to unintended suicide.

    Orthodox economics is built upon this hard core set of axioms: “HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states.” (Weintraub, 1985, p. 147)

    Methodologically, these premises are forever unacceptable. It is pretty obvious that the neo-Walrasian axiom set contains THREE nonentities: (i) constrained optimization (HC2), (ii) rational expectations (HC4), (iii) equilibrium (HC5). Every model that contains only one nonentity is A PRIORI false. The discussion of models that contain nonentities is not different from a medieval angels-on-a-pinpoint discussion. And this is essentially what happens in the quality journals and on this blog.

    It is pointless to try to repair RE and keep the rest. The WHOLE thing has to go out of the window. The microfoundations approach has already been dead in the cradle 140 years ago. To put new lipstick on long defunct RE will not work. Face the fact: economics is a failed science and economists are incompetent scientists. The issue has been decided!

    Egmont Kakarot-Handtke

    Morgenstern, O. (1941). Professor Hicks on Value and Capital. Journal of Political Economy, 49(3): 361–393. URL
    Porter, T. M. (1994). Rigor and Practicality: Rival Ideals of Quantification in Nineteenth-Century Economics. In P. Mirowski (Ed.), Natural Images in Economic Thought, pages 128–170. Cambridge: Cambridge University Press.
    Weintraub, E. R. (1985). Joan Robinson’s Critique of Equilibrium: An Appraisal. American Economic Review, Papers and Proceedings, 75(2): 146–149. URL

    1. "And this proves the utter scientific incompetence of economists."

      Inductive methodology {as 'used' by the natural sciences and most scientific disciplines} is the basis of this economist's approach.

      "The critics of neoclassical economics agree that economics should be about economic reality and should be demonstrably relevant to it. This will strike the non-economist as obvious. However, it is not obvious in mainstream economic thinking: the neoclassical school of thought is based on the deductive approach. This methodology argues that knowledge is brought about by starting with axioms that are not derived from empirical evidence, to which theoretical assumptions are added (again not empirically backed), and on the basis of which tools of logic (mathematics) are utilized to prove theoretical results. There is an alternative approach. This approach examines reality, identifies important facts and patterns, and then attempts to explain them, using logic, in the form of theories. These theories are then tested and modified as needed, in order to be most consistent with the facts of reality. This methodology is called inductivism."

  5. Anonymous7:08 PM

    "So the burden of proof is on the RE-hunters - they have to show that an alternative model of expectations"

    Why is the burden of proof on the RE-hunters? What about the burden of proof on the proposers of REH?

  6. Anonymous7:16 PM

    "Noahpinion condemns the practice of whaling, and also believes that whale meat tastes like stale Hamachi."

    So how was this belief formed? Given you decry whaling, one can only presume you have not tasted whale meat.

  7. A good argument against RE is that so many economists have been predicting inflation for most of the last decade. They've even been insisting that this inflation has been so imminent that the Fed needed to take preemptive action and raise rates ASAP. Maybe we need to think about sticky expectations instead of rational expectations.

  8. Quasi Rational Expectations, which was a term coined by Nerlove, seems like a reasonable balance between AE and RE, atleast for simpler models. Nerlove's book ( I think Chapter 13 ) is recommended for a better exposition than I ever could give here.

  9. Anonymous3:34 AM

    I am not encouraged by this modelling of beliefs and expectations. Fundamentally you are dealing with aspects of human and social behaviour which is not conducive to mathematical or quantitative expression. What needs to change are the fundamental micro-economic axioms that underpin modern macro-economics which has continues to allow abstraction to supplant real knowledge.

    1. Anonymous1:15 AM

      Gimme a break, you don't know what those "fundamental axioms" even are, do you?

    2. Anonymous26:35 PM

      Axioms? That is theory based not fact based. Mire theory.

      Economics is on much more shaky footing than geometry!

      You see the problem? Geometry works, we all are conditioned to it's use of the word axiom to never fail geometrically.

  10. I'm sure you could sell the idea that expectations have some specific adaptive formulation, the key is explaining business cycles or long-term growth: not over a specific region and time period, but many. I haven't seen any such model.

    The key is that many 1970s macro models were predicated on consistently underestimating inflation--how you get the Phillips curve--which was clearly not a good assumption.

    The current DGSE models are worthless, but I suspect the key to improvement does not lie in simple adaptive expectations, which was the prior failed paradigm.

    1. In the late 1920's, yule and slutsky both showed that cycles could arise purely from operations on random data. Some economists pursued this line of reasoning ( moran showed how moving averages could turn into cycles ) into the late 1940's but then it seems to have died atleast from what I can tell. why is that ?

    2. That's a very real business cycle way to look at it. Generating a time series that has periodic serial correlation is pretty easy. In this case, turning a random walk into a serially correlated time series. I don't find that approach very fruitful. Theories discovered decades ago by famous people were not abandoned because they work; academia is not that inefficient.

  11. Barkley my recollection is that Herbert Simon adumbrated the 'Smith effect' before Stigler, but implicitly believed it made more sense to try to identify the decision-making algorithms people use in practice (and how they learn to upgrade them) than to model information search as an optimal stopping problem. Mark, the systems theorists at MIT took up Yule's ideas, maybe Slutsky's too, I don't know.

    1. The difference between Simon and Stigler is that the latter was quite certain that people would be able to optimize on their information costs. Simon did not buy this, and said one must fall back on heuristics and satisficing and so on. Ultimately there is an infinite regress problem that Simon was aware of but that Stigler was not, that one also must solve the problem of how long one works on minimizing information costs, which implies that one must also solve the problem of how long to work on that problem, ad infinitum. Simon was far more sophisticated than Stigler and such concerns led him into artificial intelligence, where he became the world's leading expert.

      Simon had a PhD in poli sci/public admin and was never in an econ dept. He published 956 papers in many disciplines. At his death he was in four depts at CMU: computer science, one of the top depts in the world with their building named for him, cognitive science, psychology, and management, also having been in the philosophy dept earlier. I could quote some of his private comments to me on all this, but will skip doing so.

      Not obvious that Noah is aware of any of these complications, one more reason he is sort of jumping the gun on naming this after himself.

    2. Hmm, I tried to post a reply to you earlier, Fred, but it has not shown up. Will make this version less snarky.

      So, you are basically right that Simon had it before Stigler. But Simon never said people optimize because of bounded rationality. Best they can do is use heuristics to satisfice. He was aware of various problems such as infinite regress problems in optimizing the optimizing of the optimizing...of figuring out how to minimize information costs, given that one is starting out without full information. Simon knew that, but Stigler did not. However, lots of people identify Stigler with the idea because he simplistically declared that people resolved the Simon problems because one just minimized information costs, which, unless I am mistaken, is what Noah is proposing should be named after him.

      Look, I have an equation named for me (google it), and my late mathematician father has about a dozen things named for him. All of those names were given by other people, not by us.

  12. Cheerleading the cargo cult
    Comment on Barkley Rosser

    Economics is a cargo cult science ― not a science. In science the criteria true/false apply and nothing else. By diligently applying these criteria, as a matter of principle, every intelligent person can find out that Walrasianism, Keynesianism, Marxianism, Austrianism is provable false, i.e. materially/formally inconsistent. Economists have not found out this until today.

    There is reality and social hyper-reality. Social hyper-reality is a historically evolved mental construct composed of multiple elements from religion, philosophy, art, politics, entertainment, PR/propaganda, storytelling/gossip, and its strength depends critically on the number of participants and the intensity of their mutually reinforcing interactions. Hyper-reality is created and maintained by communication and is for all practical purposes MORE real than objective reality except in the case of a head-on confrontation.

    Economists have talked themselves and the general public into the hyper-real belief that what they do is science. It is NOT, it is storytelling/gossip. Barkley Rosser, for example, does not talk about the economy at all but about economists: “The difference between Simon and Stigler is that the latter was quite certain that people would be able to optimize on their information costs.”

    Now, as a matter of fact, there is NO REAL difference between Simon, Stigler and the representative economist because they ALL share the social science delusion, that is, the belief that economics is about human behavior and therefore economic theory has to be based on some fundamental behavioral assumptions. Where they differ is what the most “realistic” assumption is.

    What cargo cult economists fail to realize is that NO WAY leads from the understanding/explanation of human behavior to the understanding/explanation of how the actual economy works.

    Economics is methodologically defective. The foundational defect is given with the very definition of the subject matter: “It is a touchstone of accepted economics that all explanations must run in terms of the actions and reactions of individuals.” (Arrow, 1994)

    The scientific incompetence of economists consists in accepting the behavioral/psychological/sociological/antropological definition of economics.* From this Ur-blunder the way leads to accepting the three nonentities constrained optimization/rational expectations/equilibrium, to supply/demand/equilibrium, to general equilibrium and eventually to DSGE/RBC at the end of the cul-de-sac.**

    By evaluating the respective merits of Stigler and Simon, Barkley Rosser in effect distracts from the fact that BOTH are cargo cult scientists and have no scientific merits at all. Worse, he distracts from the fact that economics as a whole has decoupled itself entirely from science.

    It does not matter what Barkley Rosser thinks or claims he is doing, the social reality is that he is promoting cargo cult science and the real reality is that he impedes science.

    Egmont Kakarot-Handtke

    * For details see ‘Confused Confusers: How to Stop Thinking Like an Economist and Start Thinking Like a Scientist’

    ** For Keynesianism see ‘The unfinished Keynes’

    1. I mostly do not waste time replying to you anymore, Egmont, but while Stigler might be a cargo cult scientist, Herbert Simon was not. Go read what I wrote and double check it all you want. While he got a Nobel Prize in economics, Simon did not get his degree in economics and he was never in an economics department. He published 956 papers in many disciplines, some of them more influential and important than his ones in economics, especially his ones in computer science and artificial intelligence, where he was considered to be one of the world's leading experts. Do you wish to trash his work in those areas with your silly drivel?

  13. " modeling expectations" <<
    Like history, economics seeks to explain what happened, in the past.
    Like any science worker (scientist), an economist attempts to predict what the economic consequences of his or his client's actions will be.
    Prediction is a modelling exercise.
    Without prediction there is no "science".

    The value of the science is based on the usability and accuracy of the prediction. More precisely in decision analysis, the value of information is the increased expected value of your decision results with the info over the expected value of results when you decide w/o any further info.

    RE will be quickly abandoned if, and only if, a better way of modeling behavior leads to better predictions and more control/ influence by the decision makers.

    Ain't gonna happen -- 'cause when it comes to making money, enough folk are rational enough often enough to insure that no other paradigm allows traders to make money with the alternate explanations.

  14. Tom Grey

    You say: “Without prediction there is no ‘science’.” This is a popular misunderstanding among economists who have never grasped what science is all about.* Take notice that Feynman, a genuine scientist, clearly stated: “The future is unpredictable”.

    Note also that ― since the ancient Greeks invented science more than 2000 years ago ― the purpose of science has never been to enable traders to make money. Traders know this well, and, being rational, they rely less on science and more on time tested rip-them-off.

    Note finally that your prediction “enough folk are rational enough often enough to insure that no other paradigm allows traders to make money with the alternate explanations” is absolutely hallucinatory and as unscientific as can be.

    Egmont Kakarot-Handtke

    * For details see ‘Science does NOT predict the future’

    and ‘ICYMI Prediction/Forecasting’