Tuesday, January 29, 2013

The power and the terror of Irrational Expectations



In September 2011, in an interview with the Wall Street Journal, Robert Lucas gave the following justification for the use of Rational Expectations:
If you're going to write down a mathematical model, you have to address that issue. Where are you supposed to get these expectations? If you just make them up, then you can get any result you want.
So, are Rational Expectations not "just made up"? Does the evidence tell us that this is how people form expectations? I don't think so. It seems to me that Lucas is saying that we should pick Rational Expectations because they are appealing in some a priori way. I'm not sure what that is, though.

Be that as it may, figuring out how people actually form expectations, in the real world, is devilishly hard. Thomas Sargent and many others have experimented with models of Bayesian learning. Roger Farmer has advanced the idea that agents use a "belief function" in cases where rational expectations of the Lucas variety can't be formed. Greg Mankiw and Ricardo Reis have experimented with macro models in which people don't always update their beliefs on time, and Christopher Sims and many others have tried to microfound this idea with various models of rational inattention (in fact, rational inattention is now a hot topic in behavioral finance).

Of course, there are older, simpler ideas of expectation formation that were pushed out by the Lucas revolution, but which may have received a bad rap. One of these is Milton Friedman's theory of "adaptive expectations", which in its simplest form doesn't seem to explain the data, but may actually be going on in some more complicated form.

That is the conclusion of a recent paper by Ulrike Malmendier, a star of the behavioral finance field. Malmendier shows that people's inflation expectations are strongly affected by recency bias; in other words, people who have experienced higher inflation during a large percentage of their lifetime tend to expect higher inflation, even if their lifetimes haven't been that long yet. From the abstract:
How do individuals form expectations about future inflation? We propose that past inflation experiences are an important determinant absent from existing models. Individuals overweigh inflation rates experienced during their life-times so far, relative to other historical data on inflation. Differently from adaptive-learning models, experience-based learning implies that young individuals place more weight on recently experienced inflation than older individuals since recent experiences make up a larger part of their life-times so far. Averaged across cohorts, expectations resemble those obtained from constant-gain learning algorithms common in macroeconomics, but the speed of learning differs between cohorts.
This comes via Carola Binder, a grad student blogger at Berkeley (whom you should follow, by the way).

Binder discusses the implications of this finding for Japanese exchange rates, but I wish she had touche more on the basic idea that this sort of expectation formation might be responsible for the persistence of Japan's deflationary trap itself. Japan has been in deflation, or near it, for two decades now. That's a large fraction of the working lifetimes of many of Japan's current adults. If inflation expectations are set in the backward-looking way that Malmendier suggests, then it might take far more dramatic and sustained central bank action than anyone realizes in order to produce a return to an inflationary environment.

But to me, that's not even the most disturbing implication of Malmendier's finding, and of this type of expectations model in general. In most theories of non-rational expectations, like Bayesian learning or rational inattention, expectations evolve in a smooth, stable way. And so these models, as Chris Sims writes, look reassuringly like rational-expectations models. But there is no guarantee that real-world expectations must behave according to a stable, tractable model. I see no a priori reason to reject the possibility that expectations react in highly unstable, nonlinear ways. Like tectonic plates that build up pressure and then slip suddenly and unpredictably, expectations may be subject to some kind of "cascades". This can happen in some simple examples, like in the theory of "information cascades" (In that theory, people are actually rational, but incomplete markets prevent their information from reaching the market, and beliefs can shift abruptly as a result). In the real world, with its tangle of incomplete markets, bounded rationality, and structural change, expectations may be subject to all kinds of instabilities.

In other words, to use Lucas' turn of phrase, expectations might just make themselves up...and we might get any result that we don't want.

What if inflation expectations change suddenly and catastrophically? That would probably spell the death knell for macro theories in which the central bank can smoothly steer the path of things like inflation, NGDP, etc. It would raise the specter of an "inflation snap-up" (or "overshoot", or "excluded middle") - the central bank might be unsuccessful in beating deflation, right up until the moment when hyperinflation runs wild.

And what would be the implications of financial markets and financial theories of the macroeconomy? Belief cascades could obviously cause asset market crashes. It seems like sudden changes in expectations of asset price appreciation might also cause abrupt and long-lasting changes in saving and investment behavior. Which in turn could cause...well, long economic stagnations.

A very disturbing thought.

81 comments:

  1. Phil Koop8:25 AM

    Maybe this, and not "capital controls", is the reason why America was able to inflate away so much of her WWII debt.

    BTW, you say that adaptive expectations "in its simplest form doesn't seem to explain the data", but the Wikipedia article you link to says that "[ratex] has largely replaced adaptive expectations in macroeconomic theory since its assumption of optimality of expectations is consistent with economic theory"! (My emphasis.) Oh dear. A Freudian slip? Perhaps you should edit that.

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    1. No, Wikipedia simply doesn't know about the evidence against fixed-lag adaptive expectations. Essentially, the speed at which people update their beliefs is highly variable, meaning that any test of the classic, Milton Friedman-type "adaptive expectations" will fail, even if expectations are in fact purely backward-looking.

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    2. Is this evidence against fixed-lag adaptive updating of Wikipedia?

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    3. Wonks Anonymous4:10 PM

      Somewhat ironic because Friedman was known for claiming the effects of monetary policy had "long and variable lags", making it hard to test his hypothesis. Scott Sumner would say that the effects appear in market prices very shortly after information is released, which is often before the policy actually takes effect.

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  2. The fact that a vast swathe of models still assume rational expectations even given clear evidence to the contrary itself seems to falsify rational expectations.

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    1. Anonymous2:45 PM

      In some markets people do form RatEx: http://economiclogic.blogspot.com/2013/01/the-impact-of-valuation-disagreement-on.html

      Noah is simply cherry picking his papers, as he is wont to do.

      Second, many people have been working on alternatives like the robustness approach of Sargent and Hansen. Everyone knows the short comings of RatEx for many situations. The difficulty is viable alternatives.

      Cowen's point stands: http://marginalrevolution.com/marginalrevolution/2009/06/why-its-worth-defending-rational-expectations-theory.html

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    2. In some markets people do form RatEx

      In some markets, sure. Also in quite a lot of lab experiments (but not all!).

      Noah is simply cherry picking his papers, as he is wont to do.

      You mean, citing the papers that gave me the ideas I now have?

      Second, many people have been working on alternatives like the robustness approach of Sargent and Hansen. Everyone knows the short comings of RatEx for many situations. The difficulty is viable alternatives.

      Exactly...that was kind of the point of this post...

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    3. Everyone knows the short comings of RatEx for many situations. The difficulty is viable alternatives.

      Expectations can become self-fulfilling prophesies sometimes. Humans can spot trends and form expectations around them. The problem, though, with trying to formalise this. Much of this is irrational, to the extent that predictions of the outputs of complex dynamical systems are often systemically wrong.

      This means that macroeconomists should — if they want to produce accurate predictive models — model expectations. Doing so is quite another matter, and leads me to the conclusion that quite possibly macroeconomists would do better for the time-being to focus on generalised emergent phenomena, rather than trying to tease out microfoundations.

      I guess that means I think Lucas was way, way, way ahead of his time...

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  3. Noah,

    "So, are Rational Expectations not "just made up"? Does the evidence tell us that this is how people form expectations?"

    Given that RE means that people *know* the complete specification of the model of the universe I think it's pretty safe to say that it's not how expectations are formed. Not only is the world, of course, infinitely complex, but as we now know (thanks to more meticulous mathematical researchers) even rational observers, living in ridiculously simple toy model worlds and endowed with unbounded powers of observations, cannot, even in principle, discover the parameters of those worlds. Even with reasonable, high-information priors, the posterior distributions are hugely fat-tailed total fails. So if the Bayesian agent, even in the *limit* of unbounded observation and processing power, doesn't converge to RE, it's probably safe to assume that RE is, in fact, totally bogus, not even a remote approximation to reality in a world of incomplete markets.

    The great genius of Lucas is how he managed to pull a fast one, that rationality implies RE, on the entire field of macro. He endowed his agents with information only knowable to God, and then he pretended that that was the only way to imagine the real world.

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    1. Wonks Anonymous3:58 PM

      Rational observers can still be quite ignorant about the world they live in. That's the basis of Lucas' "islands" model. Rational agents guess as well as they can given limited information, and learn appropriately from new information (Noah is citing claims that people seem to over-weight more recent information). The importance for policy-making is that with adaptive expecations, a policy-maker might keep increasing the rate of inflation, and each time they would get the same boost from exploiting the "money illusion" of workers. Rational expectations says you can't fool all the people all the time, they will catch on to what you're doing and start demanding much higher wage increases.

      Whether tails are fat is a completely separate question. I've come across people claiming that the EMH must be false because Mandelbrot showed tails are fat, when that very finding is about half of Fama's original EMH paper! And as Noah wrote above, information cascades are compatible with a combination of rational expecations AND incomplete markets. Of course that last element doesn't exclude RE.

      The adaptative expectations wiki page doesn't have much on the empirical evidence that led people to prefer rational expectations, but it links to a page on the cobweb model, which does.

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  4. Anonymous11:20 AM

    Nice post with some cool links, Noah! Could you could give some links to behavioural finance papers that make use of rational inattention, as you say? I have only seen applications in macro. If behavioural finance starts using rational inattention much, I would consider that to be a shame. This whole rational inattention thing was never about getting more psychologically realistic models.

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    1. Check out Xavier Gabaix's papers on sparsity! E.g. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1781234

      I saw this presented at the Miami behavioral finance conference.

      Also check out the work that's being done on "salience" in asset pricing (note: I'm not really convinced by this research...yet...but I think it shows great promise):

      http://www.economics.harvard.edu/faculty/shleifer/files/Salience_Asset_Pricing_final_standard.pdf

      I saw this at AEA this year.

      I'd say that inattention is receiving the most...um...attention out of all behavioral finance ideas right now...

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    2. Anonymous12:45 PM

      Lots of thanks!

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  5. Anonymous11:33 AM

    I think one basic problem with the idea of "Rational Expectation" models of consumer behavior is that the begin with the assumption that the basic supply/demand/cost determiners are in operation. As any one who has worked in a restaurant (and any mathematician) can testify, consumers fulfill appetites according to the Poisson distribution, which is quite different from an economist's "Rational" curve. Perhaps you should begin with that function, and see how past behavior fits.

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    1. I don't think anyone disputes that, I think they assume it smooths out in the aggregate. Whether that assumption is justified or not, I can't say...

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    2. Anonymous1:31 PM

      Are the "Rational" models providing useful predictions? So far it does not seem like it. If that is the case, then a question to investigate could be: "Does consumer activity for a particular sector of the economy in the aggregate smooth out, or still follow Poisson?" If you review housing purchases in run up to the Great Recession, which had a profound economic effect, will the mismatch in Rational curves vs. Poisson help explain what went so wrong?

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    3. Anonymous2:28 PM

      PPS. For instance, take a look at the Securitized Mortgage activity graphs in your January 20 post. Which looks easier, determining an underlying rational function to explain the activity, or fitting the activity to a Poisson curve and determining how variables such as housing unit cost, mortgage availability, and units per purchaser might affect the overall profile? To apply this to inflation look at Govt. Bond purchases, and at what inflection point will the purchase activity suggest a change similar to what looks like happened in the 2005-06 period of the graphs.

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  6. Noah,

    I'm not an economist, but your idea that inflation expectations might suddenly, unpredictably, and uncontrollably accelerate strikes me as highly implausible.

    The reason it strikes me as implausible is that it runs counter to the experience that the US has had with central banking. When people started to realize in the late 60's that the Fed had increased the growth rate of the money supply, inflation expectations increased, but they didn't portend hyperinflation. Why not? Because the change in the Fed's policy was not akin to Zimbabwe style, pedal-to-the-metal money printing. Rather, it was a substantial, not catastrophic change in policy that produced a substantial, not catastrophic change in inflation expectations.

    I think that your theory -- that "the central bank might be unsuccessful in beating deflation, right up until the moment when hyperinflation runs wild" -- is pure speculation that does NOT necessarily follow from the observation that people's inflation expectations are strongly affected by recency bias. A LAG in expectations adjustment does not imply greater volatility in those expectations when they do adjust.

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    1. Well, Japan's experience has not been at all akin the 60s in the U.S. So far, Japan's "substantial, not catastrophic changes" in monetary policy have not led to any appreciable increase in inflation.

      I think that your theory -- that "the central bank might be unsuccessful in beating deflation, right up until the moment when hyperinflation runs wild" -- is pure speculation that does NOT necessarily follow from the observation that people's inflation expectations are strongly affected by recency bias. A LAG in expectations adjustment does not imply greater volatility in those expectations when they do adjust.

      Sure, it doesn't necessarily imply it, but it allows for the possibility...

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    2. I just find it really weird for you to speculate that the market's surprisingly low expectation of inflation *increases* the likelihood of future hyperinflation. That makes no sense to me.

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    3. Well, the idea is that almost anything a central bank could do would have no effect whatsoever on inflation. This might raise the probability that the central bank, determined to inflate at any cost, would unknowingly and accidentally "overshoot".

      So, the probability of hyperinflation would still be very low, but it would actually be higher than if central banks were able to raise inflation smoothly.

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    4. Sam, think of anchored inflation expectations as playing a facilitative role in massive central bank balance sheet expansion. Due to entrenched and exceptionally low inflation expectations, the central bank is at liberty to increase the money supply dramatically without stoking inflation, so it prints more, no inflation, more printing, and so on. When expectations finally shift, the genie is out of the bottle and you have hyperinflation.

      A far-flung possibility, perhaps. The lesson to take away though is that mandarins with their hands on policy levers likely have far less control over the behaviour of a few hundred million people than they've have come to believe. There is a risk that central bankers conclude that the absence of inflation is their doing, that is, a result of insufficient monetary expansion, when it is in fact a function of people's expectations. The remedy would thus be prescribed on a misdiagnosis, and the consequences would be, well, unexpected.

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    5. To add on to MJV's explanation, the central bank cannot control the demand side of the currency. I think it is a fallacy to assume that the central bank can control both supply and demand of the currency. The demand is firmly on the users of the currency. Velocity being inversely related to demand. Extremely high demand such as 2008 financial crisis causes currency velocity to dip alarmingly low, which then allows the central bank to increase the monetary base exponentially, but it does not stoke inflation immediately. This is why Austrians such as Robert Murphy were completely wrong (and Brad Delong does point this in one of his recent posts).

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    6. @ Noah, MJV, & SS

      Thank you for the further explanation, I think I do understand your points. I know analogies are imperfect, but it sounds like what you all are describing could be compared to driving a car with extreme turbo lag, where the driver presses the accelerator too much because there's no immediate acceleration, but when the car finally accelerates it does so much faster than initially planned.

      Here's where I think you all are wrong - in any plausible hypothetical involving the Fed (or the Japanese Central Bank) - the central bank will have been warning people that it will NOT tolerate hyperinflation. That is, if the car goes too quickly, the CB will slam on the brakes. If market participants know this, why should the market's expectations of inflation "snap" so high? Why won't they just snap from 2% to 3%? I know that Noah thinks that a sudden surge in expected inflation from 2% to 50% (doesn't "hyperinflation" mean >50%?) is somehow possible, but I see no plausible reason why it should be so. I also don't see any support for this theory in Noah's summary of the Malmendier paper. In fact, I think that the evidence discussed in this post cuts the opposite way. It seems to me that because inflation expectations are so tough to budge, they'll be *less* volatile, rather than more. But I would posit that neither I nor Noah have any way of proving which view is correct. So, for him to draw a logical connection between the Malmendier paper and the possibility of hyperinflation is wrong. Recency bias leading to anchored inflation expectations does not logically make hyperinflation any more or less likely.

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    7. I know analogies are imperfect, but it sounds like what you all are describing could be compared to driving a car with extreme turbo lag, where the driver presses the accelerator too much because there's no immediate acceleration, but when the car finally accelerates it does so much faster than initially planned.

      Basically, yeah!

      Here's where I think you all are wrong - in any plausible hypothetical involving the Fed (or the Japanese Central Bank) - the central bank will have been warning people that it will NOT tolerate hyperinflation. That is, if the car goes too quickly, the CB will slam on the brakes. If market participants know this, why should the market's expectations of inflation "snap" so high? Why won't they just snap from 2% to 3%?

      Ah, but maybe in this situation, they will stay at 0%.

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  7. Enjoyed the post, Noah.

    "the central bank might be unsuccessful in beating deflation, right up until the moment when hyperinflation runs wild"

    Is there anything else we can rationally expect (cute, huh?) to happen in Japan? And what can the U.S. learn from it?

    The timing is hard to determine, but doesn't the fundamental problem of the buildup of an impossible-to-service quadrillion yen in gov't debt (which will immediately implode if average yields reach even just 2 or 3%) make a sudden shift in expectations inevitable?

    Default or devalue - these will be the options left on the table once "kick the can" is taken away by the market. (see Greece, Spain etc.)

    Why then - is the US following the same path of ZIRP and attempting to "support" the economy by replacing unsustainable private debt creation with unsustainable public debt creation?

    All with the expectation that eventually sustainable economic growth will magically emerge to help us grow out of this little temporary problem we've been in for the past 10 years?

    We live in interesting times...

    www.MoneyForNothingTheMovie.org

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  8. "...expectations react in highly unstable, nonlinear ways..."

    Oh, you Keynesian, you!

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  9. Noah,

    Very interesting post. Since adaptive learning is a domain of neuroscience, could macro econ use the mathematics used in brain science, such as spatio-temporal multi fractal analysis? Time series of dynamic complex systems do exhibit this behavior, e.g., human sleep, human heart, etc.


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  10. ok but you and I both know that "rational expectations" is not an individual phenomenon. It's an expression of the efficiency of aggregate behavior (Sumner would cry "fallacy of composition"). We can have many people following rules of thumb or forming expectations in an irrational way, but which average out in the market place...because its really the distribution of beliefs that matter. To put in a different context, we both know that an electron in a potential well has a small probability of escaping... but we don't say that the electron violated the laws of physics if we observe that a few electrons out of 10000 escaped. The laws of individuals do not (necessarily) aggregate. In finance we have arbitrage. It only takes one sufficiently motivated individual with contrarian beliefs and enough capital to make the market as a whole efficient.

    To talk to me about rational expectations in the context of, say, inflation expectations you have to tell me not about whether each individual is rational, but about the distribution of those beliefs (and the correlation). That is, are beliefs sufficiently diversified and/or is there herd behavior. I don't know if a particular individual is prone to sudden and "catastrophic" changes in expectations (Dennis Gartman certainly seems to change his mind a lot), but what is the probability that most of the market shifts their beliefs, unless (say) Ben Bernanke tells them to? Is there a critical mass of people that need to change their mind? in other words, if beliefs are a random walk, what matters is that they are unbiased and uncorrelated ... not rational.

    All i can say is that after a zillion years of looking at squid deals, if its too good to be true it usually is. If the market appears irrational at the root is some sort of moral hazard or tax (or regulatory) peculiarity that is driving incentives and the market. Individuals *might* be individually less than rational, but its a herd of hedge fund managers going to the same conference and crowding the same trade that piques my interest.

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    1. dwb, great minds think alike! :-) It seems I was writing (below) while you were posting.

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    2. ok but you and I both know that "rational expectations" is not an individual phenomenon. It's an expression of the efficiency of aggregate behavior (Sumner would cry "fallacy of composition"). We can have many people following rules of thumb or forming expectations in an irrational way, but which average out in the market place...because its really the distribution of beliefs that matter.

      Sure. I never said "individual expectations". What I'm saying in this post applies perfectly well to aggregate expectations.

      in other words, if beliefs are a random walk, what matters is that they are unbiased and uncorrelated ... not rational.

      Think carefully about this. What does it mean for a time-series to be "unbiased"? Remember that the average over time is not the same thing as aggregation over individuals. If the expectation of the aggregate belief time series is equal to the true value, that still allows aggregate beliefs to differ wildly from the true value, possibly for long periods of time. That could have big economic consequences.

      In other words, saying "On average, over time, the economy neither overpredicts nor underpredicts inflation" tells us very little about whether the market overpredicts or underpredicts inflation at a point in time...and knowing the latter is very important for understanding macroeconomic dynamics.

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    3. not everyone uses their lizard brain to form expectations, and those who use models don't use the same data or even functional form. Its hard to make a case for this in a mature developed market. In a new, opaque market maybe.

      But if the lizard brain mechanism for expectations formation exhibited weird dynamics or switching behavior it would not just show up in financial markets. I think it would show up in elections, for example. People form expectations of who will win, and this affects turnout. Polling data would be unstable. You couldn't even do something as simple as go into starbucks, because the manager would have no idea how much coffee to have on hand to satisfy demand.

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  11. I find the criticism of rational expectations rather misplaced. I do not think anyone, not even Lucas, would argue that every person forms their expectations in the RE manner. At the individual level, models of bounded rationality resulting in a heterogeneity of expectations are much more descriptive of the real world. As Muth has pointed out, the point has always been whether individual errors are correlated or not. If they are not, given their simplicity and elegance, assuming RE for all agents would be a good way to model expectation formation even if no individual actually behaves this way. If they are, then we have a problem. So, I think, this is the discussion we ought to be having.

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    1. I find the criticism of rational expectations rather misplaced. I do not think anyone, not even Lucas, would argue that every person forms their expectations in the RE manner.

      Fortunately, I never accused Lucas of saying this...see my earlier comment to dwb. We're talking about aggregate expectations here.

      As Muth has pointed out, the point has always been whether individual errors are correlated or not.

      Yep.

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    2. Noah, sure, I did not have you in mind. I meant the general discussion!

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    3. Noah, so do you find aggregate expectation cascades likely?

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    4. Noah, so do you find aggregate expectation cascades likely?

      Um...yes, I guess. I doubt that the mechanism in the 1990s "information cascade" literature is correct; I suspect most real cascades are a function of inattention/attention processes, or of behavioral herding ("stories", as Gene Fama would say).

      I suspect there is some of this going on. I don't really know how much, though...it's a huge area of inquiry.

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    5. A good example is the 1987 stock market crash.

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  12. My "rational expectation" is that the financial statements of many large corporations are works of fiction and Wall Street is full of people who are incompetent, dishonest or both. I also have a "rational expectation" that the Republican Party has a goal of steering wealth from the middle class to the very wealthy.

    Given those rational expectations I am not investing. My expectations of course can be moved by some simple expedients - the accounting profession cleans up its act, the SEC and DOJ get on with their jobs, a few thousand bankers get sent to prison and the Republicans start publishing policy proposals that go beyond magical thinking.

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    1. Wonks Anonymous4:03 PM

      So you think bank deposits will get you the best return, or are you keeping cash/gold bullion under the mattress? If you think stocks are going to tank, you could try shorting them.

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    2. I have more money than usual in term deposits. I have from time to time shorted stocks and made money at it overall but you run up against the problem that "the markets can stay irrational longer than you can stay solvent." Right now you also have the problem that government, including the Fed, is working very hard to manipulate the markets higher.

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  13. Noah,

    "non-rational expectations, like Bayesian learning"

    At this point you really should capitalize Rational Expectations. It's *bad* to imply that Bayesian learning is not rational. It is RE which is, in fact, deeply irrational, involving agent belief in some kind of God-given model dynamic. Rational agents *are* Bayesians who suffer deep uncertainty about the model of future dynamics, because that's all they've got! Who endowed them with transcendent knowledge of the model of the universe?

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  14. dwb,

    "ok but you and I both know that "rational expectations" is not an individual phenomenon. It's an expression of the efficiency of aggregate behavior"

    "if beliefs are a random walk, what matters is that they are unbiased and uncorrelated ... not rational."

    Your comment doesn't clearly distinguish between "rational" and "Rational Expectations." What you seem to be saying is that financial market competition leads to an efficient implied market measure, which could reasonably be thought of as the probability measure of a rational representative agent. That would be a very weak definition of RE, since it's perfectly consistent with Bayesian updating. If these definitions are to mean anything, we ought to stick with RE in the Lucas sense of the agent measure being the same as the "true" measure, which is a much stronger claim.

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    1. Yes. You can definitely get informationally efficient markets without RE. RE is a MUCH stronger assumption than the EMH.

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  15. Anonymous3:44 PM

    If you want recent evidence on the formation of expectations, Yuriy Gorodnichenko has a couple papers:
    http://emlab.berkeley.edu/~ygorodni/CoibionGorodnichenko.pdf
    http://emlab.berkeley.edu/~ygorodni/CG_expform.pdf

    He shows how you can differentiate between full-information rational expectations, adaptive expectations, rational inattention and sticky information. They also derive similar predictions for some other models. He and his coauthors then take these predictions to the data for different kinds of agents. The punchline seems to be that rational inattention works best in most respects.

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    1. Thanks for sending me those!!

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  16. Anonymous3:46 PM

    It seems to me that RE exists because it is the only basis on which economists can claim relevancy.

    If one instead looks at the entire array of human factors that go into perceptions about the future, well then economics really doesn't matter much as all.

    I just finished Vincent Bugliosi's Reclaiming History: The Assassination of President John F. Kennedy. Mr. Bugliosi justifies his work based on the belief cascades washing across our Country due to the abuses of the Media and the Conspiracy cabal of the simple truth that Oswald acted alone.

    When I see an economic model with Hitler playing a prominent role in the 1930s, well then I might pay some attention. If people had RE, after 1933, they were putting their few dollars under a mattress.

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    1. Wonks Anonymous4:06 PM

      Scott Sumner has actually presented some interesting data on how markets reacted to the political situation in Germany at that time.

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  17. Wonks Anonymous,

    "Rational observers can still be quite ignorant about the world they live in."

    I wasn't talking about rational vs irrational agents. I was talking about the limits of the ability of *rational* agents to form model consistent expectations.

    "incomplete markets. Of course that last element doesn't exclude RE."

    Actually, it kind of does. If markets are complete, the agent can compute the measure from market prices. If not, agents have to compute the measure based on historical observations (econometrics). So the question is, given some *unknown* true dynamic, how well can an embedded econometrician back out the parameters of that dynamic? Here you really should read Martin Weitzman's Subjective Expectations paper. What he shows is that even for very simple dynamics, the econometrician *cannot*, given arbitrarily many observations of the process, even in principle determine the
    parameters of the dynamic. Even starting with a prior that is very close to the true measure, the posterior does not converge to the true measure in the limit of infinitely many observations, and fails to do so in a manner that has enormous impact on the thickness of the tails of the distribution of asset returns.

    Though the agents *could* have model consistent expectations, there is no way they could know whether they did or not (barring complete markets). So in practice, incomplete markets do, in fact, exclude Rational
    Expectations.

    "Rational observers can still be quite ignorant about the world they live in. That's the basis of Lucas' "islands" model."

    Lucas' Island model merely *assumes* RE, so this totally misses the point. The whole point is that agents do not, in general, have an adequate way to develop such expectations. I don't see why that would invalidate Lucas' Philips curve critique, which you can surely make without RE, using Bayesian agents alone. It does, however, illustrate the long and harmful macro tradition, created by Lucas, of treating RE as a direct implication of the Lucas Critique.

    The Weitzman result shouldn't, BTW, be very surprising to anybody who knows just a little bit about continuous stochastic processes. Even in the basic case of drifted Brownian motion, it is not possible *in principle* to distinguish one drift rate from another, even given perfect knowledge of a particular path. If that Brownian motion drives the path of future volatility of income, not knowing the dynamics of the drift will be extremely detrimental to capital asset risk premia.

    "Whether tails are fat is a completely separate question."

    No, these are deeply related issues. Read Weitzman.

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    1. Yep, everyone should read Weitzman.

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  18. Anonymous7:02 PM

    I don't know who taught you rational expectations in grad school; you don't seem to have gotten it. RE is internal consistency : the aggregate behaves as the sum of the singles and people know&believe that's how the whole thing works. In other words, the law of motion of the aggregate variables ends up being consistent with the individual behavior of the agents. That's it. That's why Lucas is saying that it's the requirement you need to avoid making shit up.
    If you don't get it (as , to be fair, many first year ph d students many times don't: it's no big deal), read some paper that uses the recursive competitive equilibrium concept. It becomes all of a sudden crystal clear.
    Good luck.

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    1. I don't know who *you* are addressing (me or Noah), but you are wrong that "[RE is] the requirement you need to avoid making shit up."

      That's what Lucas said, or at least, he certainly implied it. And that's what first year phd students think. In fact, there are lots of perfectly rational behaviors which are not RE. The expectations of rational Bayesian econometricians with perfect knowledge of the model history is a far more "rational" agent model than RE, and does not, in general, converge to RE.

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    2. Anonymous9:37 AM

      I was addressing Noah.
      To answer to your comment, "Rational expectations" has never pretended to be the only perfectly rational behavior (?). The paper you posted before is an example, of course (maybe that's why it would be better just to call rational expectations an internal consistency requirement). The problem is that once you decide that your model doesn't need to be internally consistent, then anything goes. The equity premium puzzle is a puzzle for models with internal consistency and the other usual stuff we know; once you take that away, there's no puzzle anymore and that should be obvious. The problem is that after you take away that requirement, there's not an obvious way to discipline your modelling choices either. Period...

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    3. The paper you posted before is an example, of course (maybe that's why it would be better just to call rational expectations an internal consistency requirement). The problem is that once you decide that your model doesn't need to be internally consistent, then anything goes.

      No, I disagree. Labeling RE "internal consistency" is just the same as inventing a new definition for "internal consistency". Non-RE models can easily be mathematically consistent. RE requires that expectations be consistent with outcomes. That is the definition of RE. Thus, saying "RE = internal consistency" is just restating the RE hypothesis. But it still could easily be wrong.

      The problem is that after you take away that requirement, there's not an obvious way to discipline your modelling choices either. Period...

      That's right. But why should we want an "obvious way to discipline our modeling choices"? We should seek models that match observed reality, even if the methods used in those models are non-obvious.

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    4. Anonymous10:49 PM

      "That's right. But why should we want an "obvious way to discipline our modeling choices"? We should seek models that match observed reality, even if the methods used in those models are non-obvious"

      As long as you impose internal consistency to your model, be my guest.

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    5. Essentially all models are internally consistent, mathematically. Rational Expectations is not required to make a model internally consistent.

      A model can be perfectly internally consistent and have the most irrational, crazy expectation formation process imaginable.

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  19. I think the point of RE is that it's the simplest way (in a stochastic context) to exclude the possibility that a model will be vulnerable to the Lucas critique. Given that human behavior is so hard to model accurately, I would be suspicious of a more "accurate" model of expectations that was vulnerable to Lucas critique if people turn out to behave a bit differently from the way it assumes. On the other hand, RE can lead you to some obviously foolish conclusions, even in a world where it almost (but not quite) literally holds. There is a need for a counterbalance to the Lucas critique (call it the Rowe critique, perhaps, until a better name, or a more generally articulated version, comes along) to show how the rational expectations assumption could lead policymakers to behave foolishly.

    I see RE as a tool, a type of sanity check to make sure you're not doing something that depends on being able to fool people, and I think it's a good tool. But it's a shame that it seems to be taken so seriously these days, as if it were actually a good approximation of how people really behave.

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    1. Anonymous7:50 PM

      "I see RE as a tool, a type of sanity check to make sure you're not doing something that depends on being able to fool people, and I think it's a good tool."

      EXACTLY.

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    2. I think the point of RE is that it's the simplest way (in a stochastic context) to exclude the possibility that a model will be vulnerable to the Lucas critique.

      Yes. But it is not the only way to exclude this. And it may exclude much, much more.

      Also, remember that forecasting doesn't care about the Lucas Critique.

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    3. "Also, remember that forecasting doesn't care about the Lucas Critique."

      Oh, yes, definitely. Private sector forecasters who use RE are being foolish IMO (and I doubt there are a whole lot of them, because they will have learned that it was foolish if they hadn't already figured it out).

      However, forecasting by policymakers is a bit more complicated issue. If the forecast is just meant to be an honest best guess of the outcome, for its own sake, then there's no point in using RE. On the other hand, if the forecast is going to guide policy, then the Lucas critique applies, so there's a case for using some Lucas-robust model of expectations to generate a forecast, or at least to test the robustness of the forecast. As you note, Lucas-robust doesn't imply RE, but I'm a bit skeptical of introducing more complexity by using more realistic but still Lucas-robust models of expectations. The more complicated things get, the more opportunity there is to draw conclusions without really knowing what's going on.

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    4. The more complicated things get, the more opportunity there is to draw conclusions without really knowing what's going on.

      Possibly the most perspicacious sentence I have ever read...

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  20. Anonymous7:17 PM

    I looked at the malmendier paper
    It is about how people responded to a telephone survey, where the interviewer asked people what they thought about inflation.
    is there any data showing that these responses reflect peoples actual behaviour in the real world ?

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    1. Not unless we can observe the financial portfolios of various age cohorts!

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  21. Bill Ellis7:50 PM

    So a policy that relies on expectations to boost GDP is Inferior to a Fiscal policy that actually boosts GDP by spending more and putting actual salaries into the hands of people that HAVE to spend it. (the recently unemployed ) ?

    You sound like a Keynesian .

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    1. Anonymous7:00 AM

      Anyone with any sense is a Keynesian.

      We (the World) have been, since June 2007, running experiments, everyone proving him correct.

      He even correctly predicted low information comments, like yours.

      Mostly importantly, Keynes said that deficits in the US would help, but not that much. The Countries that needed to run large deficits were those with high positive current accounts (high exports) (China and Germany) who were exporting their excess capacity, causing unemployment elsewhere.

      GB is learning the lesson. It wants a total re-balance in the EU. Why, because GB has come to realize that it cannot solve its problems without ending imports.

      If anyone thinks otherwise about GB, I would love to hear the answer.

      The same is true for France and all the Southern European countries. They must re-balance and end their current account deficits.

      Our current account deficit is $500 billions. If we ended imports, totally, that would be $500 billion in new jobs.

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  22. "the central bank might be unsuccessful in beating deflation, right up until the moment when hyperinflation runs wild."

    FWIW, I once tried to think about such discontinuity in terms of "phase transition" and "latent heat" here.

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  23. Noah, the difficulty of updating expectations also jibes with the idea that for right-wing economists, it's always the 1970's again.

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  24. Great idea, and I think there are lots of examples of this. Larry Summer just did an interview where he quoted his adviser as having said that things always take longer than you think they should and then go faster than you think they will. It takes a long time to become a flash-in-the-pan!

    There are oodles of examples of discontinuous events. The question to start with would be why WOULDN'T expectations exhibit discontinuity?

    Lucas himself will of course be the cause of just such an event in Economics. He's clearly wrong, a tremendous amount of work is being expended on making this case. There will be a moment where the weight of the evidence outweighs the weight of his influence, (when the 100th monkey gets it so to say) and viola! Macro will be free to advance.

    [as an aside, the 'weight of Lucas' influence is another phenomena, you likely saw the recent post about the military term for how highly dubious ideas become not just accepted, but viewed as certainties. “Incestuous amplification” happen when a closed group of people repeat the same things to each other – and when accepting the group’s preconceptions itself becomes a necessary ticket to being in the in-group. A fundamentally flawed notion becomes part of what everyone knows, where “everyone” means by definition only people who accept the flawed notion. IE creates discontinuity when the evidence overwhelms beliefs.]



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    1. Incestuous amplification, you mean, like you coming here to repeat Krugman's theories?

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    2. Incestuous amplification is just another name for resonance. When the wavelength of the bullshit is an integer divisor of the size of the echo chamber, the bullshit reinforces itself until everything explodes. PHYSICS!

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  25. I wonder: wouldn't the simplest way to get (reliable) expectations to feed into models be simply to, you know, ask people ? A good old-fashioned survey. I can't fathom why economists insist on stumbling on what is perhaps the toughest problem in all of the sciences, instead of circumventing it.

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    1. The Malmendier paper is a survey.

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    2. Surveys are plagued by multiple problems which make them relatively less trustworthy. I haven't looked into the Malmendier paper, so I can't say anything about that. However, in what order you ask, how you ask, etc., all have tangible effects on the outcomes. What's the most objective way of wording questions, and what's the most reasonable order, etc.? Who knows.

      Hence why you think they circumvent. It is a good point, though. I imagine it wouldn't be too difficult to do. I'd just take it with a grain of salt.

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    3. Anonymous6:59 AM

      In addition to the general problems of surveys, there are some additional problems which prevents researchers from using expectations in their models.

      First, there does not exist an aggregation theorem for beliefs, i.e. something similar to the aggregation of preferences. So researchers have to rely on static models that can be solved or keep the numbers of agents small in a computational model.

      Second, to get interesting dynamics the beliefs of the agents in a model have to change, i.e. in an asset pricing model with fixed heterogeneous beliefs agents will only trade because of endowment/dividend shocks. Hence, we will get the same aggregate dynamics as in the standard model.

      So, in order to get some interesting dynamics in the model we will need the beliefs to change, i.e. we need some theory for learning. However, many learning theories have the property that the beliefs of everyone will converge. Whether you consider this a bug or a feature of the model depends on your preferences.

      The third problem is the welfare evaluation in these models, i.e. ex-ante at most one belief can be correct but the question is which one.

      To sum it up: Deviating from the rational expectations hypothesis and allowing for heterogeneous beliefs is not as trivial as it sounds. While some progress has been made, there is still a lot to do.

      There is also a nice survey from Woodford about the different approaches in the literature:

      http://www.columbia.edu/~mw2230/AREcon.pdf

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    4. @Noah Smith: The paper uses a survey but AFAICT building a model is a stated goal. My point was: is it possible to skip the expectation-modelling stage altogether and use survey data directly in macro models ?

      @Injured: To produce an expectation model you have to either (a) simulate the brains of a few million humans and their environment (b) make one up or (c) parametrize and (fit to/validate with) survey data. To this non-economist (c) looks like the only viable (i.e. scientific) option. Any noise in the surveys will end up in the model anyway.

      @Anon: Interesting, thanks.

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    5. @To

      "parametrize and (fit to/validate with) survey data."

      Why survey data? There's a lot of different ways of finding estimates for parameters.

      "Any noise in the surveys will end up in the model anyway."

      No, not necessarily "noise" if there's bias in the survey that leads people to consistently pick one way. The classic example was:

      Are you happy? Do you have a significant other?

      And

      Do you have a significant other? Are you happy?

      That's not noise since it will systematically make the first group happier, and the second less happy.

      Unless you mean multiple different surveys and their effects average out. I don't think that's the case, but even if it is, I'd say that still doesn't eliminate other ways of estimating parameters.

      Good points, though. What do you mean by "make one up"? As in a representative agent?

      @Anon

      "Whether you consider this a bug or a feature of the model depends on your preferences."

      Very interesting, but I guess it depends on the scenario. Perhaps it could diverge to a distribution of beliefs? Although that brings in noise, it won't account for the more tangible effects of why people have heterogeneous expectations.

      All good points, and thanks for the link.

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  26. I have been hearing my Canadian federal government (Conservatives, I'm afraid) for the past couple of years warning citizens to beware of the inevitable rising interest rates on the horizon. None of the Harper team, as far as I have heard, have explained what they think will trigger this rise.

    As I understand it, prices rise when demand increases or supply falls. Is our prime minister implying that the money supply is going to tighten up? Since we have sovereign currency, I can't see how that would happen. (Though he has banished the Canadian penny, and is talking about scrapping the nickel, too.)

    So, can we look forward to higher demand then? I'm not sure where that demand would come from. Although Canadian citizens are not so bad off as the Americans, we're also not springing forward with higher wages, more secure jobs, and in general better prospects for our households. We're going the opposite direction, if anything.

    So, do our conservatives expect to see businesses or foreign investors driving up interest rates? In which case, I am thinking that the time for ordinary Canadians to borrow is now, while rates are laughably low, before the big financial hippos jump in the watering hole and get it all churned up.

    Or lastly, do they not actually expect rates to rise, but are saying so at every opportunity for some arcane reason of their own?

    Anyone who can offer some illumination on this topic would be my best buddy. This week, anyway.



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    1. Anonymous3:14 AM

      They are trying to scare Canadians into laying off from a debt fueled consumption bubble that is rivaling the American pigs at their high point of greed. Real estate in Vancouver and Toronto would be unaffordable to an average Canadian and stagnant productivity means most of the recent consumption has been enabled by ultra cheap money. And while its true that if you can afford it now is the time to lock down cheap credit, the problem is that most credit in Canada is on a 10 year re-financing schedule and if you go out and buy a Vancouver condo for 400,000 expecting to pay 1000/1500 a month and in 5 years when you try to refinance it jumps to 3000 a month youll be out of a home. And your bank will have a bunch of holes in its balance sheet where its customers used to be.

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    2. I have been hearing my Canadian federal government (Conservatives, I'm afraid)

      The Canadian government is probably to the left of the Obama administration.

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    3. Probably, but the Harper government is far to the right of most Canadian citizens.

      I have long suspected that we are far to the left of Americans because we are so closely involved with them. We see their news, we have many relatives cross border, we visit and travel in the US, and we share enough culture that we can easily watch -- and judge-- their culture and politics.

      Unfortunately, they don't seem to learn from our example of cheaper health care, much lower violent crime levels, much smaller prison system, etc. also unfortunately, their political strategies have been percolating across the border. Harper had Republican advisors during the last election, and has taken a lot of their strategies and approaches.

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  27. Aren't there many real time surveys such as TIPS and Treasuries which implicitly embed expectations in prices?
    Wouldn't it be very difficult to design a survey that adds any information that a spot price for a physical would not have.

    I am also bothered by your closing few paragraphs, they seem to invert the map and the territory. RE is an imperfect map, but that doesn't have any effect at all on the territory. Expectations are what they are. Whether or not some model of expectations turns out to be wrong has no scary implications whatsoever on expectations or what expectations may be. The only possible implication of showing an existing effort at modeling expectations to be incorrect is positive in as much as it would reflect an advancement of our collective knowledge of what expectations are.

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