Uncertainty, learning, and rational expectations

20 Aug, 2020 at 11:12 | Posted in Economics | 19 Comments

The rational expectations hypothesis presupposes — basically for reasons of consistency — that agents have complete knowledge of all of the relevant probability distribution functions. And when trying to incorporate learning in these models — trying to take the heat of some of the criticism launched against it up to date — it is always a very restricted kind of learning that is considered. A learning where truly unanticipated, surprising, new things never take place, but only rather mechanical updatings — increasing the precision of already existing information sets – of existing probability functions.

Nothing really new happens in these ergodic models, where the statistical representation of learning and information is nothing more than a caricature of what takes place in the real world target system. This follows from taking for granted that people’s decisions can be portrayed as based on an existing probability distribution, which by definition implies the knowledge of every possible event (otherwise it is in a strict mathematical-statistically sense not really a probability distribution) that can be thought of taking place.

But in the real world it is — as shown again and again by behavioural and experimental economics — common to mistake a conditional distribution for a probability distribution. Mistakes that are impossible to make in the kinds of economic analysis — built on the rational expectations hypothesis — that mainstream economists are such adamant propagators for. On average rational expectations agents are always correct. But truly new information will not only reduce the estimation error but actually change the entire estimation and hence possibly the decisions made. To be truly new, information has to be unexpected. If not, it would simply be inferred from the already existing information set.

In rational expectations models new information is typically presented as something only reducing the variance of the parameter estimated. But if new information means truly new information it actually could increase our uncertainty and variance (information set (A, B) => (A, B, C)).

Truly new information give birth to new probabilities, revised plans and decisions – something the rational expectations hypothesis cannot account for with its finite sampling representation of incomplete information.

In the world of rational expectations, learning is like being better and better at reciting the complete works of Shakespeare by heart — or at hitting bull’s eye when playing dart. It presupposes that we have a complete list of the possible states of the world and that by definition mistakes are non-systematic (which, strictly seen, follows from the assumption of ‘subjective’ probability distributions being equal to the ‘objective’ probability distribution). This is a rather uninteresting and trivial kind of learning. It is a closed world learning, synonymous to improving one’s adaptation to a world which is fundamentally unchanging. But in real, open world situations, learning is more often about adapting and trying to cope with genuinely new phenomena.

The rational expectations hypothesis presumes consistent behaviour, where expectations do not display any persistent errors. In the world of rational expectations we are always, on average, hitting the bull’s eye. In the more realistic, open systems view, there is always the possibility (danger) of making mistakes that may turn out to be systematic. It is because of this, presumably, that we put so much emphasis on learning in our modern knowledge societies.

So, where does all this leave us? I think John Kay and Mervyn King sum it up pretty well:


The disregard of radical uncertainty by a generation of economists condemned modern macroeconomics to near irrelevance … Keynes’ critique of ‘getting on the job’ without asking ‘whether the job is worth getting on with’ would prove to be as true of the new macroeconomic theorising as of the older econometric modeling …

Over forty years, the authors have watched the bright optimism of a new, rigorous approach to economics dissolve into the failures of prediction and analysis which were seen in the global financial crisis of 2007-08. And it is the pervasive nature of radical uncertainty which is the source of the problem.


  1. Kingsley and Bruce, thanks for forcing me to clarify my thoughts. My goal is to write a prospectus for a Green hedge fund and pitch it to the Bezos Earth Fund and local governments, so this practice is invaluable.
    My strongest reaction is like Solow’s in the quotation Lars keeps reposting: I’m getting drawn into a discussion of cavalry tactics at the battle of Austerlitz when I really want to challenge the efficiency of markets. If prices aren’t efficient in the real world, what enforces the theory that derivatives must be zero sum?
    Second, even if you allow that a single derivative trade must be zero sum, that does not preclude the possibility of several derivatives being combined into a trade in such a way that all counterparties can book a profit. If you are hedging delta risk and a counterparty is hedging gamma risk, or some other derivative risk measure, you can both book trading profits on the ensemble of the derivative trades.
    An analogy: bits are singly binary, but you can combine bits into programs that execute non-binary logic. Although single derivatives are zero sum, combinations of derivatives can add up to a net positive.
    Kingsley’s quotation contains phrases such as “the value of the firm remains unchanged”, which I challenge. Such reasoning takes market efficiency as a given. But real market agents know that price is a liar.
    “In the capital market, the value of the two cash flows are the same.” This may be trivially true, but ignores the psychological signaling involved in paying a lower borrowing rate. If you are good enough credit risk to get such a low rate, you can get even better terms from another lender. You can thus psychologically leverage a low rate which you got in a zero sum swap, into even lower cost of capital on a subsequent loan. If you are getting a low rate, you can mark up the asset as being low-risk. In a market where the Fed’s administered prices dominate, any notion of efficient markets must be abandoned. The balance sheet valuation of assets becomes a highly subjective exercise, which allows for lots of free lunches and emergent money.
    Bruce said: “A so-called Hedge fund may be a counterparty to a business firm’s investment in a risk-reducing hedge.”
    It gets worse because they can both be part of the same parent firm, and they can make the parent firm money even if one seems to be losing …
    Rehypothecation is yet another strategy whereby one asset can be multiplied across different balance sheets, again violating the core assumptions that drive the Modigliani-Miller theorem in the first place. In the real world, hedge funds mark up assets arbitrarily and bluster their way out when caught, or into a Fed bailout, or into a legal victory (like Leland Stanford was acquitted of financial fraud because he had appointed the majority of the judges himself …).

  2. Robert,
    As you know, there is a vast literature on hedging and Modigliani-Miller. So it would be inappropriate for us to get into an extended discussion here.
    However, let me just mention that I think you are seriously incorrect in suggesting that M-M is only relevant to the initial finance of a business and that “hedging and trading generate new value”.
    Most risk management literature agrees with the following on the assumptions of M-M:
    “The M-M Proposition of Hedging states that the value of a firm is independent of whether or not it hedges. Again, the argument is: the cash flow stream generated by the firm’s assets determines a firm’s value. If the firm lowers the risk of its cash flow stream by selling a risky cash flow in the capital market in exchange for a low risk cash flow—i.e., by hedging—the value of the firm remains unchanged. The value of the unhedged, high-risk cash flow is equal to the value of the hedged, low-risk cash flow. While this may seem counterintuitive at first, a moment’s reflection resolves the problem. When selling the high risk cash flow to the capital market, the firm is, of course, forced to also surrender a correspondingly high return. It receives in exchange a low risk, but also low return cash flow. In the capital market, the value of the two cash flows are the same.”

    The rest of this brief article is similarly very clear and worth reading.

    • Strictly speaking, M-M stands for proposition that the total value of the business firm’s cash flow is independent of how it is leveraged not whether it is hedged. The argument is that leverage, per se, does not alter the cash flow from business operations and so the sum of market value for various debt and equity claims on that cash flow must continue to equal the market value of the cash flow in total.
      Classic M-M does not encompass the possibility the firm might be forced to liquidate or constrain operations by an unfortunate choice of extreme leverage, so a hedge is not within its scope of reason.
      Leverage is usually explained as a means of amplifying equity returns, with arguably some increase in risk of financial failure and extinction. Hedging is an investment taken to reduce risk: insurance against failure for example. The cost of a Hedge would reduce the cash flow from the business operations available to pay the claims of equity and debt.
      A so-called Hedge fund may be a counterparty to a business firm’s investment in a risk-reducing hedge. This makes Robert’s argument somewhat confusing.

  3. Kingsley:
    The Modigliani-Miller theorem is about the irrelevance of how you get initial capital. I could borrow, issue stock, or use savings to start a Green Hedge Fund; it doesn’t matter. Then I use the money to invest in defined-risk and perfectly-hedged trades. The hedging and trading is how I generate new value.
    “The M&M propositions remind us that it is corporate strategy that produces value” (from http://pages.stern.nyu.edu/~adamodar/New_Home_Page/articles/MM40yearslater.htm ). The hedging is the corporate strategy. The financial innovations are the firm’s business; they are why you raised capital in the first place.
    Thus, Modigliani-Miller is somewhat irrelevant to my point. Financial innovations create new value, no matter how you financed the original capital.
    Kingsley also said:
    “It might help me if you could give simpler more authoratitive references. I find that your links are difficult to understand and that your interpretation of them seems to be based on a peculiar understanding of business finance.”
    I think you owe it to yourself to try to understand the links without relying on “argument from authority”. See for example Jeff Snider’s latest ( https://alhambrapartners.com/2020/08/18/part-2-of-june-tic-the-dollar-why/ ):
    > Within the old paradigm, the one that still operates as convention, people including all the “experts” operating within it can’t understand nor appreciate this significance; collateral is just shadows dancing on the wall of the cave to them. Forever blind by adhering to that old way of interpreting the world, even some really smart people will end up appearing as bumbling, incoherent idiots.
    @ billinscd who said: “Why should the Fed back up the counter party default risk?”
    Because the Fed thinks that things will be much much worse if they don’t. In 1929 they let banks fail; Bernanke learned the lesson and turned on the money printers in 2008. Powell learned from Bernanke, and ramped up the printers even more. I hope one day they learn that they can print a universal basic income while using indexation and inflation swaps to neutralize nominal inflation’s unwanted effects.

  4. The eminent logician,mathematican and philosopher of science, Imre Lakatos long ago defined whole neoclassical school of economics as pseudoscientific alongside with with among other Ptolemaic astronomy, Immanuel Velikovsky’s planetary, Lysenko’s biology,cosmogony etc.

    According to the demarcation criterion of pseudoscience proposed by Lakatos, a theory is pseudoscientific if it fails to make any novel predictions of previously unknown phenomena or its predictions were mostly falsified, in contrast with scientific theories, which predict novel fact(s).

    Progressive scientific theories are those which have their novel facts confirmed and degenerate scientific theories, which can degenerate so much they become pseudo-science, are those whose predictions of novel facts are refuted. As he put it:

    “A given fact is explained scientifically only if a new fact is predicted with it….The idea of growth and the concept of empirical character are soldered into one.” See pages 34–5 of The Methodology of Scientific Research Programmes, 1978.

    Lakatos divided these ‘methodological rules’ within a research programme into its ‘negative heuristics’, i.e., what research methods and approaches to avoid, and its ‘positive heuristics’, i.e., what research methods and approaches to prefer. While the ‘negative heuristic’ protects the hard core, the ‘positive heuristic’ directs the modification of the hard core and auxiliary hypotheses in a general direction.

    Since mainstream economics is dominated by more or less of variated versions of old neoclassical ideas and constantly fail to predict almost any novel facts,best exemplified by the failure to predict the great financiel crisis of 2007/8, that only about 10-20 heterodox economist had a warned about. As I see it the mainstream economics as the Rational Expectations school should be treated equaly as Voodo or Astrology and in it´s shame that this sort economist has still such power in society,and get the prestige of a faked “Nobel Price every year.

  5. Robert,
    It might help me if you could give simpler more authoratitive references. I find that your links are difficult to understand and that your interpretation of them seems to be based on a peculiar understanding of business finance.
    Perhaps a better starting point is the very powerful and well known Modigliani-Miller Theorem. This suggests that the methods of financing and the character of financial risks are likely to have little effect the overall market value of a firm.
    So financial techniques (including compicated hedging schemes and even “perfect” hedging) are unlikely to increase the market value of a firm. To the contrary, hedging is likely to reduce the value of a firm because of the costs of financial advisors, brokers’ commisions, etc).

  6. If radical uncertainty is pervasive, aren’t prices arbitrary and therefore inflation mere noise as well?
    The innovation of finance is ways of hedging bets so that arbitrary price movements still net you profit. You can make directionless bets: the stock can move up or down but if you exit within your defined range, you’ll profit either way.
    Counterparty default risk is assumed by clearinghouses and ultimately the Fed.
    I think economists are unaware of financial trades that clearly define risk and allow you to perfectly hedge. Lars certainly never mentions options or butterflies, which are financial methods designed to minimize uncertainty. Big banks don’t make trading profits by trading on noise, they define risk and hedge so that they win no matter what uncertainty manifests in prices.
    Keynes can possibly be excused because finance has evolved so much since his day. But modern economists who disregard financial methods of handling uncertainty seem to be missing a very important part of how the world really works …

    • Robert,
      “But modern economists who disregard financial methods of handling uncertainty seem to be missing a very important part of how the world really works …”
      Hedging strategies explained in textbooks or manuals is not reality.
      The people who probably make money in these things are the market makers.
      Hedging costs money – the more your position is hedged, the higher your cost.
      Positions probably only make money to the extent they are not hedged and then it’s a matter of uncertainty.

      • Henry,
        See https://www.e-education.psu.edu/ebf301/node/536 for examples how an oil producer can set a price at which they know they can profit, and lock in that price using perfect hedges so that no matter what happens, they will get their profit.
        Thus too farmers can use financial goods to lock in profitable prices before the harvest is sold.
        You might say there is uncertainty in the farmer’s calculation of a profitable price. If they have a bad yield, the price point may not make them a profit. But the uncertainty is not in the hedge; it is in the yield, and the farmer can insure against bad crops (and factor insurance costs into the profit price point).
        Long story short, because you can hedge in different markets, you can guarantee profits.
        See also this twitter thread: https://threadreaderapp.com/thread/1142997842803351552.html
        “Because of their different approaches in managing the risk, it is possible for both sides of the trade to hope that the price goes the same way going into settlement.”
        I take from this that both counterparties to a trade can book a profit, thus leading to an emergence of money in the financial system.
        The assumption that financial bets must net to zero is as much a myth as Savings = Investment. Investment can easily enough create its own new savings. Although each individual derivative bet may be zero-sum, you can combine several derivative bets into a trade that guarantees both you and your counterparty a profit. anilvohra’s thread quoted above supports this view.

    • Interesting comments but it seems you are narrowly defining the conversation to the financial sector with which most real people have little involvement. It is clear from the stats that the little people, 90% or so, have almost no involvement. So your comments seem to apply to a select group of people whose fast thinking has been shaped by extensive training making them more likely to understand the risks. But even that group will not allow their political thinking to be affected by their supposed knowledge and rationality. In other words they cannot follow through because of irrationality leading to paradoxical decisions.

      I posed the exponential problem of the algae growth on a pond from Thinking Fast and Slow to my kids. One has a degree in mathematics and the other is just ridiculously smart — top 1%ile — and they both got the answer correct almost instantaneously without seemingly thinking about it.

      But the numerous other people — many well educated and intelligent — to whom I have posed the question usually get it wrong. Some knowing it may be a trick spend a lot of time thinking about it but still get it wrong.

      Two of the clearest examples follow about understanding that federal government debt is not just a liability but is also a private sector asset.

      That befuddles many especially on Wall Street and Bay Street from what I can tell. My neighbour, a former senior accountant with a major bank, agrees this accounting position as does another accounting friend of mine. One shares my political beliefs agreeing with the MMT folks but the one from the major bank is a card carrying conservative so her rational thought and training are overwhelmed by her political stripes. So she denies the position of MMTers that the debt does not need to be paid down.

      Bad beliefs cannot easily be changed by rational argument even when directed towards those with training and experience and education. Their Animal Spirits take over.

    • Why should the Fed back up the counter party default risk? Maybe if those sociopaths took a loss now and then, they wouldn’tbe so intent on destroying the world for their own profit

  7. We are NOT rational beings. We operate from unconscious or subconscious beliefs and then when they become conscious rationalize them rather than change them. It is NOT about information as Henry Rech seems to believe. I have included a link to a social psychology article below.

    To make a long story shorter, several years ago I pointed out to a man with a degree in business administration who had studied macroeconomics as part of getting his degree that the bank from whom he gets his money for his business in his line of credit creates it out of thin air.

    We were at a hockey arena watching our kids play and it was the first intermission. He grabbed my shirt and raised his fist to threaten to hit me and said “That is the most f**king stupid thing I have ever heard.” I am used to violence at hockey arenas but this was a little over the top. I offered to buy him a coffee and at the next intermission asked about when he studied economics. He told me and I had an economics text from that era — I have them from most eras, I should really get a life!

    I went home and photocopied the part of his text that talked about money creation out of thin air and the optional description of fractional reserve banking which is merely an elaborate explanation of the same thing.

    I gave him the photocopy and we talked about it. He had been told as a child about the intermediary function of banking so did not alter that early formed belief despite having to take a course that included material that contradicted it.


    • Antireifier,
      “It is NOT about information as Henry Rech seems to believe.”
      I didn’t say it was.
      It is Lars that is making that point but in a seemingly perverse way.

    • But, what is the function of the phrase, “creates it out of thin air” other than a provocation? Does it explain “money” in any useful way? I don’t see that it does. It’s just a bit of conceit — “I am smarter and more insightful than you” — combined with pretty much nothing. At least he got a coffee out of it.

      • Speaking of provocation, the function of the phrase, “out of thin air” is to identify the fact that the bank is acting as an emitter of money de novo, not an intermediary between savers and borrowers. Is there a particular reason why you would resent identification of that fact so keenly as to call it “conceit”? It also usefully explains money as primarily created by private banks, not the government That fact has critically important implications, as it causes the “business” (actually asset-price) cycle.

      • I am surprised by your comment about creating money out of thin air as if it is news to you. I did explain intermediary theories and referred to fractional reserve ideas in my post. But then perhaps you are not familiar with the empirical work of Richard Werner showing the validity of my use of that phrase.

  8. ” But if new information means truly new information it actually could increase our uncertainty and variance (information set (A, B) => (A, B, C)).”
    Is the corollary then that less information increases certainty?
    Seems nonsensical.

    • Recall that Claude Shannon defined information as necessarily unexpected and therefore equivalent to uncertainty!

  9. As a social worker with 48 years of experience, it is my observation that very little of what human beings individually or collectively do is rational. Two conditions are necessary for that and neither can be show to be present most of the time. Especially since most of our behaviour — the choices we make moment to moment — stems from unconscious processes. Even those that are made consciously are rationalized by those unconscious processes after the fact.

    The first is that humans must form beliefs in order to function but even minor beliefs are part of the survival schema of the brain where habits are formed. And then submerged in the unconscious. So we operate on autopilot. To change those beliefs is very difficult if not impossible. Rational arguments seldom work to do that.

    Rational thought requires that we analyze data consciously but people do not like to do that. The thinking fast and slow research by Kahneman shows some aspects of that.

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