Sometimes we do not know because we cannot know

18 April, 2018 at 17:11 | Posted in Economics, Statistics & Econometrics | 8 Comments

Some time ago, Bank of England’s Andrew G Haldane and Benjamin Nelson presented a paper with the title Tails of the unexpected. The main message of the paper was that we should not let us be fooled by randomness:

The normal distribution provides a beguilingly simple description of the world. Outcomes lie symmetrically around the mean, with a probability that steadily decays. It is well-known that repeated games of chance deliver random outcomes in line with this distribution: tosses of a fair coin, sampling of coloured balls from a jam-jar, bets on a lottery number, games of paper/scissors/stone. Or have you been fooled by randomness?

blNormality has been an accepted wisdom in economics and finance for a century or more. Yet in real-world systems, nothing could be less normal than normality. Tails should not be unexpected, for they are the rule. As the world becomes increasingly integrated – financially, economically, socially – interactions among the moving parts may make for potentially fatter tails. Catastrophe risk may be on the rise.

If public policy treats economic and financial systems as though they behave like a lottery – random, normal – then public policy risks itself becoming a lottery. Preventing public policy catastrophe requires that we better understand and plot the contours of systemic risk, fat tails and all. It also means putting in place robust fail-safes to stop chaos emerging, the sand pile collapsing, the forest fire spreading. Until then, normal service is unlikely to resume.

Since I think this is a great paper, it merits a couple of comments s.

To understand real world ”non-routine” decisions and unforeseeable changes in behaviour, ergodic probability distributions are of no avail. In a world full of genuine uncertainty – where real historical time rules the roost – the probabilities that ruled the past are not those that will rule the future.

Time is what prevents everything from happening at once. To simply assume that economic processes are ergodic and concentrate on ensemble averages – and a fortiori in any relevant sense timeless – is not a sensible way for dealing with the kind of genuine uncertainty that permeates open systems such as economies.

When you assume the economic processes to be ergodic, ensemble and time averages are identical. Let me give an example: Assume we have a market with an asset priced at 100 €. Then imagine the price first goes up by 50% and then later falls by 50%. The ensemble average for this asset would be 100 €- because we here envision two parallel universes (markets) where the asset-price falls in one universe (market) with 50% to 50 €, and in another universe (market) it goes up with 50% to 150 €, giving an average of 100 € ((150+50)/2). The time average for this asset would be 75 € – because we here envision one universe (market) where the asset-price first rises by 50% to 150 €, and then falls by 50% to 75 € (0.5*150).

From the ensemble perspective nothing really, on average, happens. From the time perspective lots of things really, on average, happen.

Assuming ergodicity there would have been no difference at all. What is important with the fact that real social and economic processes are nonergodic is the fact that uncertainty – not risk – rules the roost. That was something both Keynes and Knight basically said in their 1921 books. Thinking about uncertainty in terms of “rational expectations” and “ensemble averages” has had seriously bad repercussions on the financial system.

Knight’s uncertainty concept has an epistemological founding and Keynes’ definitely an ontological founding. Of course, this also has repercussions on the issue of ergodicity in a strict methodological and mathematical-statistical sense. I think Keynes’ view is the most warranted of the two.

The most interesting and far-reaching difference between the epistemological and the ontological view is that if one subscribes to the former, Knightian view – as Taleb, Haldane & Nelson and “black swan” theorists basically do – you open up for the mistaken belief that with better information and greater computer-power we somehow should always be able to calculate probabilities and describe the world as an ergodic universe. As Keynes convincingly argued, that is ontologically just not possible.

If probability distributions do not exist for certain phenomena, those distributions are not only not knowable, but the whole question regarding whether they can or cannot be known is beside the point. Keynes essentially says this when he asserts that sometimes they are simply unknowable.

John Davis

To Keynes, the source of uncertainty was in the nature of the real — nonergodic — world. It had to do, not only — or primarily — with the epistemological fact of us not knowing the things that today are unknown, but rather with the much deeper and far-reaching ontological fact that there often is no firm basis on which we can form quantifiable probabilities and expectations at all.

Sometimes we do not know because we cannot know.



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  1. Quants use linear algebra to hedge everything. Insurance hedges risk of black swans. Finance knows how to make money no matter what the outcome. If some piece breaks, such as the insurance piece in 2008, the Fed proved it can print money to cover insurance claims until world financial markets get over their panic and start creating credit as money as profligately as in normal times. Insurance pays out today based on future promises, which when due can be rolled, forgiven, or themselves paid from insurance. Thus market risk is stripped out by financial instruments such as derivatives. Quaint objections about uncertainty ignore the fact that companies have figured out how to insure and re-insure, making money no matter what improbable catastrophe occurs, psychological or otherwise.

    • “Thus market risk is stripped out by financial instruments such as derivatives.”

      What about systemic risk?

      The only reason the western world still has a viable financial sector is because governments bailed it out 10 years ago.

      • Risk is mainly psychological. What is the risk of everyone panicking at once? Even that can be insured against. Collateral Debt Obligations were insured against downgrades and other credit events. The insurance piece broke and supposedly they have fixed that now. The Fed provided enough liquidity to meet money demand in a psychological panic that shut down money markets. The Fed expanded its balance sheet, in other words expanded world dollar reserves. There was no taxpayer cost to the Fed’s action.

        Uncertainty about the physical world can be insured against; financial instruments can be constructed to profit from a black swan, and profit if the black swan doesn’t occur.

      • “What about systemic risk?”

        Systemic risk can be paid for by central banks, linked in an unlimited currency swap network that serves as a proxy for one world central bank. In a system with one bank, there are no bank runs. So the bank (in 2008 it was the Fed) can always issue enough of the principal currency preferred by private firms to settle obligations.

        Thus, systemic risk is handled by money-printing to backstop wanton private credit creation. Then the system is “fixed” and they go right back to creating credit wily-nilly.

        • Yeah, but I think Henry’s point is that it took the government to bail these financial firms out. Finance does not know how to make money no matter what the outcome all by itself- without the government fixing it for them many or most would have folded. There may have been no “tax payer” cost to the Fed’s actions, but there were other costs- maybe they can be called ‘citizen costs’. Things like trust in the justice of a system that allows ordinary citizens to lose their jobs and houses while more or less insulating a class of well paid financial ‘geniuses’ from their own mistakes.

          In any case, you are only talking about financial risk. While the Fed can always insure a financial risk in US Dollars, it can’t ensure that real resources are not going to be wasted through wasteful investments. Risk of financial penalty if you are not successful might be required so that resources are not squandered chasing purely financial rewards. You might as well play roulette all day everyday if every loss is backstopped by the Fed while your winnings remain yours. While there may not be a cost to taxpayers, there is certainly a real cost of building and staffing the casino and even a cost of your own time being spent rather unproductively.

          • “it took the government to bail these financial firms out.”
            The firms created so much credit, that they became too big to fail. The created credit was circulating as money, it was behind the cash you withdraw from cash machines. No public backstop for all that created credit meant a real risk of cash machines not working. Instead of seeing if that would happen, the Fed realized it was easier to press buttons on computers to supply enough money that banks could fund their daily settlement operations.
            Again, the real risk was that everyone would panic at once, the risk of mass hysteria. The Fed proved it can cover that risk even if the insurance that is supposed to cover it failed in 2008. Supposedly they learned their lesson; AIG is right back to insuring against those risks again today.
            “[…] trust in the justice of a system that allows ordinary citizens to lose their jobs and houses while more or less insulating a class of well paid financial ‘geniuses’ from their own mistakes.”
            Yes, I don’t know why the Fed allowed foreclosures to continue on houses whose mortgages were bundled in the toxic assets it bought. That was policy, and that should change.
            I think the problem is that the ordinary taxpayer does not understand that the Fed has the power to generate liquidity without limit, on demand. We should use that power to rescue individuals in daily financial crises, as well as financial institutions …
            “there is certainly a real cost of building and staffing the casino ”
            My goal is to virtualize the casinos. Let neoliberals play money-maximization games with virtual assets. Recessions are good for trees because logging decreases. Now they are back to logging like mad, and selling the oversupply like mad. Soon I hope the financial part of loggers’ balance sheets will so far exceed the logging revenues that they stop logging altogether. Then people on a basic income can treat trees more respectfully, not as sources of profit.

  2. There’s a lot to be said for the Knightian, “epistemological” view, not least of which is that learning in the future implies uncertainty in the present. There’s warrant enough, imnsho, that people do learn. You are not learning anything from the flip of a fair coin or a spin of a balanced roulette wheel. But, someone had to learn quite a lot to machine a fair coin or a balanced roulette wheel.
    The Keynesian “ontological” view that you cannot know some things about the future resolves into the Knightian expectation that you will learn about some future events only when the future arrives. Learning in the future implies you do not / can not know in the present. Keynes’s examples offered as illustrations of unknowables (in his present) are of this Knightian type: in 1930, no one usefully knows the price of copper in 1970, but in 1971, people know; no one in 1930 can usefully conjure a point estimate of the chances of a general European war ten years hence, but in 1940, a probability of 1 has been realized.
    The “fat tails” interpretation is an egregious bit of hand-waving, understandable I suppose as a way of trying to salvage the work of financial quants, but it makes for bad economics. Most of the work of firms in the economy is organized around controlling processes of production and distribution, which is to say organized around applying what little we do know and learning what we can and externalizing the rest. That mainstream economics ignores the organization of technical engineering and administrative management in favor of pretending that efficiency in the allocation of resources is the only game in town is one of those pretenses that makes mainstream economics so empty of substance. The normal distribution well describes the residual variation of a process under control: once you’ve built the casino and machined the well-balanced roulette wheel, “risk” can be well-managed thru an appreciation of the law of large numbers. It is the building of the casino and the machining of the roulette wheel that constitutes the economic activity that ought to be of interest to the economist (but too often isn’t).
    Most business ventures during their formation are far from the refined routines of an established casino, which I take it to be Knight’s main point. The Knightian entrepreneur isn’t managing a process with a residual well-described by a normal distribution; the Knightian entrepreneur is struggling to get his firm to a point where a normal distribution emerges from establishing control, which is to say, a struggle to learn and contain or channel chaos.
    I think the Keynes of the General Theory can be faulted for not recognizing the implications of uncertainty for the organization of the archetypal firm: that most firms will make large sunk cost investments that leave them with low and declining marginal unit costs in the relevant range of output, for example, that prices are administered, that wages are what are now sometimes called efficiency wages, fixed and conditional on following directions, with embedded contingency and insurance.

  3. “The ensemble average for this asset would be 100 €- because we here envision two parallel universes (markets) where the asset-price falls in one universe (market) with 50% to 50 €, and in another universe (market) it goes up with 50% to 150 €, giving an average of 100 € ((150+50)/2).”

    Why are you equating an average of two trials to the ensemble average? This is not the ensemble average; it is just an average. In general, the average of a sample is not equal to the ensemble average, which is the mean or expectation of the distribution of a random variable.

    Obviously in this article you want to point to the difference between ensemble averages and geometric (time) averages. The choice of the example is not good in my opinion. Furthermore, the apparent differences between the two averages can lead to strawman arguments. it is not one against the other, this is a false dichotomy fallacy. An ensemble average is just one particular statistical property: the mean of the distribution in the limit of sufficient samples. A time average reflects just one path and considering many such paths reveals additional properties. Both are important in studying stochastic processes as any student of probability theory is taught. If some people just use one or the other to make decisions, it is because they do not udnerstand probability theory, not that there is something wrong with it that is remarkably resolved if one considers time averages.

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