Why everything we know about modern economics is wrong

19 Dec, 2020 at 20:12 | Posted in Economics | 7 Comments

The proposition is about as outlandish as it sounds: Everything we know about modern economics is wrong. And the man who says he can prove it doesn’t have a degree in economics. But Ole Peters is no ordinary crank. A physicist by training, his theory draws on research done in close collaboration with the late Nobel laureate Murray Gell-Mann, father of the quark …

His beef is that all too often, economic models assume something called “ergodicity.” That is, the average of all possible outcomes of a given situation informs how any one person might experience it. But that’s often not the case, which Peters says renders much of the field’s predictions irrelevant in real life. In those instances, his solution is to borrow math commonly used in thermodynamics to model outcomes using the correct average …

If Peters is right — and it’s a pretty ginormous if — the consequences are hard to overstate. Simply put, his “fix” would upend three centuries of economic thought, and reshape our understanding of the field as well as everything it touches …

Peters asserts his methods will free economics from thinking in terms of expected values over non-existent parallel universes and focus on how people make decisions in this one. His theory will also eliminate the need for the increasingly elaborate “fudges” economists use to explain away the inconsistencies between their models and reality.

  .                                                                                                                          Brandon Kochkodin / BlombergQuint

sfiOle Peters’ fundamental critique of (mainstream) economics involves arguments about ergodicity and the all-important difference between time averages and ensemble averages. These are difficult concepts that many students of economics have problems with understanding. So let me just try to explain the meaning of these concepts by means of a couple of simple examples.

Let’s say you’re offered a gamble where on a roll of a fair die you will get €10  billion if you roll a six, and pay me €1 billion if you roll any other number.

Would you accept the gamble?

If you’re an economics student you probably would because that’s what you’re taught to be the only thing consistent with being rational. You would arrest the arrow of time by imagining six different ‘parallel universes’ where the independent outcomes are the numbers from one to six, and then weigh them using their stochastic probability distribution. Calculating the expected value of the gamble — the ensemble average — by averaging on all these weighted outcomes you would actually be a moron if you didn’t take the gamble (the expected value of the gamble being 5/6*€0 + 1/6*€10 billion = €1.67 billion)

If you’re not an economist you would probably trust your common sense and decline the offer, knowing that a large risk of bankrupting one’s economy is not a very rosy perspective for the future. Since you can’t really arrest or reverse the arrow of time, you know that once you have lost the €1 billion, it’s all over. The large likelihood that you go bust weights heavier than the 17% chance of you becoming enormously rich. By computing the time average — imagining one real universe where the six different but dependent outcomes occur consecutively — we would soon be aware of our assets disappearing, and a fortiori that it would be irrational to accept the gamble.

From a mathematical point of view, you can  (somewhat non-rigorously) describe the difference between ensemble averages and time averages as a difference between arithmetic averages and geometric averages. Tossing a fair coin and gaining 20% on the stake (S) if winning (heads) and having to pay 20% on the stake (S) if losing (tails), the arithmetic average of the return on the stake, assuming the outcomes of the coin-toss being independent, would be [(0.5*1.2S + 0.5*0.8S) – S)/S]  = 0%. If considering the two outcomes of the toss not being independent, the relevant time average would be a geometric average return of squareroot [(1.2S *0.8S)]/S – 1 = -2%.

Why is the difference between ensemble and time averages of such importance in economics? Well, basically, because when assuming the processes to be ergodic, ensemble and time averages are identical.

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.

On a more economic-theoretical level, the difference between ensemble and time averages also highlights the problems concerning the neoclassical theory of expected utility that I have raised before (e. g.  here).

When applied to the mainstream theory of expected utility, one thinks in terms of ‘parallel universe’ and asks what is the expected return of an investment, calculated as an average over the ‘parallel universe’? In our coin tossing example, it is as if one supposes that various ‘I’ are tossing a coin and that the loss of many of them will be offset by the huge profits one of these ‘I’ does. But this ensemble average does not work for an individual, for whom a time average better reflects the experience made in the ‘non-parallel universe’ in which we live.

Time averages give a more realistic answer, where one thinks in terms of the only universe we actually live in and ask what is the expected return of an investment, calculated as an average over time.

Since we cannot go back in time – entropy and the arrow of time make this impossible – and the bankruptcy option is always at hand (extreme events and ‘black swans’ are always possible) we have nothing to gain from thinking in terms of ensembles.

Actual events follow a fixed pattern of time, where events are often linked to a multiplicative process (as e. g. investment returns with ‘compound interest’) which is basically non-ergodic.

flaw-of-averages-1

Instead of arbitrarily assuming that people have a certain type of utility function – as in the neoclassical theory – time average considerations show that we can obtain a less arbitrary and more accurate picture of real people’s decisions and actions by basically assuming that time is irreversible. When our assets are gone, they are gone. The fact that in a parallel universe they could conceivably have been refilled, is of little comfort to those who live in the one and only possible world that we call the real world.

7 Comments

  1. “Let’s say you’re offered a gamble where on a roll of a fair die you will get €10 billion if you roll a six, and pay me €1 billion if you roll any other number.
    .
    Would you accept the gamble?”
    .
    This is not how betting works in finance. You have to include futures and options markets, so you pay more like 100 Euros, not 1000 Euros, to win 10 billion Euros. Dealers are pricing options in liquid markets like S&P 500 index funds, and the like. The premium to place a bet decreases so as not to bankrupt you, even if you lose it all.
    .
    There are predictable pricing movements in option prices. If the underlying moves by this much, the option price will move by an exact, predetermined amount. Financial innovation has created bets that guarantee you a profit that exceeds your premium paid. There is a profit curve over the underlying’s price, with clearly defined, predictable, precisely numerical prices beyond which you will lose the entire premium you paid. You “labor” by watching the price and selling the options before the loss points are reached.
    .
    Thus, your betting model should include financial innovations that allow you to make E10 billion if I roll a six, but only pay you an option that is scaled down by a factor of ten or more from the price of the equivalent underlying stock. I buy an option to buy the payoff from financial dealers, paying them E100. If I roll 6, I exercise the option and collect E10 billion. If I roll another number, I lose my E100 premium. The dealer makes money by delta hedging. Everyone involved can insure their bets and get a payout no matter what; I can sell my option as the dice roll and it looks like it won’t hit the six. I am guaranteed a price that generates a net profit for me if I sell before the underlying stock moves a certain amount in price.
    .
    Options markets have surpassed stock markets in trading volumes.
    .
    Your model of betting is archaic. Please study some finance!

  2. “when assuming the processes to be ergodic, ensemble and time averages are identical.”
    .
    This is what happens with an exchange-traded fund. My individual time-series average return on an S&P 500 index fund is the same as the ensemble average return.
    .
    “When our assets are gone, they are gone.”
    .
    Many of us declare bankruptcy, get our debts forgiven, and get new credit card offers.
    .
    Peters has nothing to say about the real out-the-window world, as he ignores financial innovations and bankruptcy recoveries: Trump has gone through six bankruptcies, and still has more money than Peters …

  3. How? Doesn’t the first micro textbooks an econ major read talk about risk aversion? Expected value being positive does not mean expected utility is positive.

  4. There is absolutely nothing new or profound in Ole Peters and Syll accounts of ergodicity except the unhelpful, obscure and weird language of “ergodicity”, “ensemble averages”, “time averages” etc.

    Economists, businessmen and ordinary folk have understood for many centuries that time is irreversible, that there are both lucky breaks and risks in life, and that bankruptcies and black swans can occur.

    One example is from Marshall’s Principles of Economics 8th edition 1920 p.258:
    “The Germans say that success in business requires “Geld, Geduld, Genie and Gluck.”… .Some of the most successful wholesale dealers in perishable commodities such as fish and fruit have begun life as market porters.”
    Marshall: Principles of Economics 8th edition 1920 p.258

    Chaucer (1343-1400) gives numerous examples the fortunes and fates of famous men in his “The Monk’s Tale”.
    For example:
    “By wisdom, manhood and the works of war
    From humble bed to royal majesty
    Arose great Julius Caesar, conqueror.
    Who won the Occident by land and sea

    Up to the Capitol this Julius went
    A certain day as he was wont to do.
    There he was taken by the malcontent
    False-hearted Brutus and his scheming crew.
    They stabbed him there with daggers through and through.
    Many the wounds, and there they let him die.”

  5. Not everything. But economics is facing its greatest relevance crisis since the Great Depression. In this millennium 3 things occurred that would forever change the main paradigms of the capitalism system, to the point that we can’t call it that anymore. Peak Oil Global Warming Globalización This last one started in 1990s but grew out of proportion in the 2000s and is best to live it to another discussion. But the first 2 really threw a pail of reality bricks to “old economics” and broke some of its main foundations, like unlimited growth which we now know is impossible; , that all inputs can be found, build with technologies or traded for-not true either; that environment problems are unimportant;, in short that enough money can be the cure of all ills. These theories ran into a brick wall that is inexplicable to pre-21 Century economics-let alone Solowenian growth functions, because it’s answers from the supply side or production belongs to the field of science; particularly energy science and economist are totally ignorant on anything that has to do with that subject. And they don’t, generally, want to learn about it because of laziness and because of excessive pride. I think most fall inside what I call the Harry Truman trap; he said “An expert is a fellow who never wants to learn anything new, because if he ever had to he wouldn’t be an expert anymore” Behavioral economics is a demand side concept that is now on the forefront of thinking because the world can’t behave as if the limits of growth and global warming never happened. They are physically here and we must adapt or die. We must change from a material outlook and wasteful society to a sustainably more intelligent behavior -were we keep things and minimize our consumption of products that consume fossil fuels and harm our environment. Old economic textbooks are no help at all. These are:

    Enviado desde mi iPhone

    > El 19 dic. 2020, a las 3:12 p. m., LARS P. SYLL escribió: > > >

  6. This explains some of what is wrong with what economists like Nordhaus say about climate change. They ignore: individual life prospects over time; who gets to pay, and who benefits from action/inaction; irreversible tipping points; and the possibility of civilization ending catastrophic impacts by relying on dubious equilibrium calculations.

  7. I recently saw a Twitter thread, although I can’t remember who it was, that completely debunked Peters and his theory. Perhaps you saw it.

    As to ergodicity, I’ve always felt it was pretty simple, as you said above, we don’t live in parallel universes, just one, with time as an immutable factor. Ensemble averages just don’t cut it.


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