Why ergodicity matters

2 Apr, 2021 at 11:04 | Posted in Economics | 8 Comments


Paul Samuelson once famously claimed that the ‘ergodic hypothesis’ is essential for advancing economics from the realm of history to the realm of science. But is it really tenable to assume — as Samuelson and most other mainstream economists — that ergodicity is essential to economics?

In economics ergodicity is often mistaken for stationarity. But although all ergodic processes are stationary, they are not equivalent. So, if nothing else, ergodicity is an important concept for understanding one of the deep fundamental flaws of mainstream economics.

Let’s say we have a stationary process. That does not — as Adamou shows in the video — guarantee that it is also ergodic. The long-run time average of a single output function of the stationary process may not converge to the expectation of the corresponding variables — and so the long-run time average may not equal the probabilistic (expectational) average.

Say we have two coins, where coin A has a probability of 1/2 of coming up heads, and coin B has a probability of 1/4 of coming up heads. We pick either of these coins with a probability of 1/2 and then toss the chosen coin over and over again. Now let H1, H2, … be either one or zero as the coin comes up heads or tales. This process is obviously stationary, but the time averages — [H1 + … + Hn]/n — converges to 1/2 if coin A is chosen, and 1/4 if coin B is chosen. Both these time averages have a probability of 1/2 and so their expectational average is 1/2 x 1/2 + 1/2 x 1/4 = 3/8, which obviously is not equal to 1/2 or 1/4. The time averages depend on which coin you happen to choose, while the probabilistic (expectational) average is calculated for the whole “system” consisting of both coin A and coin B.

Instead of arbitrarily assuming that people have a certain type of utility function — as in mainstream 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 it could conceivably have been refilled, are of little comfort to those who live in the one and only possible world that we call the real world.

Time average considerations show that because we cannot go back in time, we should not take excessive risks. High leverage increases the risk of bankruptcy. This should also be a warning for the financial world, where the constant quest for greater and greater leverage — and risks — creates extensive and recurrent systemic crises.


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  1. Bra,
    Speciellt slutsatsen varför vi är obenägna att ta risker. Jag har inte tänkt på det på det viset.

  2. “When our assets are gone, they are gone.”
    In a world where Trump went bankrupt six times before becoming president of the US, the above statement has no export warrant.
    In the real world, betting includes Exchange-Traded Funds which capture ensemble averages. Your betting options are not limited in the way the blog describes. Using options, you can sell high and buy low, reversing the arrow of time.
    High leverage creates more fortunes than bankruptcies, especially when bankruptcies are forgivable.
    Extensive and recurrent systemic crises are due mostly to excessive, ignorant regulations by those who do not understand how bets are being made in real financial markets.
    Instead of trying to prevent others from taking risks, we should insure each individual against psychological market panics by printing money for an inflation-proofed basic income.

    • A. Mostly it was Trump’s companies going bankrupt, not himself

      B. There are assets that aren’t financial in nature

      I think we shouldn’t let risk takers ruin our economy because similar to austerity risk takers destroying the economy don’t usually pay, but the relatively poor do. A basic income may be a good idea, but it is so far from being implemented that other things must be done in the mean time.

      • Your well-meaning regulatory policies cause more harm than good, because regulators are unaware of continually-evolving financial innovation that avoids regulatory capture. Why continue that endless game? Financial risk can be fully insured by the Fed without debiting any taxpayer’s account. Quantitative Easing proves this …

        • LTCM refutes your premise …

          • Who paid for LTCM bailouts? Which taxpayer account was debited by the Fed?
            Born was misguided and ill-informed. Well-meaning, but ignorant about the ill effects of regulation which invariably fall disproportionately on me rather than the biggest financial players, who figure out how to get around them.
            Just as ergodic economists have no clue how real-world bets are made, Born had no clue about the potential of financial innovation to insure all financial risk without any cost other than the Fed marking up its balance sheet.
            For example, at the end of the video in the blog entry above, Adamou sternly proclaims that the ensemble average for repeated simulated runs of “the equation of life” rises while each time series declines. But why leave it there? Finance has figured out how to create index products that capture the ensemble average. Thus, each time-average individual can tie their average returns to the ensemble average. Instead of trying to pick stocks to beat the market, you simply buy the market’s ensemble average.
            Ergodocists have completely missed the invention of Exchange Traded Funds. Regulators are similarly clueless (or as you point out are industry insiders who see no need to stop innovation that can help us all). Regulations by the would-be Borns thus end up ineffective and hurt little guys like me more than anyone.
            If Born really wants to help, she should support individual Fed-supplied insurance against market panics via inflation-proofed basic income.

            • Born had actual experience where the Chicago boys where shooting from the proverbial ideological rational agent axiom hip. Larry’s acumen almost did in Harvard’s endowment fund and the rest are just dim memories with a perch somewhere for a job well done to maintain the image PR.

              Basic income or UBI is just fobbing off state responsibility to the market, zero productivity = inflation of the bad kind, conducive to a permanent underclass, has absolutely no targeted distribution vectors and best for last puts the onus on the individual for all out comes aka neoliberalism.

              BTW I know Gross from back in the day so desist with the small guy shtick please.

        • BTW your statement of regulators is self defeating due to the revolving door private/public aspect and only experts from the private sector can good from bad just like the Chicago boy did with Born.

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