Why assuming ergodicity makes economics totally irrelevant

11 July, 2013 at 13:10 | Posted in Economics, Theory of Science & Methodology | 4 Comments

Suppose I offer you a simple gamble. Throw a dice: If you get a six, you win $10; if not, you lose $1. The loss is more likely; the win brings more money. Willing to play?

The generally accepted way for deciding in such cases — developed originally by the French mathematician Blaise Pascal in the 17th century — is to think of probabilities. The outcome will always be a win or loss, but imagine playing millions of times. What will happen on average?

Clearly, you’ll lose $1 about five times out of six, and you’ll win $10 about one time out of six. Over many gambles, this averages out to about 83 cents per try. Hence, the gamble has a positive “expected” payoff and is worth it, even if the gain is trifling. Play a million times and you’re sure to win big.

tumblr_mn26z9Bmbm1rq1w2xo2_500But here’s something odd. Suppose I offer precisely the same gamble, only scaled up. Roll a six and you now win not $10, but 10 times your total current wealth; if you roll anything else, you lose your entire wealth (including property, pensions and all possessions). Your expected profit is now far bigger — equal to 83 percent of your total current wealth. Still want to play?

It turns out that most people won’t take the latter bet, even though it will, on average, pay off handsomely. Why not? For most of us, putting everything on the line seems too risky. Intuitively, we understand that getting wiped out carries a brutal finality, curtailing future options and possibilities.

Economic theories generally ascribe such cautious behavior to psychology. Humans are “risk averse,” some of us more than others. But there’s a fundamental error in this way of thinking that still remains largely unappreciated — even though it casts a long and distorting shadow over everything from portfolio theory to macroeconomics and financial regulation. Economics, in following Pascal, still hasn’t faced up honestly to the problem of time.

Anyone who faces risky situations over time — and that’s essentially everyone — needs to handle those risks well, on average, over time, with one thing happening after the next. The seductive genius of the concept of probability is that it removes this history aspect, and estimates the average payoff by thinking of a single gamble alone, with two outcomes. It imagines the world splitting with specific probabilities into parallel universes, one thing happening in each. The expected value doesn’t reflect an average over time, but over possible outcomes considered outside of time …

Especially whenever downside risks get large, real outcomes averaged through time are much worse than the expected value would predict. Even in the absence of risk aversion, there can be sound mathematical reasons for being unwilling to take on gambles (or projects), despite wildly positive expected payoffs …

So what? Well, the assumption of the equality of these different averages — technically known as the assumption of “ergodicity” — is considered a given by most of contemporary economics. It makes the mathematics easier in the financial portfolio theory that influences countless investors and in frameworks for designing regulations to keep financial risks at acceptable levels. Unfortunately, this error systematically underestimates prevailing risks.

It also may encourage overly optimistic ideas about the ability of an economy to recover from a crisis. For example, those who support policies of fiscal austerity believe that companies, in seeking to maximize their profits, will naturally drive an economy back to steady growth. The economy will spring back if companies and individuals have confidence that their investments will pay off. If that’s the case, why aren’t businesses investing globally when interest rates are at historic lows. What’s holding them back?

The fairly obvious answer is serious downside risk, which makes the reticence entirely sensible — if you live in the real world where time matters.

Mark Buchanan

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4 Comments

  1. It seems to me that Kelly’s Theorem, or the Kelly Criterion ( https://en.wikipedia.org/wiki/Kelly_criterion ) is relevant here. Instead of maximizing the expected result of any bet, you maximize the expected return on investment (viewing your stake as your investment). That means that you never put your whole stake at risk unless you have a sure thing. Such a strategy seems quite rational to me. 😉 (OC, there are still problems related to probability itself, as you have pointed out.)

    I would appreciate your comments. 🙂 Thanks.

  2. It is trivial to know that an economy seeking equilibrium is dead as a dodo. Seeking equilibrium is seeking death.

    I enjoy your posts about how social sciences such as economy make ergodic assumptions. This is laughable for me who work with non-ergodic chemical reactivity. It is pathetic in my eyes to try and lend respectability to ones nonsens by via analogy trying to lend respectability from thermodynamics.

    But it is FAR from the only error in thermodynamics that economists do. Let me give you a another enormous error that thermodynamics economists do.

    In the labb yesterday my diploma worker was confused by a result she got, she wondered how a much smaller amount of a substrate had an extreme effect on the equilibrium, it had much more effect than much more of another very similar substrate. How can this be, the smaller quantity should not shift equilibrium more than the larger quantity, this violated her understanding av equilibrium. So I had to explain to her the concept of “activity”.

    Activity is a term in equilibrium that takes into account effective concentration, to simplify and make calculations simpler for students this is usually a term that is omitted since in most instances we can assume that it is 1. But this assumption is not true for many applications, if one entity move on a different timescale than another entity we get different activity. For instance a solid that reacts in a liquid, the molecule in the solution do not experience an effective concentration of the solid, activity can only be assumed to be 1 for the solution in very close contact with the solid, the further out from the solid a solute is the lower activity of the solid this solute experience. If the solid has a surface of molecules that react with the solute, equilibrium is not a linear function of concentration of surface molecules, since activity of the molecule on the surface become a function of concentration, increasing concentration shift equilibrium MUCH more than would be expected with a constant activity, since increased concentration increase both the contribution from concentration AND the contribution from activity.

    In economy the instances one can assume activity to be 1, rather than a function must be extremely rare. Capital concentration for instance is one effect of activity. As the saying goes, it takes money to make money, this is due to activity. Once I have a lot of money it becomes easier to make money, my activity coefficient in equilibrium has increased and my ability to affect equilibrium has increased. This is why the market isn’t the perfect equilibrium where everything eventually will even out, this is why we observe the opposite trend, that capital concentration begets more capital concentration. This is why a crisis on the stock exchange only make the superrich richer and the smaller investors are eliminated.

    This is why the free market always help the superrich at the expense of the poor.

    Assuming ergodicity and assuming activity to 1, makes equilibrium economics into the biggest example of half-bakery in history!


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