Ole Peters and Murray Gell-Mann find foundational mistake in economics (and a solution)

[bananas]

http://www.sciencedaily.com/releases/2016/02/160202124003.htm

Exploring gambles reveals foundational difficulty behind economic theory (and a solution)
Date: February 2, 2016
Source: American Institute of Physics (AIP)

Summary: Ole Peters and Murray Gell-Mann asked: Might there be a foundational difficulty underlying our current economic theory? Is there some hidden assumption, possibly centuries old, behind not one but many of the current scientific problems in economic theory? Such a foundational problem could have far-reaching practical consequences because economic theory informs economic policy. The story that emerged is a fascinating example of how human understanding evolves, sticks, unsticks, and branches.


In the wake of the financial crisis, many started questioning different aspects of the economic formalism.

This included Ole Peters, a Fellow at the London Mathematical Laboratory in the U.K., as well as an external professor at the Santa Fe Institute in New Mexico, and Murray Gell-Mann, a physicist who was awarded the 1969 Nobel Prize in physics for his contributions to the theory of elementary particles by introducing quarks, and is now a Distinguished Fellow at the Santa Fe Institute. They found it particularly curious that a field so central to how we live together as a society seems so unsure about so many of its key questions.

<snip>

"The first perspective -- considering all parallel worlds -- is the one adopted by mainstream economics," explained Gell-Mann. "The second perspective -- what happens in our world across time -- is the one we explore and that hasn't been fully appreciated in economics so far."

<snip>

They put it to the test after their friend Ken Arrow -- an economist who was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972 -- suggested applying the technique to insurance contracts. "Does our perspective predict or explain the existence of a large insurance market? It does -- unlike general competitive equilibrium theory, which is the current dominant formalism," Peters said.

<snip>

This concept reaches far beyond this realm and into all major branches of economics. "It turns out that the difference between how individual wealth behaves across parallel worlds and how it behaves over time quantifies how wealth inequality changes," explained Peters. "It also enables refining the notion of efficient markets and solving the equity premium puzzle."

<snip>

What's the next step for their work? "We're very keen to develop fully the implications for welfare economics and questions of economic inequality. This is a sensitive subject that needs to be dealt with carefully, including empirical work," noted Peters. "Much is being done behind the scenes -- since this is a conceptually different way of doing things, communication is a challenge, and our work has been difficult to publish in mainstream economics journals."

<snip>

Story Source:

The above post is reprinted from materials provided by American Institute of Physics (AIP). Note: Materials may be edited for content and length.

Journal Reference:

1. O. Peters, M. Gell-Mann. Evaluating gambles using dynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2016; 26 (2): 023103 DOI: 10.1063/1.4940236

[bananas]

1. Bernoulli: "the first rebellion against the dominance of the expectation value"

One historically important application is the solution of the 303-year-old St. Petersburg paradox, which involves a gamble played by flipping a coin until it comes up tails and the total number of flips, n, determines the prize, which equals $2 to the nth power. "The expected prize diverges -- it doesn't exist," Peters elaborated. "This gamble, suggested by Nicholas Bernoulli, can be viewed as the first rebellion against the dominance of the expectation value -- that average across parallel worlds -- that was established in the second half of the 17th century."

[bananas]

2. The paper is free

http://scitation.aip.org/content/aip/journal/chaos/26/2/10.1063/1.4940236

[bemildred]

7. Thank you. nt

[bemildred]

3. Yes.

Especially the empirical approach and use of "development over time", wealth accumulates, and like mass it warps the area around it.

[leveymg]

4. Economics is like Catholic theology. Much of it is self-referencing dogma in a foreign language.

Anyone want to take a stab at an English translation of the article, and explain what it means? What is the foundational mistake? What is the solution?

[bananas]

6. From the paper

which is open access at http://scitation.aip.org/content/aip/journal/chaos/26/2/10.1063/1.4940236

Much of current economic theory is based on early work in probability theory, performed specifically between the 1650s and the 1730s. This foundational work predates the development of the notion of ergodicity, and it assumes that expectation values reflect what happens over time. This is not the case for stochastic growth processes, but such processes constitute the essential models of economics. As a consequence, nowadays expectation values are often used to evaluate situations where time averages would be appropriate instead, and the result is a “paradox,” “puzzle,” or “anomaly.” This class of problems, including the St. Petersburg paradox and the equity-premium puzzle, can be resolved by ensuring the following: the stochastic growth process involved in the problem needs to be made explicit; the process needs to be transformed to find an appropriate ergodic observable. The expectation value of the new observable will then indeed reflect long-time behavior, and the puzzling essence of the problem will go away. Here we spell out the general recipe, which we phrase as the solution to the general gamble problem that stood at the beginning of the debate in the 17th century. We hope that this recipe will resolve puzzles in many different areas.

[bemildred]

8. "we propose to evaluate gambles by averaging wealth growth over time. No utility function is needed"

In other words the expected value is what it has produced on average in the past, determined empirically, by the market.

This will not generally lead to "growth", since the expectation is stability, not growth, so the financial services people won't like it.

[arendt]

12. That is going to be difficult.

Essentially, the mistake is saying that expectation values (EVs) over ensembles are equal to EVs over time. The paper argues that they are not equal, and that ensembles are the wrong model for the real world, in which the time order of events makes a huge difference.

Proving that a particular EV(time) = EV(ensemble) was first formulated in the late 1800s as Ergodic Theory. Some EVs are ergodic, others are not. This needs to be proved on a case by case or class by class basis.

Without wading through the entire paper, the fundamental mistake seems to have been codified by Menger in 1934, and used to dogmatically rule out all kinds of behavior that is actually observable in the real world.

That's all I have for now. Maybe if I have time to read it --- it seems fairly well written, with colloquial English language verbiage paired up with equations.

----

It's funny. There is a critique recounted by one of the SFI guys: economists are much better mathematicians than physicists, because physicists can do an experiment, can have "rules of thumb" to guide their math. Economists are building castles in the air, so the construction has to be absolutely bulletproof - more an exercise in mathematical logic than a scientific endeavor.

[bemildred]

13. +1.

I concur. You hit all the main points.

It is math, not science. If they treated it as such, no problem, "Theory of Games and Economic Behavior" is innovative math, it is not science, and it is not for the most part how people behave in real life.

[rogerashton]

5. Well, no.

"The second perspective -- what happens in our world across time -- is the one we explore and that hasn't been fully appreciated in economics so far."

Actually, the "dominant paradigm" in macroeconomics this century is DSGE -- "dynamic stochastic general equilibrium" -- is precisely about "what happens in our world across time" (and by the way, is a terrible failure.) But "what happens in our world across time" has been central to economics for two centuries -- and the authors have Bernoulli and Menger backward. And the date for Menger is fifty years off -- it is the date of the English translation.

Whenever someone with no education in economics tells us that he has discovered the basic problem of economics and has its solution, you know that you have a pot that needs mending. That's especially true if the pot happens to be a very distinguished scholar in another field.

I don't mean to say that economists are right -- as I said, DSGE is a failure -- but at least economists know what economists actually think. These pots don't.

[Odin2005]

9. I didn't know Murray Gell-Mann was even still alive.

[arendt]

11. I didn't know Ken Arrow was still alive.

I knew Gell-Mann was one of the "Old Turks" at the SFI.

[arendt]

10. The fundamentals of economics have been shot full of holes so many times, I lost count

Here's another interesting experiment that demonstrates how wealth accumulation is driven by chance events.

Entrepreneurs, Chance, and the Deterministic Concentration of Wealth

But economic theory is some kind of vampire. No matter how many times you prove its BS (like after the Great Depression), it rises from the grave (curse you Milton Friedman).