Thursday, October 25, 2012

Rick Bookstaber — A Crack in the Foundation of Economics -- More Readings

Last year I did a post on a mathematical error that has dictated the direction of important work in economics, and more especially finance. The discovery of this error, by U.K. mathematician Ole Peters, has slowly gained some recognition, though for some reason the journal where the original paper was published has not been willing to publish this correction.

At its root the error is obscure -- as would inevitably be the case for it to have persisted for so long and for its incorrect conclusion to be relied on by such luminaries as Paul Samuelson and Kenneth Arrow.
Rick Bookstaber
A Crack in the Foundation of Economics -- More Readings


Matt Franko said...

"There's actually a paper about Babylonian commodity
prices that were found on clay tablets, and they seem to follow a multiplicative dynamic. 5"

I wonder what units those prices were in?

Matt Franko said...

More from the Legg Mason interview:

"Time averages are interesting because they are what we observe in physics. We usually
measure some sort of macroscopic property, like the pressure in a balloon. That pressure, in
terms of the microscopic model, is the rate of momentum transfer per unit area to the balloon
membrane resulting from a gazillion collisions of molecules with the membrane. Any device that
we use to measure this is so sluggish that it will only give us a long-time average value of that
momentum transfer. The very clever insight of Boltzmann was that under very special conditions,
we just have to calculate an expectation value of the rate of momentum transfer per area, and
that will coincide with the time average pressure that we actually observe.

So, practically, ergodic means that time averages are the same as ensemble averages, or
expectation values. Non-ergodicity means that they are different. Since there are many more
ways of being different than there are of being identical, it comes as no surprise that most
systems are non-ergodic.
Why would this be important in economics and finance? Quite simply because Boltzmann's trick
doesn't work. We cannot equate the behavior over time (i.e., what really happens) to this elusive
mathematical object, the expectation value.
I'm not arguing for new models, I'm just arguing that we should have a look at the very sensible
models that economists have devised and to see whether they are ergodic. The ones I'm
interested in are non-ergodic, and so my work has focused on pointing that out and asking about
the consequences. Where did we miss the lessons of these models because we were wearing
the wrong glasses?
MM. Let me jump in here and note that Paul Samuelson, a Nobel-prize winner, claimed that the
“ergodic hypothesis” is essential for advancing economics from the realm of history to the realm
of science. So he thought that assuming ergodicity is essential to economics and finance.2
OP: Your Samuelson quote really gets to the heart of the epistemological issue. Samuelson said
that we should accept the ergodic hypothesis because if a system is not ergodic you cannot treat
it scientifically. First of all, that's incorrect, although I think I understand how he ended up with this
impression: ergodicity means that a system is very insensitive to initial conditions or perturbations
and details of the dynamics, and that makes it easy to make universal statements about such
systems. In physics we know this all too well—ergodic equilibrium systems naturally fall into
strongly attracting universality classes."

Bolded area above we can see the human brain in action. Doing the best we can in developing methods to deal with systems that we have absolutely no authority over.... There is today a Boltzmann's constant:

But remember the point Mike made wrt his RT hit from yesterday, there are no constants in the economic equation MV=PQ, imo there are no constants to be used in ecomonics, as we (humans) are set under authority to operate our own economic systems under our own civil laws. We dont have to resort to "tricks" in economics as we possess the authority over these systems...

Those that seek to apply mathematical "constants" or other mathematical "tricks" wrt economic analysis/policy deny that humans possess this authority ... eg. Taylor "Rule": here we literally subject ourselves to "The Rule of Taylor"... rsp

Matt Franko said...

found it!:

"Archaeological excavations started
in 1899 by Robert Koldewey have uncovered astronomical diaries, written in cuneiform on clay tablets, from
the period 652 B.C. to 69 A.D. Since the tablets contain
celestial observations, all information inscribed on them is
dated, including records of the weather, the level of the
Euphrates River, socio-political events and market quotations of six commodities: barley, dates, mustard (cascuta),
cress (cardamom), sesame and wool. The commodity
prices are expressed in weight quantities that could be
purchased per shekel of silver
, recorded three times a

Just as I suspected, weight measures of silver... oh boy.... bad news...

"17 Behold Me rousing against them the Medes, who are not accounting silver, And gold - they are not delighting in it." (Isaiah 13:17)

Thank God for FDR and Dick Nixon...


paul meli said...


Interesting. I think you're on to something here.

Unfortunately it's too abstract for 95% of the population to be able to "see" easily. Only the curious will pay any attention.

You need to work on a Fisher-Price version.