Response to “Worrying Trends in Econophysics”

Joseph L. McCauley
Physics Department
University of Houston
Houston, Tx. 77204
jmccauley@uh.edu

and

Senior Fellow
COBERA
Department of Economics
J.E.Cairnes Graduate School of Business and Public Policy
NUI Galway, Ireland

Abstract

This article is a response to the recent “Worrying Trends

in Econophysics” critique written by four respected
theoretical economists [1]. Two of the four have written
books and papers that provide very useful critical
analyses of the shortcomings of the standard textbook
economic model, neo-classical economic theory [2,3] and
have even endorsed my book [4]. Largely, their new
paper reflects criticism that I have long made [4,5,6,7,]
and that our group as a whole has more recently made
[8]. But I differ with the authors on some of their
criticism, and partly with their proposed remedy.
1. Money, conservation laws, and neo-classical economics

Our concerns are fourfold. First, a lack of awareness of work

which has been done within economics itself. Second,
resistance to more rigorous and robust statistical
methodology. Third, the belief that universal empirical
regularities can be found in many areas of economic activity.
Fourth, the theoretical models which are being used to explain
empirical phenomena.

The latter point is of particular concern. Essentially, the

models are based upon models of statistical physics in which
energy is conserved in exchange processes.

Gallegati, Keen, Lux, and Ormerod [1]

Since the authors of “Worrying” [1] begin with an attack on

assumptions of conservation of money and analogs of
conservation of energy in economic modelling, let me state
from the outset that it would generally be quite useless to
assume conserved quantities in economics and finance (see
[4], Ch. 1). There is no reliable analog of energy in economics
and there are very good reasons why no meaningful
thermodynamic analogy can be constructed (see [4, Ch. 7]). In
particular, money is not conserved. Money is created and
destroyed rapidly via credit. Leveraging leads to big
changes in ‘money’. Are there any conservation laws at
all in real markets, and if so do they have any
significance for deducing market dynamics?

Conservation laws follow from invariance principles [8],

so one should not expect conservation laws in socio-
economic ‘motions’ like financial transactions or
production and consumption [4,5]. We have identified
exactly one invariance principle in finance: no arbitrage is
equivalent to a discrete version of rotational invariance
of the price distribution [see [4], Ch. 7). For inviolable
mathematical laws of motion rather then era-dependent
mathematical modelling we know from Wigner’s
explanation why mathematics has been so ‘unreasonably
effective’ in physics [8] that we would need the
equivalent of all four space-time invariance principles:
translational invariance, rotational invariance, time
translational invariance, and Galilean invariance. Those
local invariance principles are the foundation for the
discovery of mathematical law in classical mechanics,
quantum mechanics, and general relativity, as Wigner
has explained. Wigner pointed out that without those
underlying invariance principles mathematical law might
well exist, in principle, but the world would be too
complicated for us to discover mathematical law in
practice. That is exactly where we stand in trying to
make a science of socio-economic phenomena [7], but
even in the absence of inviolable mathematical laws of
trading behavior we are still able to generate finance
market statistics dynamically accurately [4] in our era.

In the definition of the neo-classical economic model

(‘general equilibrium theory’ [9]) one global conservation
law is assumed at the start. However, for the global
integrability presumed for the existence of equilibrium
there actually must be n global conservation laws, where
n is the number of different goods exchanged by agents.
The budget constraint combined with price dynamics,
dp/dt=D(p)-S(p) (where D is total demand at price p
and S is the total supply), yields Walras’ law, a global
conservation law that puts the motion in price space
(phase space) on an n-sphere [4,9]. The budget
constraint is conservation of money, and that constraint
is badly violated in the real world, where money is
created and destroyed with the tap of a computer key
via credit.

In the beginning of our current era of credit and

deregulation, which we can date from the early 1970s,
the supply-demand curves predicted by neo-classical
economics [9] were falsified by Osborne [10], who
simultaneously predicted the observable microeconomic
supply and demand curves. In a strict gold-standard
economy money would be conserved if mining
production were ignored. Credit is required for the
expansion of both industry and consumption, which is
why we’re no longer on any sort of gold standard.
Nixon took the Dollar off the (Rooseveltian) gold
standard in 1972 due to the inflation created by the
Vietnam War. Option pricing was deregulated in 1973,
accidentally parallel with the revolutionary Black-Scholes
paper. OPEC correctly understood the Dollar
devaluation and raised the price of oil dramatically to
compensate for the rapid inflation that would follow the
degradation of the dollar. The deregulation of financial
markets that followed is described in Liar’s poker [11].

In contrast with the main concern of “Worries” [1], the

work done in Fribourg, Boston, Alessandria, UCLA,
Palermo, Oldenburg, and Houston, to name a few
centers of econophysics research, do not assume
conservation of money or any analog of conservation of
energy. Searches for conservation laws can be found in
the neo-classical economics literature [12,13], but those
efforts bore no fruit at all for lack of a firm basis in
empirical data.
There is one econophysics model assuming conservation
of money that is interesting within the historical context
of neo-classical economic theory. Radner had observed
in 1968 [14] that money/liquidity cannot appear in neo-
classical economics: with perfect foresight, perfect
planning into the infinite future, there can be no liquidity
demand (in real markets we have, in contrast, largely
total ignorance, market as pure nonGaussian noise).
Radner speculated that money/liquidity arises from
uncertainty and also computational limitations, although
he did not say what he meant by “computation” and
apparently had no idea at all of a Turing machine [15].
Conservation of money is assumed in the simple trading
model made by Bak, Nørrelyke and Shubik [16]. There,
expected utility was maximized (so the paper is neo-
classsical) and then noise was added to see if “money”
would emerge from the dynamics of trading. The
attempt failed, the model is empirically irrelevant (as is
every model of optimizing behavior) but can be
understood as an honorable effort to address the
mathematical problem posed by Radner’s discussion. I
have no evidence that Per Bak was aware of Radner’s
paper, but maybe Shubik was aware of it. The Bak et al
model is asymptotically a pure barter model because
statistical equilibrium is reached, and in general the
authors of “Worries” are right that making further barter
models is generally (both empirically and theoretically
seen) useless. In our era, conservation of money is a silly
assumption. The paper by Bak et al tried to bridge the
gap between standard economic theory and
econophysics but was too ambitious, the gap is a chasm.
2. Should econophysicists rely on the economics
literature for guidance?

Our concerns about developments within econophysics arise

in four ways:

• a lack of awareness of work which has been done within

economics itself
• resistance to more rigorous and robust statistical
methodology
• the belief that universal empirical regularities can be
found in many areas of economic activity
• the theoretical models which are being used to explain
empirical phenomena

…. One of the present authors has drawn the analogy of

imagining ‘a new paper on quantum physics with no
reference to received literature’ […].
Gallegati, Keen, Lux, and Ormerod [1]

This leads into another concern expressed in [1], that

ideas of production in economics theory are ignored by
econophysicists. The problem with that criticism is that
neo-classical models of production are no better than
neo-classical exchange models: there is inadequate or
nonexisting empirical basis for any neo-classical
assumption. Econophysicists are safer to ignore the
lessons taught in standard economics texts (both micro-
and macro-) than to learn the economists’ production
ideas and take them seriously (see Dosi [17] for non
optimizing models of production, and see Zambelli [18]
for a thorough and very interesting study of the degree
of computational complexity of neo-classical production
models). To be quite blunt, all existing ‘lessons’ taught in
standard economics texts should be either abandoned or
tested empirically, but should never be accepted as a
basis for modelling. It’s important to understand what
economists have done previously mainly to avoid making
the same mistakes. Toward that end, see also Velupillai
[19] for a critical discussion of the neo-classical
equilibrium model from an economists’ perspective,
where lack of computability of the neo-classical model
would prevent agents from locating equilibrium even if
the equilibrium point were stable, and even if the agents
were as unrealistically well informed as the standard
model so uncritically presumes.

I will explain below why statistical analyses performed

from the economists’ standpoint are generally
untrustworthy, with few exceptions [20]. Our
alternative to taking advice from economics texts and
papers for the purpose of modelling markets will be
stated below.

Osborne [21] first introduced the lognormal stock pricing

model in 1958 and should be honored as the first
econophysicist, but even econophysicsts cite Bachelier
while ignoring Osborne. Bachelier independently of
Einstein, Markov and Smoluchowski produced some of
the first results on Markov processes, but his finance
model predicted negative prices and did not describe
any market correctly, even to zeroth order.
Econophysicists have contributed mightily in recent
years to the study of financial markets, but that work is
not yet finished. The authors of [1] are correct that the
so-called ‘rigorous and robust’ methods of statisticians
have generally not been used in econophysics, and for
good reasons. In our group we begin with market
histograms and then deduce an empirical model [4,21].
We have no mathematical model in mind a priori. We do
not ‘massage’ the data. Data massaging is both
dangerous and misleading. Econometricians mislead
themselves and others into thinking that their models
help us to understand market behavior. The reason is
that economists assume a preconceived model [22,23]
with several unknown parameters, and then try to force
fit the model to a nonstationary time series by a ‘best
choice of parameters’ (using ‘rigorous and robust
methods’). Their conclusion is that the data are too hard
to fit over long time scales [23]. Because we deduce our
model from the data [4,7,24], we arrive at exactly the
opposite conclusion: due to nonuniqueness in fitting any
infinite precision model (stochastic or deterministic
model) to inherently finite precision data, it is too easy to
fit any set of histograms constructed from time series.
We’ve illustrated this fact for financial time series but the
lesson of nonuniqueness is not new: we anticipated it
from our experience in nonlinear dynamics [4,5]. The
reason why our group has not yet ventured into
nonfinancial economic data analysis is that the problem
there is horrendous: because of the sparseness of
nonfinancial market data, it will likely be possible to fit
the data using too many different unrelated classes of
models [4,7]. The best one can hope for there will be to
rule out certain model classes. One will never be able to
‘understand’ the market data the way that we’ve
managed to ‘understand’ financial markets.

There is another very good reason to concentrate on

finance markets in this era. With the magnitude and
frequency of the enormous daily and even second by
second transfers, finance markets dominate all other
markets. Finance markets drive other markets globally.
For some reason that I fail to understand, economists still
tend to see finance markets as only one relatively
insignificant market in their panoply.

It is easy to generate hypothetical data sets which, when

binned, can give misleading pictures of the statistical
distributions which characterise them. [...] shows that data
generated from a lognormal distribution can be easily
misinterpreted as evidence of power laws.
Gallegati, Keen, Lux, and Ormerod [1]

It’s an old fractal-wive’s tale from the 1980s that

lognormal densities mimic fat tails if you merely ‘eyeball’
them [25]. In a careful analysis using logarithmic returns,
no such crude error is made. The reader must be aware
that, with few enough decades in a log-log plot, lnf(x)
looks linear in lnx where f(x) is a large class of smooth
functions. About nonuniqueness in fitting infinite
precision models to finite precision data, we have written
enough [4,5,7].

However, the authors of [1] are correct that statistical

physicists often express an unjustified expectation for
universal scaling exponents even when there is no
evidence for a critical point/bifurcation [4,5]. There is
apparently no universality of scaling exponents in
finance, where the fat tail exponents range from roughly
2 to 7 [26] and are market dependent. Moreover, there is
no reason at all to expect universality in socio-economic
behavior [4,5].

There is other criticism that can be levelled at

econophysics and economics alike: most of us have not
read and understood Osborne’s 1977 falsification [10] of
standard economics theory, and so are not aware that
we can expect only misguidance from most economics
texts and papers. In econophysics, agent based
modelling is often performed in an effort to explain fat
tails, but fat tails without other market constraints are
too easy to ‘explain’ [4]. Again, the authors of “Worries”
are right that background in statistical physics has
generally led to unjustified emphasis on scaling and
universality. Agent based models have been constructed
where the motion is asymptotically stationary, but
stationary markets do not exist (I give no references here
in order to protect the guilty, some of whom are my
friends).

Markets are not merely nonstationary, the time series

generally exhibit nonstationary increments [27] as well,
meaning that x(t+T)-x(t)≠x(T), where by equality we
mean ‘equality in distribution’ (in addition, x(t) is
assumed defined so that x(0)=0). This means that the
increments depend not merely on the time difference T
but on the starting point t as well. This complication makes
time series analysis devilishly tricky. We are not yet
satisfied that we understand how to perform a
noncircular or mistake-free analysis of finance data that
searches for scaling behavior [28]. The scaling of interest
to us is of the form f(x,t)=t-HF(x/tH), where x is the
logarithmic return and f is the returns density. That is,
we look for a data collapse of the form F(u)=tHf(x,t)
where u=x/tH. If such scaling holds, then the variance
scales as tH, but that alone is not evidence for market
correlations [27]. Papers have been published by very
respectable finance researchers claiming market
correlations on the basis of a Hurst exponent H≠1/2, see
e.g. [29], but a Hurst exponent H≠1/2 does not imply
long time correlations unless it has been first established
that the time series has stationary increments [27] (see
also [30,31] for a discussion of the scaling dynamics and
lack of autocorrelations in Levy models). These different
ideas are usually confused together into a thick soup by
physicists and economists alike. In particular, one
should question any paper claiming to deduce a Hurst
exponent from a spectral density: nonstationary time
series have no spectral decomposition, and all financial
time series are nonstationary (the moments of prices p(t)
or returns x(t)=lnp(t)/pc never approach constants,
where pc is dynamically defined ‘value’ [24]). Further, a
nonstationary time series with unknown dynamics
cannot be transformed into a stationary one (try it, as an
exercise, using Ito calculus). The transformations
purported to perform such magic in econometrics are
akin to wishful thinking or praying for rain. Our dynamic
definition of value is new and applies to nonfinancial
markets as well, but has so far been ignored by
economists.

3. Was econophysics previously anticipated?

Econophysics has already made a number of important

empirical contributions to our understanding of the social and
economic world. Many of these were anticipated in two truly
remarkable papers written in 1955 by Simon … and in 1963
by Mandelbrot … , the latter in a leading economic journal.

Gallegati, Keen, Lux, and Ormerod [1]

Ignoring Osborne altogether, Simon and Mandelbrot are

named [1] as having anticipated the main results of
econophysics. This is false. Mandelbrot’s main
contributions were the introduction of Levy distributions
(fat tails for tail exponents in the range from 1 to 3) [32],
the discussion of efficient markets in finance [33], and his
explicit model of fractional Brownian motion (fBm) [34].

Real financial markets are very hard to beat. The efficient

market hypothesis (EMH) states that markets are
impossible to beat: there are no correlations, no
systematic patterns in prices that can be exploited for
profit. If the drift can be subtracted out of a returns time
series, then financial markets are Markovian (pure
nonGausssian noise) to zeroth order, meaning that
correlations like fBm would have to be a higher order
effect [27]. Mandelbrot did not anticipate the correct
description of the dynamics of financial markets, which is
diffusive [4,27] rather than Levy [30,31]. Our modelling
is a generalization of Osborne’s Gaussian returns model
to the case where the diffusion coefficient D(x,t) is (x,t)
dependent. Osborne’s model satisfies the EMH as does
every Markov model.

Fat tails in real markets are generally not described by

Levy distributions because the Levy exponent range is
from 1 to 3, whereas market exponents range from 2 to
7. We can generate the observed fat tail densities via our
approach, including all exponents from 2 to infinity [27]
and with finite variance for exponents from 3 to infinity.
But fat tails are not the main feature of interest in
financial market dynamics. E.g., option prices blow up if
fat tails are included [24,35]. Option traders must
anticipate the dynamics of markets for small to moderate
returns, but VAR requires the entire range of the returns
distribution.

So far as I can see, Herbert Simon anticipated no

quantitative results from econophysics. Simon wrote
many words but produced no mathematical market
model. His paper on asymmetric distributions [1] is not
an anticipation of econophysics. Levy distributions are
generally asymmetric, exponential distributions are
generally asymmetric, so are nearly all distributions. The
trick is to generate the empirically observable market
distributions dynamically, and Simon did not do that. His
main idea, ‘Bounded Rationality’, can be interpreted as
constraint on optimizing behavior (albeit not necessarily
leading to equilibrium) and is therefore still a neo-
classical rather than an empirically based idea, although
behavioral economists have tried through experiments to
ground ‘bounded rationality’ empirically. The Bak et al
model [16] can be seen as one of the few mathematically
specific bounded rationality models (see also [36,37]). So
far as I know, bounded rationality has produced no
falsifiable predictions whereas econophysics, like
physics, is based on on falsifiable predictions. But the
mainstream in the economics profession did not follow
Simon, they instead followed game theory via Nash,
whose ‘every man for himself’ equilibria they found to be
comfortably neo-classical in spirit [38]. So far, that
approach has not managed the transition from the
nightmares of Dr. Strangelove [39] to the empirical reality
of generating realistic market statistics or explaining
markets qualitatively. But Nash’s game is not the only
game in town.

It’s well known that Brian Arthur inspired the Minority

Game, which indeed has been solved extensively using
analysis from statistical physics [40]. The game
theoretical approach does not describe money
transactions in real finance markets quantitatively, but
some members of the Fribourg school have also made
interesting agent based trading models based on actual
limit book data [41]. We know now that an agent based
model should reproduce at least three aspects of real
markets in order to be taken seriously: nonstationarity
with nonstationary increments, volatility (described
locally by an (x,t) dependent diffusion coefficient,
characterizing the noise traders), and fat tails.
Predictions of fat tails from stationary distributions are
both easy and uninteresting.

In our group we’ve found that statistical physics alone

does not provide an adequate background for
econophysics. The advanced methods of statistical
physics are confined to motions near statistical
equilibrium whereas real financial markets exhibit no
equilibrium whatsoever. Empirical evidence for statistical
equilibrium has never been produced for any real market.
We’ve found our experience in nonlinear dynamics to be
very useful for thinking about the dynamics of real
markets, although finance markets are not at all
approximately deterministic. For example, the distinction
between local and global behavior is stressed in
nonlinear dynamics, and one understands better why
‘general equilibrium theory’ (neo-classical economics) is
an impossible candidate for describing real markets if one
has background in nonlinear dynamics (where
integrability vs. nonintegrability and local vs. global are
the key ideas). The stochastic models that we’ve
discovered [27,42] in our (unending) attempt to
understand financial markets cannot be found in any
physics or math text. They were anticipated by no one,
including Mandelbrot, Osborne, and Simon. They
constitute an entirely new contribution to the theory of
Markov processes. Finally, we place little or no weight
on the related notions of ‘data mining’ and ‘financial
engineering’. Nothing fundamental about how markets
work has been discovered by following either path.
Neo-classical economics has been falsified [10]. That it’s
still the central topic of economics texts means that it can
be understood as the mathematized ideology of our era
[4]. In physics and econophysics there are also trends
that can be understood largely as mathematized
philosophy. One of these is the Tsallis movement.
Initially, the Tsallis model was proposed ad hoc as a
statistical equilibrium model. Then, it was generalized to
a dynamical model, but the original equilibrium model
cannot be reproduced by the dynamic one applied in
finance [43,44] with Hurst exponent H=1/(3-q), where q
is the index in the model. Worse, the Tsallis dynamics
model was presented for years as ‘nonlinear’ and
nonMarkovian [43,44], while at the same time implicitly
assuming a Markovian description in the form of an
equivalent Langevin equation. No one in the Tsallis
movement bothered to ask if a nonlinear diffusion
equation is consistent with a Langevin equation. A
Langevin equation with ordinary functions (rather than
functionals) as drift and diffusion coefficients is always
Markovian [27]. A Langevin description of truly
nonlinear diffusion is impossible because a nonlinear
diffusion equation has no Green function, and the Green
function (transition probability density) is the defining
feature of a Markov process. We showed recently that
the Tsallis model is merely one special case of Markov
dynamics, linear diffusion, for the general class of
quadratic diffusion coefficients that scale with a Hurst
exponent [27]. For the entire class of scaling quadratic
diffusion coefficients a ‘nonlinear disguise’ is possible for
the probability density, but the motion is generated by a
(necessarily linear!) Fokker-Planck equation and so is
strictly Markovian. Contrary to all the unjustified claims
in the literature [43,44], there is no such thing as a
‘nonlinear Fokker-Planck equation’. Mathematized
philosophy like neo-classsical economic theory and the
Tsallis model drain energy and effort away from
meaningful research.

... the ‘log-periodic’ business had been exaggerated into

doomsday speculations published in serious journals [... for
example], although not even its prophecies for the mundane
world of the stock markets had ever been scrutinized in a
rigorous fashion.

The logperiodic model [45] is another model from

econophysics. It gets both a plus and some minuses from
us. The plus side is that the idea of a finite time
singularity is interesting and should either be established
or else falsified by a more careful and more critical
empirical analysis. This leads to the minus side: there is
no reason in that model (or in real data) to claim a
bifurcation or critical point, all that appears in the model
is a finite time singularity. Unfortunately, the model as
constructed is not falsifiable: it has far too many free
parameters.

4. Where are we headed?

‘I believe in God and I believe in free markets.”

Enron CEO Kenneth Lay,
San Diego Union-Tribune, 2001

There is little or nothing in existing micro- or

macroeconomics texts [9,46,47] that is of value for
understanding real markets. Economists have not
understood how to model markets mathematically in an
empirically correct way. Their only (once-) scientific
model so far, the neo-classical one, has been falsified.
What is now taught as standard economic theory will
eventually disappear, no trace of it will remain in the
universities or boardrooms because it simply doesn’t
work [48,49]: were it engineering, the bridge would
collapse. The reigning economic theory, based on the
assumptions of optimizing behavior with infinite
foresight, will be displaced by econophysics (where
noise rather than foresight reigns supreme), meaning
empirically based modelling where one asks not what we
can do for the data (give it a massage), but instead asks
what can we learn from the data about how markets
really work. Existing standard economics texts are filled
with scads of graphs [46,47], but those graphs are
merely cartoons because they don’t represent real data,
they represent only the falsified expectations of neo-
classical equilibrium theory [4]. No existing economic
model provides us with a zeroth order starting point for
understanding how real markets function. No current
economics model or idea provides a starting point for
building an interesting falsifiable market model. The
future economics theory/econophysics texts will be filled
with histograms, time series, and with graphs with big
error bars, all representing real markets. They will look
more like nuclear physics data (few data points, big error
bars) than like the smooth curves in the existing
economics texts. The aim will be to try to understand
how markets work, not to present an irrelevant model
about how a real market ideally should (but cannot)
behave. Comparisons of neo-classical economics with
Newton’s first law are irrelevant and terribly misleading:
Newton’s first law is realized locally in every observable
gravitational trajectory. Neo-classical behavior, in
contrast, approximates no real market locally. Future
economics texts will ask many questions but will provide
few answers. That is uncomfortable, but that is the
reality of markets. The good news is that economics
research will not end because most of the important
questions there can likely never be answered. Soros’
message [49] must be taken seriously and understood
because he’s right. In social behavior, each agent has a
perception/illusion of reality but one never knows how
big is the gap between one’s illusion and ‘social reality’,
which is always unknown. We get an incomplete picture
of social reality from history (market time series). As time
goes on, one gains new knowledge and has the chance
to correct one’s perception of reality, one has the chance
partly to correct one’s mistakes [49], but our illusions can
never completely or in controlled fashion be corrected.
Skepticism, not belief, must reign supreme in economics,
finance, and politics. Soros has repeated his basic ideas
in too many books, but we can see him as one of the
most perceptive social scientists of our era. No one
knows yet how to mathematize what Soros tries to teach
us about markets [24]. Our empiric-dynamic
identification of ‘value’ is the starting point for thinking
about Soros’ type of ‘technical analysis’. To try to follow
Soros’ argument and mathematize it is to deal with true
mathematical complexity, something that we have done
neither in economics nor in econophysics (see Zambelli
[18] for an example of how to program a Turing machine
and study the algorithmic complexity of a model on your
laptop). True complexity has been handled so far only in
biology (the genetic code and its consequences), where,
as Ivar Giæver has noted [50], there are many facts and
very few equations.

Let me end anecdotally and then with a suggestion.

Physicists have gone into biology and econophysics
because that's where the interesting problems are.
Turbulence and quantum coherence (mesoscopics)
remain the outstanding unsolved problems of physics.
We meet real complexity in nature in cell biology, also in
quantum computation, along with econophysics they’re
the fields of the future in physics. Every physics student
should be required to take a good, stiff course in cell
biology from a text like „Fat Alberts“ [51], as Ivar
Giæver calls it. Physicists were hired by banks and
trading houses beginning in the 1980s. It's no mistake
that Fischer Black, the driving force behind the Black-
Scholes-Merton model (which assumes Osborne's
lognormal distribution without referencing it) was
trained as a physicist. Physicists go into econophysics
largely because it's interesting, and with the hope of
getting a well-paying job after the Ph. D. Trading houses
do not hire many people from economics or finance
because the products of economics and business
departments don't know enough math and are
unprepared for both data analysis and computer
intensive modeling. I gave a talk to the Enron modelers
in June, 2000. Of the thirty, they were overwhelmingly
from physics and engineering, with two from math.
None were from economics. Two group leaders had
Ph.D.s in experimental physics. The management, not
the modellers, made Enron go belly up. George Soros, if
he’s true to his words, does not carry any belief that’s
free of skepticism. Enron wanted our group to work for
them in 2000. We refused because they wanted data
mining and also technical research aimed at pricing
weather options. The offer of money was not seductive,
we strongly and rightly preferred to stick with
fundamental research of our own choice, so we refused.
The Arrow-Debreu-Merton program [52] fails: when
insufficient liquidity exists, meaning market statistics are
too sparse or even nonexistent (as with gas stored in the
ground, or predicting details of the weather). In such a
case option pricing is like a stab in the dark, but Enron
modelers were required by management to price options
on gas stored in the ground. It was necessary to invent
statistics out of thin air. You simply cannot put a price
on everything when the noise traders [4, 53] are too few
to provide liquidity.

The real problem with my proposal for the future of

economics departments is that current economics and
finance students typically do not know enough
mathematics to understand (a) what econophysicists are
doing, or (b) to evaluate the neo-classical model (known
in the trade as ‘The Citadel’) critically enough to see, as
Alan Kirman [54] put it, that ‘No amount of attention to
the walls will prevent The Citadel from being empty’. I
therefore suggest that the economists revise their
curriculum and require that the following topics be
taught: calculus through the advanced level, ordinary
differential equations (including advanced), partial
differential equations (including Green functions),
classical mechanics through modern nonlinear dynamics,
statistical physics, stochastic processes (including solving
Smoluchowski-Fokker-Planck equations), computer
programming (C, Pascal, etc.) and, for complexity, cell
biology. Time for such classes can be obtained in part by
eliminating micro- and macro-economics classes from the
curriculum. The students will then face a much harder
curriculum, and those who survive will come out ahead.
So might society as a whole.
Acknowledgement

I’m grateful to Gemunu Gunaratne, Kevin Bassler, and

Cornelia Küffner for discussions and comments. I’m grateful
to Rebecca Schmitt, Vela Velupillai, and Giulio Bottazzi for
stimulating discussions of how to improve the current
economics curriculum mathematically, and to a referee for
information about different approaches to Herbert Simon’s
ideas.

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