[OPE-L:1924] Re: flowcharts, differential equations, and chaos theory

Steve Keen (s.keen@uws.edu.au)
Wed, 15 Dec 1999 09:09:18 +1100

Hi Jerry,

and thanks for the intro to the group too.

On the questions:
At 10:21 1999-12-14 -0500, you wrote:
>I have a few questions for Steve K:
>> The latter is his thesis, though substantially revised, and presented
>> using systems engineering "flowchart" tools rather than differential
>> equations.
>1) is this only a question of "presentation" or are there inherent
> non-presentational (i.e. analytical) advantages in the use of systems
> engineering flow charts?

It's mainly presentation, but there are also inherent advantages. The
presentation advantage is that the general public's reaction to seeing
equations in a book is to put it down and move on to the next candidate for
a purchase--a mate of mine calls it the "MEGO" effect: "My Eyes Glaze
Over". Since I want to reach a wider audience, flowcharts are far less
intimidating. And yet they (in the guise of programs like Vissim, Ithink
and Simulink) do the same thing: numerically simulate systems of ordinary
differential equations.

The advantages include the ease with which you can incorporate real-world
features such as time delays, time lags (a different phenomenon), etc., the
ability to structure a model (with sub-levels), and the ability to produce
models without having to do calculus. The latter is something I enjoy, but
f'rinstance with Vissim I can build Goodwin's predator-prey model in terms
of Y,K,L,W (output, capital, labor, wages) rather than y,k,l,w (ratios of
preceding) and without having to reduce it to a pair of coupled ODEs in w
and l.

>2) what do you see as the analytical advantages of systems engineering
> tools and differential equations rather than other tools like matrix
> algebra and game theory to model capitalist dynamics?

Matrix algebra presumes static outcomes, unless you're using matrix
notation in a system of ODEs/PDEs. I recently had an exchange with Ian
Steedman on this front, in reply to his "Questions for Kaleckians" in ROPE
in 1992 (I think). He showed that Kaleckian markup pricing is incompatible
with input output analysis; I showed that static input output analysis is
only valid if the input output matrix is dynamically stable. For example,
matrix algebra would rule out an input-output model which gave negative
equilibrium prices. However, the same matrix, when part of a linear ODE
model, results in an unstable equilibrium in which inflation occurs. Prices
therefore always diverge from the equilibrium", and so such an input-output
model is quite valid in a dynamic setting--even though it is invalid in a
static one.

Game theory... I'm a somewhat ill-informed agnostic on that area. I have
seen some good work (I very much like what Yanis Vourifakis at Sydney Uni
does in that area and the related area of experimental economics). There's
also some interesting stuff coming out of Japan generalising games into
network models and cellular automata. "Commerce, Complexity and Economics",
which should be out in March/April from CUP, has several examples of that.
But a lot of what I've seen sucks too!

>3) what branches of mathematics are best suited for the development of
> chaotic models?

Differential equations are the foundation. Beyond that, numerous
computational approaches exist--cellular automata (which get spatial as
well as temporal aspects of chaos), genetic algorithms, etc.

Anyone who isn't yet into that area and wants to check it out should buy
two books: "Ordinary Differential Equations and their Applications" by
Braun, the most readable maths book I've ever read; and Ott's introductory
book on Chaos, also very accessible.

>4) is capitalism chaotic? Why or why not?

It's highly nonlinear, so it's almost certainly chaotic. The catch is that
high dimensional chaos is indistinguishable from random noise--which fits
the neoclassical paradigm, but in a rather destructive way! But chaos
doesn't mean "out of control", as it happens (though it can in some
circumstances)--just endogenously unstable and aperiodic. Most "tests of
chaos" in economic data haven't found it, but most tests produced by
economists--such as the BDS statistic--are massively compromised by their
belief in equilibrium. A good read on this is Francisco de Louca's
"Turbulence in Economics".

Dr. Steve Keen
Senior Lecturer
Economics & Finance
University of Western Sydney Macarthur
Building 11 Room 30,
Goldsmith Avenue, Campbelltown
PO Box 555 Campbelltown NSW 2560
s.keen@uws.edu.au 61 2 4620-3016 Fax 61 2 4626-6683
Home 02 9558-8018 Mobile 0409 716 088
Home Page: http://bus.macarthur.uws.edu.au/steve-keen/
Workshop on Economic Dynamcs: http://bus.macarthur.uws.edu.au/WED

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