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Complexity theory in economics
A very good update from David Warsh.
Posted by Tyler Cowen on May 29, 2008 at 07:55 PM in Economics | Permalink
Comments
A missing reference:
"Organized complexity here means that the character of the structures showing it depends not only on the properties of the individual elements of which they are composed, and the relative frequency with which they occur, but also on the manner in which the individual elements are connected with each other." Hayek 1974
Posted by: Pedro P Romero at May 29, 2008 10:47:36 PM
A question for Tyler Cowen or anybody else who might know: are there any real, non-pseudoscientific applications of analysis on fractals to economics? All I've seen so far are suspicious-looking stock market tricks that deny the efficient markets hypothesis.
Posted by: sc at May 29, 2008 11:44:15 PM
Pedro,
It is sort of an underground fact that Hayek was a serious precursor
of complexity theory. Bruce Caldwell discusses this in his definitive
intellectual biography, _Hayek's Challenge_, with Hayek becoming more
interested in this matter later in his life, although some of it came
from his work on consciousness, _The Sensory Order_, published in the
early 1950s, which in turn drew on observations he made during his
medical work in World War I when he was quite young. Some observers
see it in earlier works in the 1940s where he proposed market structures
as spontaneous orders, and indeed that is a focus later in his career.
His most important essay on the matter appeared in 1978.
I also note that I happen to have reported independently in a 1999
paper in the Journal of Economic Perspectives on the basis of my own
findings that Hayek made links during the 1970s with the two most
important centers of complexity research in Europe that presaged the
later Santa Fe Institute, namely the Ilya Prigogine group in Brussels
and the group around Hermann Haken and Wolfgang Weidlich at the
Institute of Theoretical Physics in Stuttgart (not far from Freiburg,
where Hayek spent his last years). I have it from primary sources
that the Prigogine group did not quite know what to make of Hayek
(and, of course, he did not deal specifically in math), while he had
much better relations with the Stuttgart group, becoming a personal
friend of Haken, who was a refugee from East Germany.
I note that the late Don Lavoie of George Mason also wrote a paper that
was published in 1989 in the Cato Journal that highlights the spontaneous
order argument of Hayek and its relationship to chaos theory and complexity
theory. It should be kept in mind that chaos and complexity are not
necessarily either good or bad. It all depends on circumstances. Thus,
Dave Warsh identifies complexity with the increasing variety of goods
available in the economy, and many systems need some degree of irregular
fluctuations in order to grow and develop. Attempting to eliminate these
things can lead to greater problems than they solve in many cases.
sc,
Well, Mandelbrot, who invented/discovered fractals interpreted the
finding that asset returns can be mapped as roughly linear on a log-log
graph, which means that they fit a power-law distribution, a major
bugaboo of the new econophysicists, as reflecting fractal dimensionality,
with the slope of that line indicating it. Now, indeed most observers
view this finding as consistent with their being excess volatility,
("fat tails") in financial markets, or positive fourth moments, kurtosis,
which is not consistent with the simple forms of the efficient markets
hypothesis.
So, there is a hard nut here you need to deal with. The data in fact
is in: most asset markets do show fat tails and fit power-law distributions,
even if most economists are only vaguely aware of this. All practitioners
know this: it is now a "stylized fact." So, the issue then becomes,
how do you interpret this, what does it mean? Of course, many argue
that it means that the state should intervene somehow to reduce all this
"excess volatility." Maybe it should. But it is also the case that
nobody has come up with an obvious or easy way to do this that does not
also reduce the information and flexibility and mobility aspects that
freer finanical markets possess and exhibit. To use an older language,
our highly volatile financial markets may not be "first best," but they
may be "second best" (hard or impossible to improve through reform),
although I personally think we can do better with our housing markets
than we have, and also think that the foreign exchange markets are pretty
much a mess, although reforming them involves much deeper issues that go
way beyond just excess volatility (which they do exhibit indeed).
Posted by: Barkley Rosser at May 30, 2008 1:10:49 PM
Barkley,
Thanks for your extensive post and references. My intention in my previous post was to call attention of people who might read Warsh's post unaware of the connection to Hayek.
I learnt from your JEP 1999 article about the link between Hayek and Haken a while ago. Also I found your article on Econophysics a required reading for those who may not know of the old relationship between physics and economics. I still have to read your paper on Transdiciplinary perspectives.
About Mandelbrot and non-gaussian patterns. I suggest to read Mandelbrot's original paper from 1963 in the Journal of Business. In the same volume of that journal you will find a paper reviewing that article by Eugene Fama. He basically agreed with Mandelbrot's discovery. Fama was Mandelbrot's student. Now, a question for historians of ideas is: How Fama became the most important proponent of the Efficient Market Hypothesis since 1970, even though he knew very early about Mandelbrot's results.
But keep in mind that power laws distributions describe 'extreme events' like a crisis or bubble. In between EMH still holds.
It is interesting how Brad DeLong just recently pointed out that "we need to worry about tail risks, sudden stops, and why financial
markets have not been appropriately pricing the risks generated by largescale persistent inflows of capital to the core of the world economy." is his lecture on Capital Complements. From my point of view there is more room there for explanations a la Mandelbrot than otherwise.
Posted by: Pedro P Romero at May 30, 2008 2:32:21 PM
Pedro,
Thanks for your comments.
Regarding the EMH, I would say that its kernel of truth for financial markets resides in the remaining fact that it is very hard to beat the random walk in practice. Some people do pull it off, with some of the better high-frequency econophysics types doing it, at least for now. But, behavioral anomolies that may persist over several months tend to get competed away once people become aware of them. This all holds despite (or even more so because of) the excess volatility in these markets as measured by all those fat tails (and black swans) and power law distributions (which Taleb actually says are only "grey swans").
Mandelbrot actually wrote quite a few other related papers, some of which cognoscenti consider to be better, but the 1963 Journal of Business (which apparently has folded for reasons mysterious to me) one is the one that everybody cites. I have been on the record for sometime publicly advocating that he receive the Nobel Prize in economics, but I am not holding my breath that he will get it.
The tale of him and Fama is a murky one. It needs to be kept in mind that in Mandelbrot's original formulation he posited the asymptotic vanishing of second moments (variance) as the source of the extreme events, rather than focusing more directly on the fourth moments (kurtosis) themselves. Fama was originally an acolyte, but turned against Mandelbrot because he looked at larger and larger data sets and saw no tendency for second moments to vanish. It was after this, but while he was somehow forgetting about the existence of the fourth moments, that he promulgated and pushed for the EMH.
Now, I caused a fuss at a conference over a decade ago at which Mandelbrot was in attendance. He had given a long lecture just before lunch. I had just read a paper arguing that while second moments do not vanish, fourth moments do, which would give the fractalized power law distribution results he has long advocated. I (stupidly) asked him about this. Well, he interpreted my question as somehow defending Fama, and he launched into about a 20 minute diatribe, leading a lot of people to get very angry with me as their stomachs began to curdle. I knew I was in trouble right away, actually, because a prominent mathematician who was sitting next to me immediately told me after I asked the question that "you have just made a very big mistake," accompanied with a big scowl. I apologized to him later.
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