Complexity theory in economics

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).

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