Modelling the Crash

Nature has a special issue on ‘Modelling the Crash’. May and Haldane propose a model intended to support policy. Johnson and Lux call for empirical support, meaning a clear link to financial data. Both views have a strong pedigree, yet both seem questionable.

In some ways this discussion pre-empts some of the material I am trying to build up on this blog, and may be ‘hard going’.

May and Haldane

May and Haldane point to connectivity as a factor that was missed out of the pre-crash economic analyses. They make an analogy with ecosystems, where low connectivity is chaotic, increasing connectivity brings stability, but then more connectivity brings instability. It may be a slight digression, but I think it important to focus on what is unstable. Initially it is the components, which are stabilised by being connected. But after a critical point the parts begin to form wholes. These now become the focus of attention. They are unstable because there are few of them. In an important sense, then, maximum complexity is where one has some connectedness (as in a liquid), but the parts are not ‘locked in’ to wholes (solids). If we think of connectivity as co-emerging with growth then the problem is not the kind of growth that loosely connects, but the growth beyond that, in which bubbles of self-reinforcing behaviours develop. This model would seem to suggest that we should be looking out for such feedbacks and bubbles. I agree. In biological evolution Lamarckian inheritance would lead to such bubbles. Maybe one lesson to be learned from nature is that Darwinian evolution is better: the survival of the satisfactory, rather than the over-optimisation of survival of the very fittest, leading to a population of seeming clones.

The paper is largely about robustness and herding, but put in rather narrow terms. It identifies the key issues as homogeneity and fragility, and modularity. It does recognize its own limitations.

I found the paper quite reasonable, but I do see that the presentation invites the supposition that it is leaning too heavily on its ‘mathematical model’.

Johnson and Lux

‘Shouldn’t we test against data sets?’ This raises great challenges.  We know how to test within epochs, and conventional economic theories seem reasonable enough. The challenges are thus:

  • What should we be looking for in theories that span epochs?
  • How do we test theories when the data sets span epochs?

It is common practice to apply ‘Occam’s razor’, which seeks to simplify as much as possible, yet Keynes and Whitehead tend to lead to a contrary view: never assume regularity without evidence. Thus even if we had a theory (like May and Haldane) that fitted all the data, Keynes would predict continuing innovation and hence we would have no reason to trust the theory in future. (See my ‘statistics and epochs’ .)

So What? May and Haldane seems insightful and useful, but leaves open a gap for a more comprehensive ‘model’. Such a model would include nodes with links like those of May and Haldane. Should it be extended into detailed models of how banks work? Or should it seek to identify further key factors? I would like to see it address the issues raised by Lord Turner in ‘mathematics and real systems’.

Dave Marsay

See also ‘The Cassandra Factor’.


About Dave Marsay
Mathematician with an interest in 'good' reasoning.

5 Responses to Modelling the Crash

  1. Pingback: The Cassandra Factor | djmarsay

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  4. Pingback: Haldane’s Tails of the Unexpected « djmarsay

  5. Excellent article. I will be facing a few of these issues as

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