But Why are Economies Stable?

Robert MacKay and Marcus Miller

The question posed for the Rebuilding Macroeconomics’ Instability Hub is “Why are economies unstable?”  The answer suggested by the work of the biologist Robert May (1972) is that economies are large complex systems and such systems tend to be unstable.

A random complex system, unconstrained,

May showed should be unstable: that’s a given.

But, if from ecosystems, we can take

a deeper understanding of the ways

that complex systems do not run away,

such insights might help to avert disaster –

or stabilise a crisis rather faster.

As these lines by Nicholas Beale (our resident poet) indicate, May’s view faced a challenge from ecology: for in the natural world – at least until global warming – large, complex ecosystems such as tropical rainforests and coral reefs seemed to be the most stable! To account for this, ecologists and others have been studying key structural characteristics of biological systems.

One such feature, of food webs in particular, is what is called ‘trophic coherence’, Johnson et al (2014). A food web has high trophic coherence if members of each species eats those of species at just one level below; and it has been found that networks with high trophic coherence are much more stable than those without.

The familiar ecological pyramid shown above – with the basic plant forms at ground level, with herbivores above, and then carnivores above them – can be used to illustrate. In stylised form, a high level of trophic coherence between species can be represented mathematically as in the leftmost graph in the chart below – where there are four trophic levels (represented by layers in the graph) with well-ordered biological links between them.

When the links are less well ordered, however, with more random connections between species (as is increasingly the case moving from left to the right in the figure, with variable q as a measure of such disorder), it turns out that the system is less stable, more prone to biological collapse.

Examining biological links from this perspective encompasses so-called ‘predator-prey’ dynamics – the oscillating populations of foxes and rabbits, for example, or of mink and musk- rat, Chan and Wallis (1978) – and the spread of epidemics. In the cautionary view of Kirk et al. (2015), it should be said, stability cannot be summarily inferred from any single property of the system but will depend on adequately capturing the details.

Could concepts analogous to trophic coherence be relevant for the study of economic stability?

Farmer et al. (2018) are looking at economic supply networks from this perspective. Failures of trophic coherence could result, for example, from the common practice of iterated subcontracting – and we have seen recent examples of this. In the other direction, the increased emphasis on ‘central clearing’ in finance, for example, may be seen as a stabilising response.

Might the key features that promote stability in nature help in the restructuring of financial systems and in their regulation? Andy Haldane of the Bank of England has famously contrasted the simplicity of the Glass-Steagall legislation introduced after the Wall Street crash with the enormous complexity of the Dodd-Frank legislation that followed the recent US subprime crisis. Will the UK response – which involves ‘ring fencing’ commercial banking off from investment banking and imposing a code of conduct on bankers (including custodial sentences for ‘reckless conduct’ by senior managers) – be more effective by focusing on key structural features?

These are the sort of questions to be addressed in our project, with added input from the Global Collaboration on Financial System Stability led by Nicholas Beale, an ongoing dialogue between financial regulators and asset managers which encourages “special thinking” – including ecological approaches – with a view to checking financial instability, as for example Beale et al. (2011).

References

Chan W.-Y.T. and K. F. Wallis (1978). “Multiple time-series modelling: another look at the mink-muskrat interaction”.  Applied Statistics, 27: 168-175.

Beale, N., D.G. Rand, H. Battey, K. Croxson, R.M. May and M.A. Nowak, (2011). “Individual vs Systemic Risk and the Regulators Dilemma”. Proceedings of the National Academy of Science 108(31): 12647–12652.

Farmer, D.,  F. Caravelli,  J. McNerney and C. Savoie,(2018). “How production networks amplify economic growth”. Preprint.

Kirk,P. D. M.Y. Rolando, A. L. MacLean and M.P.H. Stumpf (2015). “Conditional random matrix ensembles and the stability of dynamical”. New Journal of Physics, 17(8)

Johnson S, V. Domínguez-García,L.  Donetti  and M. A. Muñoz (2014). “Trophic coherence determines food-web stability”. Proceedings of the National Academy of Science. 111 (50): 17923. (Also freely available at arXiv:1404.7728 )

May R. M. (1972) ”Will a large complex system be stable?” Nature, 238 (5364):413–414.