Why are Economies Unstable? Research Project
But Why are Economies Stable?
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Principal Investigator: Professor Robert MacKay, FRS
Robert Sinclair MacKay FRS FInstP FIMA is a British mathematician and professor at the University of Warwick. Robert’s research focuses on the theory and application of nonlinear dynamics. Highlights include his discovery and renormalisation explanation of how invariant tori break for Hamiltonian systems, and a proof of the existence of spatially localised timeperiodic movements in networks of oscillators with an analysis of their stability, interaction and mobility.
He is also responsible for the construction and proof of a mechanical example of a uniformly chaotic system, and the construction of indecomposable spatially extended deterministic dynamical systems exhibiting more than one space–time phase.
Robert is currently a Professor of Mathematics, Director of Mathematical Interdisciplinary Research and Director of the Centre for Complexity Science at the University of Warwick. He has published around 180 papers and articles in his field, as well as being the recipient of over 100 research grants. He served as President of the Institute of Mathematics and its Applications from 2012–2013.
CoInvestigators: Nicholas Beale (Sciteb), Richard Gunton (Winchester), Samuel Johnson (Brimingham), and Marcus Miller (Warwick)
Project Summary
The macroeconomic question: For mathematicians, the puzzle is not why economies are unstable but why they are stable. Since the 1972 MayWigner theorem, it has been known that large complex systems tend to be unstable. If current economies are mostly stable, this may be due to ‘survivorship bias’: the ones we observe are those that have acquired appropriate stabilisation mechanisms. These may include employment and product law and regulation, international trade agreements, insolvency law, credit ratings, and the prudential regulation of financial firms and systems.
In ecology, key determinants of the stability of complex systems are structural features like ‘trophic coherence’, a concept that has recently been introduced (PNAS 111 (2014): 1792317928). A food web has high trophic coherence if every species eats species at just one level below; and it has been found that networks with high trophic coherence are much more stable than those without. Are there analogies in economics, for example to the supply network? Failures of trophic coherence in economics could result, for example, from the common practice of iterated subcontracting – and we have seen recent examples of the resulting instability. In the other direction, the increased emphasis on ‘central clearing’ in finance, for example, can be seen as a stabilising response.
As for immune systems, however, these stabilisation mechanisms may not always work. To start with, there are private incentives to avoid or evade regulation, however well meant. Furthermore, microprudential financial rules may spawn instability through ‘pecuniary externalities’ – which has prompted the current focus on ‘macro–prudential’ policy intervention by Central Banks and Regulatory Authorities.
An important added consideration is robustness to external changes. Economies are not closed, autonomous systems but are subject to many external forces such as weather and natural disasters, technological and managerial innovation, and policy interventions (e.g. monetary and fiscal policy, trade tariffs, employment law, Brexit, war…). Robustness is desirable even if total stability is not.
The key question then is: if market economies are potentially unstable, what is the source of the instabilities, and how can we promote policy to regulate and stimulate economies more effectively?
This leads to a supplementary question: if too many regulations depress growth and dynamism at the system level – or adaptability and innovation at the company level – how can we develop more efficient policy tools for encouraging desirable transitions between economic states, using the natural instabilities? What answers can the control theory of unstable systems provide? Note the need to take into account the human psychological element: simple controls are more likely to succeed than complex codes of regulation.
Methods to be used: Insight from dynamical systems theory, ecosystem and evolutionary ecology, and control theory will be central throughout. We will use a wide range of quantitative methods: formal analyses of simple network models, exploratory statistical analyses of investment and production networks, and sensitivity analysis of simulation models.
Policyvalue: Our approach will help identify policies to help curb economic instabilities and to design interventions to move an economy to a more productive and stable state using increased understanding of the natural dynamics.
Novelty: The use of ecological ideas in economics is relatively recent, pioneered by D.Farmer, Sugihara, Beale, Nowak, May and Haldane. Our project will take it further, in particular adapting the recent idea of trophic coherence, a concept pioneered by one of our team (Johnson) and which has only recently been applied to economies (McNerney, Savoie, Cavelli & Farmer, arXiv 1810.07774).
Interdisciplinarity: Our team brings together a variety of expertise, and consists of:

Nicholas Beale, Director of Sciteb, a consultancy with offices in London, Cambridge MA and Beijing, and Director of the Global Collaboration on Financial Systems Stability (in which Gunton, Miller and MacKay are active) with strong connections to top policymakers in economics and finance;

Richard Gunton, ecologist, lecturer in mathematics at Winchester and postdoctoral research fellow in CECAN, an ESRC network on evaluation of policy in complex systems;

Samuel Johnson, Lecturer in Mathematics, University of Birmingham, and Turing Fellow, with expertise in ecology and seminal papers (e.g. PNAS 111 (2014): 1792317928) on trophic coherence.

Marcus Miller, Professor of Economics and Research Associate of the ESRC Centre for Competitive Advantage in the Global Economy, both at the University of Warwick;

Robert MacKay, Professor of Mathematics and Director of Mathematical Interdisciplinary Research at Warwick, with particular expertise in the application of dynamical systems theory, and involvement in the Turing Institute’s Financial and Economic Data Science programme, and CECAN.
Results
Working Paper
How Directed is a Directed Network?
R.S. MacKay, S. Johnson, B. Sansom  28 January, 2020
Abstract
The trophic levels of nodes in directed networks can reveal their functional properties. Moreover, the trophic coherence of a network, deﬁned in terms of trophic levels, is related to properties such as cycle structure, stability and percolation. The standard deﬁnition of trophic levels, however, borrowed from ecology, suffers from drawbacks such as requiring source nodes, which limit its applicability. Here we propose a simple new deﬁnition of trophic level that can be computed on any directed network. We demonstrate how the method can identify node function in examples including ecosystems, supply chain networks, gene expression, and global language networks. We also explore how trophic levels and coherence relate to other topological properties, such as nonnormality and cycle structure, and show that our method reveals the extent to which the edges in a directed network are aligned in a global direction.