A nice preprint illustrates how emergence is central to some of the biggest questions in economics and finance. Emergent phenomena occur as many economic agents interact resulting in a system with properties that the individual agents do not have.
The Self-Organized Criticality Paradigm in Economics & Finance
The paper illustrates several key characteristics of emergence (novel properties, universality, unpredictability, ...) and the value of toy models in elucidating it. Furthermore, it illustrates the elusive nature of the "holy grail" of controlling emergent properties.
The basic idea of self-organised criticality
"The seminal idea of Per Bak is to think of model parameters themselves as dynamical variables, in such a way that the system spontaneously evolves towards the critical point, or at least visits its neighbourhood frequently enough"
A key property of systems exhibiting criticality is power laws in the probability distribution of a property. This means that there are "fat tails" in the probability distribution and extreme events are much more likely than in a system with a Gaussian probability distribution.
Big questions
The two questions below are similar in that they concern the puzzle of how markets produce fluctuations that are much larger than expected when one tries to explain their behaviour in terms of the choices of individual agents.
A big question in economics
"A longstanding puzzle in business cycle analysis is that large fluctuations in aggregate economic activity sometimes arise from what appear to be relatively small impulses. For example, large swings in investment spending and output have been attributed to changes in monetary policy that had very modest effects on long-term real interest rates."
This is the "small shocks, large business cycle puzzle", a term coined by Ben Bernanke, Mark Gertler and Simon Gilchrist in a 1996 paper. It begins with the paragraph above. [Bernanke shared the 2022 Nobel Prize in Economics for his work on business cycles].
A big question in finance
The excess volatility puzzle in financial markets was identified by Robert Shiller: The volatility "is at least five times larger than it "should" be in the absence of feedback". In the views of some, this puzzle highlights the failings of the efficient market hypothesis and the rationality of investors, two foundations of neoclassical economics. [Shiller shared the 2013 Nobel Prize in Economics for this work].
"Asset prices frequently undergo large jumps for no particular reason, when financial economics asserts that only unexpected news can move prices. Volatility is an intermittent, scale-invariant process that resembles the velocity field in turbulent flows..." (page 2)
Emergent properties
Close to a critical point, the system is characterised by fat-tailed fluctuations and long memory correlations.
Avalanches. They allow very small perturbations to generate large disruptions.
The holy grail: control of emergent properties
It would be nice to understand superconductivity well enough to design a room-temperature superconductor. But, this pales in significance compared to the "holy grail" of being about to manage economic markets to prevent bubbles, crashes, and recessions.
Bouchaud argues that the quest for efficiency and the necessity of resilience may be mutually incompatible. This is because markets may tend towards self-organised criticality which is characterised by fragility and unpredictability (Black swans).
The paper has the following conclusion
"the main policy consequence of fragility in socio-economic systems is that any welfare function that system operators, policy makers of regulators seek to optimize should contain a measure of the robustness of the solution to small perturbations, or to the uncertainty about parameters value.
Adding such a resilience penalty will for sure increase costs and degrade strict economic performance, but will keep the solution at a safe distance away from the cliff edge. As argued by Taleb [159], and also using a different language in Ref. [160], good policies should ideally lead to “anti-fragile” systems, i.e., systems that spontaneously improve when buffeted by large shocks."
Toy models
Toy models are key to understanding emergent phenomena. They ignore almost all details to the point that critics claim that the models are oversimplified. The modest goal of their proponents is simply to identify what ingredients may be essential for a phenomenon to occur. Bouchaud reviews several such models. All provide significant insight.
A trivial example (Section 2.1)
He considers an Ornstein-Uhlenbeck process for a system relaxing to equilibrium. As the damping rate tends to zero [κ⋆ → 0], the relaxation time and the variance of fluctuations diverge at the same rate. In other words, "in the limit of marginal stability κ⋆ →0, the system both amplifies exogenous shocks [i.e., those originating outside the system] and becomes auto-correlated over very long time scales."
The critical branching transition (Section 2.2)
The model describes diverse systems: "sand pile avalanches, brain activity, epidemic propagation, default/bankruptcy waves, word of mouth,..."
The model involves the parameter R0 which became famous during the COVID-19 pandemic. R0 is the average number of uninfected people who become infected due to contact with an infected individual. For sand piles R0 is the average number of grains that start rolling in response to a single rolling grain.
when R0 = 1 the distribution of avalanche sizes is a scale-free, power-law distribution 1/S^3/2, with infinite mean.
"most avalanches are of small size, although some can be very large. In other words, the system looks stable, but occasionally goes haywire with no apparent cause."
A generalised Lotka-Volterra model (Sections 3.3 and 4.2)
This provides an analogue between economic production networks and ecology. Last year I reviewed recent work on this model, concerning how to understand the interplay of evolution and ecology.
A key result is how in the large N limit (i.e., a large number of interacting species/agents) qualitatively different behaviour occurs. Ecosystems and economies can collapse.
"any small change in the fitness of one species can have dramatic consequences on the whole system – in the present case, mass extinctions...
"most complex optimisation systems are, in a sense, fragile, as the solution to the optimisation problem is highly sensitive to the precise value of the parameters of the specific instance one wants to solve, like the Aij entries in the Lotka-Volterra model. Small changes of these parameters can completely upend the structure of the optimal state, and trigger large-scale rearrangements,..."
Balancing stick problem (Section 3.4)
The better one is able to stabilize the system, the more difficult it becomes to predict its future evolution!
Propagation of production delays along the supply chain (Section 4.1)
An agent-based firm network model (Section 4.3)
This has the phase diagram shown below. The horizontal axis is the strength of forces counteracting supply/demand and profit imbalances. The vertical axis is the perishability of goods.
There are four distinct phases.
Leftmost region (a, violet): the economy collapses;
Middle region (b, blue): the economy reaches equilibrium relatively quickly;
Right region (c, yellow): the economy is in perpetual disequilibrium, with purely endogenous fluctuations.
The green vertical sliver (d) corresponds to a deflationary equilibrium
Universality
The toy models considered describe emergent phenomena in diverse systems, including in fields other than economics and finance.
Here are a few other recent papers by Bouchaud that are relevant to this discussion.
Navigating through Economic Complexity: Phase Diagrams & Parameter Sloppiness
From statistical physics to social sciences: the pitfalls of multi-disciplinarity
This includes the opening address from a workshop on "More is Different" at the College de France in 2022.
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