The Physics of Economics

This is the first of two posts which began life as a single piece with the title “The Physics of Economics (and the Economics of Physics)”. In the first section, here, I discuss some ways physicists have attempted to contribute to economics. In the second half, I turn to the lessons that economics should learn from the history of a technological innovation with its origin in physics – the semiconductor industry.

Physics and economics are two disciplines which have quite a lot in common – they’re both mathematical in character, many of their practitioners are not short of intellectual self-confidence – and they both have imperialist tendencies towards their neighbouring disciplines. So the interaction between the two fields should be, if nothing else, interesting.

The origins of econophysics

The most concerted attempt by physicists to colonise an area of economics is in the area of the behaviour of financial markets – in the field which calls itself “econophysics”. Actually at its origins, the traffic went both ways – the mathematical theory of random walks that Einstein developed to explain the phenomenon of Brownian motion had been anticipated by the French mathematician Bachelier, who derived the theory to explain the movements of stock markets. Much later, the economic theory that markets are efficient brought this line of thinking back into vogue – it turns out that financial markets can be quite often modelled as simple random walks – but not quite always. The random steps that markets take aren’t drawn from a Gaussian distribution – the distribution has “fat tails”, so rare events – like big market crashes – aren’t anywhere like as rare as simple theories assume.

Empirically, it turns out that the distributions of these rare events can sometimes be described by power laws. In physics power laws are associated with what are known as critical phenomena – behaviours such as the transition from a liquid to a gas or from a magnet to a non-magnet. These phenomena are characterised by a certain universality, in the sense that the quantitative laws – typically power laws – that describe the large scale behaviour of these systems doesn’t strongly depend on the details of the individual interactions between the elementary objects (the atoms and molecules, in the case of magnetism and liquids) whose interaction leads collectively to the larger scale phenomenon we’re interested in.

For “econophysicists” – whose background often has been in the study of critical phenomenon – it is natural to try and situate theories of the movements of financial markets in this tradition, finding analogies with other places where power laws can be found, such as the distribution of earthquake sizes and the behaviour of sand-piles. In terms of physicists’ actual impact on participants in financial markets, though, there’s a paradox. Many physicists have found (often very lucrative) employment as quantitative traders, but the theories that academic physicists have developed to describe these markets haven’t made much impact on the practitioners of financial economics, who have their own models to describe market movements.

Other ideas from physics have made their way into discussions about economics. Much of classical economics depends on ideas like the “representative household” or the “representative firm”. Physicists with a background in statistical mechanics recognise this sort of approach as akin to a “mean field theory”. The idea that a complex system is well represented by its average member is one that can be quite fruitful, but in some important circumstances fails – and fails badly – because the fluctuations around the average become as important as the average itself. This motivates the idea of agent based models, to which physicists bring the hope that even simple “toy” models can bring insight. The Schelling model is one such very simple model that came from economics, but which has a formal similarity with some important models in physics. The study of networks is another place where one learns that the atypical can be disproportionately important.

If markets are about information, then physics should be able to help…

One very attractive emerging application of ideas from physics to economics concerns the place of information. Friedrich Hayek stressed the compelling insight that one can think of a market as a mechanism for aggregating information – but a physicist should understand that information is something that can be quantified, and (via Shannon’s theory) that there are hard limits on how much information can transmitted in a physical system . Jason Smith’s research programme builds on this insight to analyse markets in terms of an information equilibrium[1].

Some criticisms of econophysics

How significant is econophysics? A critique from some (rather heterodox) economists – Worrying trends in econophysics – is now more than a decade old, but still stings (see also this commentary from the time from Cosma Shalizi – Why Oh Why Can’t We Have Better Econophysics? ). Some of the criticism is methodological – and could be mostly summed up by saying, just because you’ve got a straight bit on a log-log plot doesn’t mean you’ve got a power law. Some criticism is about the norms of scholarship – in brief: read the literature and stop congratulating yourselves for reinventing the wheel.

But the most compelling criticism of all is about the choice of problem that econophysics typically takes. Most attention has been focused on the behaviour of financial markets, not least because these provide a wealth of detailed data to analyse. But there’s more to the economy – much, much more – than the financial markets. More generally, the areas of economics that physicists have tended to apply themselves to have been about exchange, not production – studying how a fixed pool of resources can be allocated, not how the size of the pool can be increased.

[1] For a more detailed motivation of this line of reasoning, see this commentary, also from Cosma Shalizi on Francis Spufford’s great book “Red Plenty” – “In Soviet Union, Optimization Problem Solves You”.

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