Research in so-called "econophysics" -- the application of ideas and concepts from physics to problems in finance and economics -- tends to be quite controversial. Many economists in particular seem to find it fairly annoying, although quite a few others either work in the area or do work that is closely associated in conceptual terms. Physicists in the area have been criticized on various occasions for being ignorant of prior work in economics (sometimes true), of using less than rigorous statistics (I haven't seen anything convincing on this) and of employing unrealistic models.
There is plenty of uninspiring work in the field, as in any area of science. Out of politeness, and to avoid boring anyone, I won't make a list. But physicists have made quite a number of lasting contributions to a deeper understanding of finance and economics; in some cases, I think, they have helped to change the direction of research in economics. So I thought it might be worth making a short list of the things that I think have indeed been success stories. Here goes:
1. More than anything, physicists have helped to establish empirical facts about financial markets; for example, that the probability of large market returns decreases in accordance with an inverse cubic power law in many diverse markets. This seems to be a universal result, at least approximately. I've written about this work here. Work by physicists has also established other generic market patterns such as the self-similar structure of market volatility. I very nice review of these patterns is this one by Lisa Borland and colleagues.
Now, did econophysicists initiate this kind of work? Of course not. Benoit Mandelbrot found the first evidence for fat tailed distributions in the early 1960s (and Eugene Fama even wrote about that work in his first paper!). But research by physicists has made our knowledge of these empirical regularities much more precise.
2. Physicists have also identified instructive links between markets and other natural phenomena. For example, in the period following a large market crash, markets show lingering activity which follows the famous Omori law for earthquake aftershocks (events become less likely in simple inverse proportion to the time after the main shock). Such connections indicate that the explanation of such market dynamics may well not depend on facts specific to finance and economics; that more general dynamical principles may be involved.
3. Physicists have also helped develop more realistic models of markets, here mostly in collaboration with economists. In the mid-1990s, researchers at the Santa Fe Institute first demonstrated how fat-tailed dynamics could arise naturally in models representing a market as an ecology of interacting adaptive agents. Models of this kind have since become widespread and used to perform some of the most sophisticated tests of policy proposals -- for the idea of a financial transactions tax, for example, as currently planned by the European Commission. For this, econophysics deserves some credit. For a nice review, see this paper by economist Blake Lebaron (I've summarized it here).
If you doubt that the early work at Sante Fe had a real effect on encouraging this work, pushing the study of computational models of heterogeneous adaptive interacting agents to the forefront of market modelling, take a look at this 2002 review by economist Cars Hommes. As seminal work in this area, he cites papers in the early 1990s by Alan Kirman, by Brad DeLong and colleagues and by the group at Santa Fe which involved a key collaboration between economists and physicists. This work helped kick off, as he describes it, a transformation (still ongoing) of style in modelling markets:
In the past two decades economics has witnessed an important paradigmatic change: a shift from a rational representative agent analytically tractable model of the economy to a boundedly rational, heterogeneous agents computationally oriented evolutionary framework. This change has at least three closely related aspects: (i) from representative agent to heterogeneous agent systems; (ii) from full rationality to bounded rationality; and (iii) from a mainly analytical to a more computational approach...
Hommes makes it sound here as if this transformation and paradigm shift is now widely accepted in economics. I'm not so sure about that as there still seem to be plenty of people eagerly working away on rational representative agent models.
4. Work in econophysics -- through the study of minimal models such as the minority game -- has also revealed surprising qualitative features of markets; for example, that a key determinant of market dynamics is the diversity of participants' strategic behaviour. Markets work fairly smoothly if participants act using many diverse strategies, but break down if many traders chase few opportunities and use similar strategies to do so. Strategic crowding of this kind can cause an abrupt phase transition from smooth behaviour into a regime prone to sharp, virtually discontinuous price movements.
If this point seems esoteric, one fairly recent study found more than 18,000 instances over five years where a stock price rose or fell by roughly 1% or more in well under a tenth of a second. These "glitches" or "fractures" may signal a transition of markets into a regime dominated by fast algorithmic trading. As algorithms compete on speed, they naturally rely on simple strategies, which encourages strategic crowding. The underlying phase transition phenomenon may therefore be quite relevant to policy. I know of nothing in traditional economic analysis that describes this kind of phase transition or does anything to elucidate the kinds of conditions under which it might take place.
5. Yale economist John Geanakoplos has argued for two decades that a key variable driving major economic booms and busts is the amount of leverage used by financial institutions. It goes up in good times, down in bad. Since the financial crisis, controlling leverage has become a major new focus of financial regulators, and their work may well benefit from physics-inspired models of the dynamics of markets in which firms compete with one another through the use of leverage. A notable study by Geanakoplos and two physicists found that such a market will naturally become unstable as leverage increases beyond a threshold. This boundary of instability is not at all obvious to market participants or made evident by standard economic theories. Such models may well help improve macroeconomic policy and financial regulation (I've written a little more on this here).
6. Physicists have also helped clarify other fundamental sources of market instability. For example, standard thinking in economics holds that the sharing of risks between financial institutions -- through derivatives and other instruments -- should both make individual firms safer and the entire banking system more stable. However, a collaboration of economists and physicists recently showed that too much risk sharing in a network of institutions can decrease stability. (Some discussion of this work here.) An over-connected network makes it too easy for trouble originating in one place to spread elsewhere. Again, this work involves an important collaboration between economists and physicists.
7. On a similar theme, fundamental analysis by econophysicists has examined the relationship between market efficiency and stability. In economic theory, markets become more efficient -- more able to pool collective wisdom and price assets accurately -- as they become more "complete," i.e. equipped with such a broad range of financial instruments that essentially any trade can be undertaken. The econophysics work has shown, however, that completeness brings with it inherent market instability, a possibility never raised (to my knowledge) by standard economic analyses.
8. The complexity of today’s markets makes is essentially impossible for financial institutions to judge the risks they face, as the health of any decent-sized financial institution depends on a vast web of links to other institutions about which little may be known. To improve risk judgement, econophysicists have recently developed a network measure called DebtRank which aims to cut through network complexity and reveal the true riskyness of any particular institution. This idea may also provide a natural means for making markets more stable, for if regulators made DebtRank results public, then anyone would, at a glance, gain a much more accurate view of the true risks associated with any bank. If banks seeking to borrow funds were forced to do so from the least risky banks, systemic instability would be improved. This is, for now, a highly speculative idea, but one that clearly has promise.
So there -- a list of 8 specific areas where I think econophysics has had an important impact on economics and finance. This is, as I said, a very short list, and of course reflects only my limited view. It also reflects limitations on how much I can write in one sitting, as there are clearly other notable achievements such as recent theories of market impact -- here and here, for example -- which make significant steps toward explaining how much prices change when someone sells an asset. I haven't mentioned applications of random matrix theory which cast serious doubt over how much empirical calculations of stock correlations really imply about the true correlations between those assets (undermining Markowitz portfolio theory). Then there's an entire field of work exploring how firm growth rates scale with firm size and what might account for this.
All of which suggests, to my mind, that econophysics has been a very valuable development indeed.