Economist Chris House wonders why so many physicists are drawn to economics. It's a fair question, and it must seem strange -- perhaps irritating -- to see people from a foreign field intruding into your territory, fully convinced that they'll be able to help out even without formal economics training. They haven’t learned what you’ve worked hard to learn, and yet they still have such annoying confidence. The explanation, Chris suggests, is that physicists often believe they're mathematically superior to economists, and so might be able to sort out some big problems quite easily.

As he puts it,

Even before the financial crisis, there has always been a surprising number of ex-physicists who find their way to graduate study in economics. ... I suspect ... that some of them are here because they have some incorrect perceptions about the field. A student with a mathematical-physics background could easily convince himself that he has superior mathematics abilities than typical economists and superior statistical and computational skills than most economists.[1] He might go on to conclude that, as a consequence of his superior mathematical and computational abilities, he should be able to enter economics and start contributing quickly and easily. He might also anticipate that he could easily adapt established models or techniques in physics to study economic phenomena and impress the profession. If you are one of these people, let me try to disabuse you of these notions. Your mathematical abilities are actually not that much better than most economists (if they are better at all). You will have to spend a lot of time acclimating to the subject and the path to actually making contributions will be long and difficult. In all likelihood, there are very few (perhaps zero) off-the-shelf models or techniques in physics (or engineering, or chemistry, …) that will produce meaningful economic results. High-tech methods and approaches will be valued only if they can be described in simple, direct ways. Economists are not held back because of a deficiency of mathematical tools and techniques. As soon as I hear a physicist (or a mathematician or whoever) start talking about the need for economists to use “the right mathematical techniques” I immediately think that the person has absolutely no idea what the main problems and questions in economics actually are.

I don’t think this is quite right, and I’ll try below to say why. If Chris has had this experience, that’s unfortunate, but I don’t think it’s typical of why some physicists choose to work on problems in economics or finance. Most of the ones I know don’t believe they’re smarter than economists, or better mathematicians, nor do they think economics is somehow “easy.” They tend to believe, in fact, that economics is harder than physics. Physicists don’t think they’re going to come in and easily work everything out.

What the physicists DO believe, however, is that markets and economies are great examples of what scientists have come to call “complex systems” — systems of many elements (people, firms, etc.) with strong interactions between those elements which create webs of non-linear feedback. The elements learn and adapt, their interactions create “emergent” coherent structures and fluctuations at the collective level, and these structures then act back downwards to influence the behavior of the elements. What happens in the system comes about through this interplay of bottom-up and top-down cause and effect. In this sense, economic systems share a deep character with many physical or biological systems from the earth’s crust to turbulent fluids to ecosystems. It’s this complex systems aspect of economics which makes physicists believe that ideas from physics (and other natural sciences) can be useful in economics.

This is precisely why many physicists, myself included, are convinced that modern economics is indeed, in an important sense, “held back because of a deficiency of mathematical tools and techniques”, to use Chris’s words. I can’t do better than to quote a short section from Brian Arthur’s excellent article Complexity Economics, which describes what many people (including physicists) believe is lacking from current economics:

The economy is a vast and complicated set of arrangements and actions wherein agents—consumers, firms, banks, investors, government agencies—buy and sell, speculate, trade, oversee, bring products into being, offer services, invest in companies, strategize, explore, forecast, compete, learn, innovate, and adapt. In modern parlance we would say it is a massively parallel system of concurrent behavior. And from all this concurrent behavior markets form, prices form, trading arrangements form, institutions and industries form. … One of the earliest insights of economics—it certainly goes back to Smith—is that these aggregate patterns form from individual behavior, and individual behavior in turn responds to these aggregate patterns: there is a recursive loop. It is this recursive loop that connects with complexity. Complexity is not a theory but a movement in the sciences that studies how the interacting elements in a system create overall patterns, and how these overall patterns in turn cause the interacting elements to change or adapt. … Complexity is about formation—the formation of structures—and how this formation affects the objects causing it. To look at the economy, or areas within the economy, from a complexity viewpoint then would mean asking how it evolves, and this means examining in detail how individual agents’ behaviors together form some outcome and how this might in turn alter their behavior as a result. Complexity in other words asks how individual behaviors might react to the pattern they together create, and how that pattern would alter itself as a result. This is often a difficult question… And so economics early in its history took a simpler approach, one more amenable to mathematical analysis. It asked not how agents’ behaviors would react to the

aggregate patterns these created, but what behaviors (actions, strategies, expectations) would be upheld by—would be consistent with—the aggregate patterns these caused. It asked in other words what patterns would call for no changes in micro-behavior, and would therefore be in stasis, or equilibrium. … This equilibrium shortcut was a natural way to examine patterns in the economy and render them open to mathematical analysis. It was an understandable—even proper—way to push economics forward. And it achieved a great deal. Its central construct, general equilibrium theory, is not just mathematically elegant; in modeling the economy it recomposes it in our minds, gives us a way to picture it, a way to comprehend the economy in its wholeness. This is extremely valuable… But there has been a price for this equilibrium finesse. Economists have objected to it—to the neoclassical construction it has brought about—on the grounds that it posits an idealized, rationalized world that distorts reality, one whose underlying assumptions are often chosen for analytical convenience.4 I share these objections. Like many economists I admire the beauty of the neoclassical economy; but for me the construct is too pure, too brittle—too bled of reality. It lives in a Platonic world of order, stasis, knowableness, and perfection. Absent from it is the ambiguous, the messy, the real. … If we assume equilibrium we place a very strong filter on what we can

see in the economy. Under equilibrium by definition there is no scope for improvement or further adjustment, no scope for exploration, no scope for creation, no scope for transitory phenomena, so anything in the economy that takes adjustment—adaptation, innovation, structural change, history itself—must be bypassed or dropped from theory. The result may be a beautiful structure, but it is one that lacks authenticity, aliveness, and creation. What if economics allowed the wider possibility and asked how agents in the economy might react to the patterns they together create? Would this make a difference? What would we see then?

In my experience, it is precisely questions like this that draw physicists into economics and finance. Their motivation is to try to go beyond the equilibrium perspective which they see as lacking “the ambiguous, the messy, the real” as well as “authenticity, aliveness, and creation.” Most of the work I have written about is in this area, and it might be worth citing just a few examples (see this article for a few more; below I’ve mentioned three from the examples listed there).

To begin with, work by physicists has been significant is establishing empirical facts about the statistics of financial market fluctuations; for example, that the probability of large market movements (up or down) decreases in accordance with an inverse cubic power law in many diverse markets (stocks, bonds, currencies, derivatives, and in many nations). This is a very simple mathematical pattern and captures in precise form the so-called “fat tails” of market fluctuations – the natural occurrence of large market upheavals much more frequently than would be expected by ordinary Bell Curve statistics. These “fat tails” seem to be a more or less universal result. (For some further detail, look here; or this nice review by New York University economist Xavier Gabaix, who actually worked with statistical physicists as a postdoc.) Work by physicists has also established other generic market patterns such as the self-similar structure of market volatility. I very nice recent review of these patterns is this one by Lisa Borland and colleagues. It is notable that these patterns arise not only in markets, but in a wide variety of natural complex systems, suggesting that seeing markets as driven, out-of-equilibrium complex systems is indeed quite sensible.

As another example, physicists studying minimal models of markets — such as the minority game -- have found some surprising qualitative features that one might expect to observe in all markets. In particular, 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. One fairly recent study suggested that high-frequency trading may be pushing modern markets through such a phase transition, with the breakdown of the continuity of prices movements (lots of mini-flash crashes) being one major consequence. The underlying phase transition phenomenon may therefore be quite relevant to policy. I know of nothing in traditional equilibrium economic analysis that describes this kind of phase transition.

Finally, I might also mention market efficiency versus stability. 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. On a similar theme, an analysis by physicists (here conducted in a general equilibrium framework quite familiar to economists!) indicates that complete markets should also necessarily be unstable markets. In standard theory, I believe, it is thought that 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 new work has shown, however, that completeness brings with it inherent market instability. Is this an old result well-known in economics? If it is — and seriously, maybe it is — I’d like to know.

OK, this post is already way too long, but one final thing. Physicists, I think, become even more drawn to economics when we look into economics and see broad resistance to research pursuing this “complexity” perspective.

It seems instead that most of mainstream research tries to get around system complexity with mathematical tricks, rather than facing up to it. I’m thinking about ideas like representative agents, or rational expectations. The assumptions make it possible to build models without having to deal with the complexity of interactions and the emergent structures they create; but the resulting models, naturally, look very pale and questionable as models of anything real. When physicists see that a small minority of (“heterodox”) economists also find the standard approach hugely limiting, they feel an urge to help out. And they believe that some of their ideas can help.

To be more provocative — maybe even arrogant?— I think that physicists are often dumfounded when they look into economics and see the way theories get built there. Significantly, it is an experience they DON’T have when they look into other fields. Neuroscientists try to understand the brain by studying the interactions among huge number of neurons, neurotransmitters and so on. They’ve recently turned to very large scale simulations as perhaps the best way to make progress, and it is easy to see why. Neuroscientists don't try to force their theories into a form where we can think of intelligence as emerging from the balanced interactions between one representative neuron and one representative neurotransmitter, because this would actually eliminate the nonlinear feedbacks and systemic network complexity that is the central phenomenon of study. Same goes in, say, ecology or weather science where modern scientists are trying to find ways to understand complexity as it is. To a physicist, economics looks truly weird in this regard.

Finally, on agent-based models, I think that Chris is perhaps not aware of how things in this field are developing. Yes, development is slow, as almost no one (in a comparative sense) is working on these things. There must be something like 50 or 100 DSGE modellers (just a guess) for any one person working on agent-based models. Even so, there have been some encouraging successes such as this one, the result of a collaboration between physicists and economists, which explores some practical questions about what caused the recent housing bubble and brings a lot of real data to bear.

I’m glad Chris wrote his post. I think it captures what many economists do believe about physicists; that they think they can come in and solve everything because economics is easy and they’re so smart:

If you are a physicist and you want to work in economics, you had better strap yourself in and prepare for a long challenging path – one that is only worth following if you are really interested in the subject itself. There isn’t very much low-hanging fruit left… Don’t think that after watching Inside Job you can jump in to economics and save the day just because you understand the Navier–Stokes equations.

I couldn’t agree more, and physicists who do think they can jump in and save the day probably aren’t very smart. Yet I don’t think there are many physicists who think this. They do expect a hard slog, and a lot more failure than success. But they think that the most profitable slogging will happen if we take the complexity of economic systems seriously, and attempt to understand it with mathematics and models commensurate to the task. Which means different mathematics and different models than what are generally used in economics today. At least, this is how it appears to me!

Follow The Physics of Finance on Twitter: @Mark_Buchanan

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