Thursday, June 16, 2011

Complexity economics

Complexity is one of the hottest concepts currently nipping at the fringes of economic research. But what is it? Richard Holt, David Colander and Barkley Rosser last year write a nice essay on the concept which makes some excellent points, and they're certainly optimistic about the prospects for a sea change in the way economic theory is done:
The neoclassical era in economics has ended and has been replaced by an unnamed era. We believe what best characterizes the new era is its acceptance that the economy is complex, and thus that it might be called “the complexity era.”
Indeed, something like this seems to be emerging. I've been writing about complexity science and its applications in physics, biology and economics for a decade, and the ideas are certainly far more fashionable now than they were before.

But again -- what is complexity? One key point that Holt and colleagues make is that complexity science recognizes and accepts that many systems in nature cannot be captured in simple and timeless equations with elegant analytical solutions. That may have been true with quantum electrodynamics and general relativity, but it's decidedly not true for most messy real world systems -- and this goes for physics just as much as it does for economics. Indeed, I think it is fair to say that much of the original impetus behind complexity science came out of physics in the 1970s and 80s as the field turned toward the study of collective organization in disordered systems -- spin glasses and glassy materials, granular matter, the dynamics of fracture and so on. There are lots of equations and models used in the physics of such systems, but no one has the intention or hope of discovering the final theory that would wrap up everything in a tidy formula or set of axioms.

Most of the world isn't like that. Rather, understanding means creating and using a proliferation of models, every one of which is partial and approximate and incomplete, which together help to illuminate key relationships -- especially relationships between the properties of things at a lower level (atoms, molecules, automobiles or people) and those at a higher level (crystal structures, traffic jams or aggregate economic outcomes).

Holt and colleagues spend quite some time discussing definitions of complexity, a task that I'm not sure is really worth the effort. But they do arrive at a useful distinction between three broad views -- a general view, a dynamic view, and a computational view. The second of these seems most interesting and directly related to emerging research focusing on instabilities and rich dynamics in economic systems. As stated by Rosser, a system is "dynamically complex" if...
it endogenously (i.e. on its own, and not because of external interference) does not tend asymptotically to a fixed point, a limit cycle, or an explosion.
In other words, a dynamically complex system never settles down into one equilibrium state, but has rich internal dynamics which persist. I'm not sure this definition covers all the bases, but it comes close and certainly strikes in the right direction.

Holt, Colander and Rosser go on to outline a number of areas where the complexity viewpoint is currently altering the landscape of economic research. I wouldn't quibble with the list: evolutionary game theory is bringing institutions more deeply into economic analysis, ecological economics is actually bringing the consideration of biology into economics (imagine that!), behavioural economics is taking account of how real people behave (again, what a thought!), agent-based models are providing a powerful alternative to analytical models, and so on.

This is all insightful, but I think perhaps one point could be more strongly emphasized -- the absolute need to recognize that what happens at higher macro-levels in a system often depends in a highly non-intuitive way on what happens at the micro-level. One of the principle barriers to progress in economics and finance, in my opinion, has been the the systematic effort by theorists over decades to avoid facing up to this micro-to-macro problem, typically through various analytical tricks. The most powerful trick -- a pair of tricks, really -- is to assume 1) that individuals are rational (hence making the study of human behaviour a problem not of psychology but of pure mathematics) and 2) assuming (in what is called the representative agent method) that the the behaviour of collective groups, indeed entire markets and economies, can be calculated as the simple sum of the rational actions of the people making it up.

The effect of this latter trick is actually quite amazing -- it eliminates from the problem, by definition, all of the interesting interactions and feed backs between people which make economies and markets rich and their dynamics surprising. Having done this, economics becomes a mathematical task of exploring the nature of rational behaviour -- it essentially places the root of complex collective economic outcomes inside the logical mind of the individual.

To put it most simply, this way of thinking tends to attribute outcomes in collective systems directly to properties of parts at the individual level, which is a terrific mistake. This might sometimes be the case. But we know from lots of examples in physics, biology and computer science that very simple things, in interaction, can give rise to astonishing complexity in a collective group. We should expect the same in social science: many surprising and non-intuitive phenomena at the collective level may reflect nothing tricky at all in the behaviour of individuals, but only the tendency for rich structures and dynamics to emerge in collective systems, created by myriad pathways of interaction among the system's parts.

Taking this point seriously is what I think most of complexity science -- as applied to social systems -- is about. It's certainly central to everything I write about under the phrase the "physics of finance." I take physics in the broad sense as the study of how organization and order and form well up in collective systems. It so happened that physics started out on this project in the context of physical stuff, electrons, atoms, molecules and so on, but that's merely a historical accident. The insights and methods physics has developed aren't bound by the nature of the particular things being discussed, and this project of understanding the emergence of collective order and organisation goes well beyond the traditional subject matter of physics.

Holt, Colander and Rosser make one other interesting point, about the resistance of macro-economists in general to the new ways of thinking:
Interestingly, these cutting edge changes in micro theory toward inductive analysis and a complexity approach have not occurred in macroeconomics. In fact, the evolution of macroeconomic thinking in the United States has gone the other way. By that, we mean that there has been a movement away from a rough and ready macro theory that characterized the macroeconomics of the 1960s toward a theoretically analytic macro theory based on abstract, representative agent models that rely heavily on the assumptions of equilibrium. This macro work goes under the name new Classical, Real Business cycle, and the dynamic stochastic general equilibrium (DSGE) theory, and has become the mainstream in the U.S.
This is quite depressing, of course, but if most of what Holt and colleagues write in their essay is true, it cannot possibly stay this way for long. Economics as a whole is changing very rapidly and macro can't remain as it is indefinitely. Indeed, there are already a number of researchers aiming to build up macro-economic models "from the bottom up" -- see this short essay by Paul De Grauwe, for example. All this spells certain near-term doom for the Rational Expectations crowd, and that doom can't come a moment too soon.