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Butterfly Economics

Paul Ormerod

posted on 30 March 2004

reviewed by Joe McCauley

In his first book „The Death of Economics“, which I still like very much because I found it useful, Paul Ormerod compared in detail the gross failure of the neo-classical equilibrium model, the standard textbook model, compared with economic data. The book did not waste time on philosophy or ideology but presented a criticism that was and remains valid. „Butterfly Econonomics“ takes a different tack. I recommend reading at least the first half of „The Death of Economics“ first, followed by this one. One must first know what is the problem before one can appreciate the solution.

In the preface, Paul Ormerod apologizes mildly to neo-classical economists and expresses hope that this new book should be easier for them to stomach. He knows, as we all do by now, that that school of thought does not take kindly to criticism. His expressed aim is to concentrate on complex, biological models instead of mechanical ones. In the Introduction, he announces boldly that he will abandon the idea of fixed preferences, an admiriable task! The ‚butterfly‘ symbolizes not deterministic chaos (the theme of the second half of his first book) but rather the ability of a biological system to interact, adapt and learn. The author‘s aim is to understand the two main problems of economics: (1) Why is there economic growth, and (2) why are there business cycles?

Complexity as the edge of chaos is alluded to, but the main point of chapter 1 is to introduce the reader to Alan Kirman’s ant model, a variation on Brian Arthur’s urn model. Here, the emphasis is on modelling the interaction of agents, or ‚agent-based modelling‘, and Paul does a fine job of explaining the ant model. One wonders, as one reads the book, why econ texts are not written in such stimulating fashion rather than presenting us with a theory that doesn’t work. Neither Kirman nor Ormerod present the ant model as solving any economic problem quantatitively, rather, it is discussed in the spirit of showing what is left out of ‚optimizing behavior‘.

In chapter 2, Paul explains why we should give up hope of short term prediction, and criticizes the efficient market hypothesis (EMH) for its failure to allow for adequate volatility. I’ll come back to this and some other points below. The third and fourth chapters discuss crime and family values in terms of the personal perferences of interacting agents. Again, this stimulates the reader to imagine how one could write an econ text to make it meaningful.

Chapter 5 mentions Radner, whose work (along with Kirman‘s) every econophysicist should know. Roy Radner is the theorist who drove all the nails in the neo-classical theory coffin back in 1968. He showed that if uncertainty is introduced into the neo-classical equilibrium model then the agents can’t locate equilibrium, so that no trades are made. In other words, uncertainty makes the model’s economic eficiency plunge from 100% to zero, which is a more realistic model of the Third World (the equilibrium model is not an empirically realistic model of any real market).

In the sixth chapter, business cycle forecasting is introduced and (pre-EU) the question is raised whether Italy can meet the fiscal requirements necessary to enter the European monetary union. I read about the way that Long Term Capital Management helped Italy to solve this problem via ‚creative financing‘ in Dunbar’s „Inventing Money“. Chapter 7 discusses the failure of econometrics to extract fixed rules of behavior (machine-like models, if noise-driven) from the data, and begins the discussion of the failure of the standard model (RBC, or real business cycle theory) to explain the data. Economists are correctly lambasted for ignoring empirical data in discussing the „correctness“ of their models, and Paul’s interesting new model of the GNP is presented in chapter 8. I found these chapters to be the most stimulating. There may still be something here for econophysicists to work on.

Interacting ants (variable preferences), the theme the entire book, are presented explicitly again in chapter 9. We‘re informed of the neo-classical idea of a ‚production function‘in chapter 11, and economists are again properly taken to task for what I would label as Aristotelian-style philosophic postulations, while roundly ignoring the available empirical data. I find the discussion of the production function to be very useful, because Paul presents it, as he presents everything, in clear, simple language. This saves me the trouble of having to read dense, rambling economics papers to learn about that idea, although another source is Mirowski’s „More Heat than Light“.

A very interesting thought is mentioned as a footnote on page 168, and I‘ll leave it to the reader to ponder that one. In chapter 13, Paul further advises governments against too much regulation, no doubt having in mind his own UK before it was Thatcherized to the opposite limit (the US is presented as a happy counter-example, but since Reagonization we have our own severe unsloved problems). Here, the basis of his recommendation is the impossibility of accurate short-term predictions, something else for econophysicists to think about. It is true that short term prediction is useless in a stochastic system. In a deterministic chaotic or complex system, one sees only regular behavoir at short times (because of local integrability). I guess the point here is that the GNP can be modelled stochastically. But however correct ‚hands off‘ advice may be in many cases, I would point out that the fixing of the Thai Baht after Thailand‘s financial collapse seems to provide a good counterexample to a complete ‚hands-off‘ policy. Also, the failure of Mexico to fix the Peso and refuse to pay international loans ca. 1997 caused nearly total economic collapse for the then-growing middle class there, who held unpayable floating mortgage loans. So there’s a lot of grist here for the econophysical mill. Ending this fine little book, Paul Ormerod emphasizes the ant model as an example of „one variant of the overall complex systems approach which (is proposed) in this book“. That model is claimed to be only an extension of neo-classical economic theory. Now for some comments, which I hope will prove useful.

First, I see no reason why neo-classical econmists should take any solace from this book (thank goodness!): the ant model doesn‘t rely on utility maximization, and is in not an extension of their model. It doesn’t begin by perturbing the neo-classical equilibrium model (as Per Bak did by adding noise in „Dynamics of Money“), and seems completely unrelated to optimizing behavior. However, the ant model, while interesting and instructive, also is not complex and so references to complexity, or to complexity as living the edge of chaos seem unnecessary. Physicists do not yet agree on a definition of „complexity“, but I like Chris Moore’s definition, where „surprises at every length scale“are the essence of complexity. This rules out scaling and attractors, and food sources in the ant model are analogous to attractors. Here’s what Moore means, I think. Chaotic and „random“/stochastic systems are simple, by this definition, not complex: the statistics of the distant future for specific classes of initial conditions can be known in advance for chaotic or stochastic systems without doing a step by step calculation. For a complex system, in contrast, there are „surprises“ that prevent one from knowing any statistical distribution at long times, for a given initial condition, other than by watching the system unfold step by step. In other words, the system cannot be characterized by any statistical distribution because ‚surprises‘ all the way to infinite time occur (volatility and fat tails are not examples of ‚surprises‘). For my taste, mutations of bacteria and viruses to new forms are the essence of complexity, physically. This kind of complexity is presumably found in markets, but where and how? We don’t know how to quantify that stuff.

Here’s a more serious criticism. The idea of the EMH presented in the text is Shiller’s notion, based on dividends discounted infinitely far into the future. This is not a useful definition because it’s not falsifiable (Modligliani-Miller even teaches that dividends are irrelevant). The best definition of the EMH, the one used by finance theorists, is represented by the Martingale condition (plus, I would add, with Hurst exponent H=0), which guarantees that there are no patterns in the statistics that can be exploited for unusual profit. Markov proceses fall into this category, and have been used to describe financial market statistics, including option pricing, quite accurately (see my new econophysics book). So the EMH doesn‘t rule out either fat tails or nonstationary processes, both of which are required to describe the observed ‚volatility‘ of financial markets.

Finally, the ant model is not really ‚biology‘ but is instead noise driven mechanics. Why is that? Every mathematical model that can be written down is a mechanical model. As Turing showed, mathematics is a mechanical process, so whatever can be mathematicized classically is classical mechanical, in some sense. Turing’s famous typewritter tape is a classical mechanical system. More to the point, financial market statistics are very accurately described by simple noise-driven ‚mechanical‘ models. The only known way to get away from fixed-machinery models (fixed hardware and fixed software) is to go to a neural net model that can learn from the environment, so that the connections change with time. The neural net may even be deterministic, but interaction with the environment prevents us from knowing the future, even theoretically. Finally, there is a reference to ‚value‘ in the text. I have described elsewhere why ‚value‘ is nonunique and therefore is an ill-defined notion.

In context, these are pretty minor criticisms, and to answer them properly (excepting the EMH error) one could not write an elementary book. So I think, in the end, that Paul Ormerod has done a fine job of using the ant model to symbolize what’s missing in the standard, boring econ texts. Again, reading this book made me think how an econ text could be written to stimulate the reader to think about solving real, empirically-driven econ problems, and if Paul doesn’t do take on that arduous task then someone else eventually will. If you want to read less than the entire book, then I strongly recommend chapters 1, 7, 8, and 12. The RBC and Paul’s model of business cycles are presented for the reader’s convenience as appendices.