The rise and fall of catastrophe theory applications in economics: was the baby thrown out with the bathwater?

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1Program in Economics, James Madison University. The author is grateful to William Brock, Dee Dechert, Christophe Deissenberg, Gustav Feichtinger, Steven Guastello, Cars Hommes, Judy Klein, Hans-Walter Lorenz, Erick Mosekilde, Tönu Puu, Willi Semmler, Floriaan Wagener, and especially Roy Weintraub for either materials or advice. None of the above are responsible for any errors or questionable interpretations in this paper.

2 Rosser (1999) agrees with Horgan that the four C’s are linked through their common use of nonlinear dynamical systems. But he argues that this is something to be celebrated and appreciated rather than denigrated or dismissed. Just as the term “impressionism” in art was originally bestowed by a critic, so the “chaoplexologists” should accept the label originally provided in derision and wear it in pride. Ironically at the time that catastrophe theory was first criticized in 1977, its main founder, René Thom, worried that it could “have the same fate as cybernetics.” (Aubin, 2001, p. 274).

3 An example of this is Wagener (2003), to be discussed below, which uses catastrophe theory without ever mentioning its name. Of course there has been a non-trivial literature in recent years that has discussed catastrophe insurance. But such discussions rarely, if ever, rely upon catastrophe theory per se. That there seem to be fewer inhibitions about this in some other disciplines can be seen by recent applications in physics (Kuznetsova, Kuznetsov, Knudsen, and Mosekilde, 2004) and biology (Li, Zhang, Ma, Xie, and Wang, 2004).

4 For good overviews of catastrophe theory and its application in many disciplines, see Poston and Stewart (1978), Woodcock and Davis (1978), Gilmore (1981), Thompson (1982), and Arnol’d (1992). Except for the last of these, which was a third edition of a book initially written earlier by this famous Russian mathematician, all of these were written during the heyday of catastrophe theory’s faddishness.


5 For more extensive discussions of such applications in economics, see Rosser (1991, 2000a).

6 Two years later, Rand (1978) would publish the first self-conscious model of chaotic dynamics in economics, although others had provided such examples earlier without realizing what they were, e.g. Strotz, MacAnulty, and Naines (1953).

Although not specifically using catastrophe theory, Debreu’s colleague in mathematics at Berkeley, Steve Smale (1974) also studied structural stability of general equilibria, drawing on his earlier work on genericity that also provided a foundation for chaos theory (Smale, 1967). Smale was in close contact with Thom and Zeeman during the early 1970s (Aubin, 2001), and would later encourage Hal Varian to study catastrophe theory, leading him to develop his business cycle model discussed below (I thank Roy Weintraub, 1983, for this information, who interviewed Varian).



7 Balasko ultimately sided with the critics of applications of catastrophe theory in economics by noting that some of the necessary mathematical conditions are rarely fulfilled, especially that of a potential function.

8 For further discussion see Cobb, Koppstein, and Chen (1983) and Cobb and Zacks (1985, 1988). It is striking that few of the critics of catastrophe theory who charge that it cannot be used practically or empirically seem to be aware of this work.

9 Puu (1989) was probably the first to analyze an economic model using both catastrophic and chaotic dynamics in a model of business cycles in which an economy experiences temporary periods of chaotic dynamics immediately after catastrophic jumps occur. Rosser (1991) has labeled such a phenomenon as being “chaotic hysteresis.”


10 Krugman’s (1991) core-periphery model of regional economic structure could also be easily put into a catastrophe theory framework, although he has not done so. However, Baldwin, Martin, and Ottaviano (2001) have used the language of “catastrophic agglomeration” in connection with a closely related model, a continuing sign that in urban and regional economics there has remained more openness to such approaches as there has also within ecological economics, in contrast with most sub-fields of economics. Another paper to specifically mention the possibility of using catastrophe theory for the model studied was Gennotte and Leland’s (1990) model of financial market dynamics. Krugman (1996) in particular once wisecracked that he had “forgotten more catastrophe theory than most people ever knew in the first place.”

11 A satire of the work of the work of Sussman and Zahler appeared under the alleged authorship of “Fussbudget and Snarler” (1979).

12 Psychology is a field that has remained somewhat more open to using catastrophe theory than some others, with good coverage in Guastello (1995).

13 They also made a number of arguments that looked serious at the time but look petty in retrospect, such as that some of the crucial papers in catastrophe theory initially appeared in unrefereed Conference Proceedings.

14 It is perhaps not an accident that there remains a more favorable attitude towards catastrophe theory in Thom’s homeland of France, home of highly abstract thought, with Lordon (1997) providing a recent application in economics.. This observer has speculated that it may also have to do with the less dramatic meaning that the word “catastrophe” has in the French language than it does in English, with minor social faux pas regularly described as “catastrophes.” Weintraub (2002, p. 182) argues that Thom was a “Bourbakist.” Although he was initially trained by French Bourbakist mathematicians, the form of intellectual abstraction he pursued in this later period was very anti-Bourbakist in spirit and abjured formal, axiomatic approaches.


15 More generally Thom would argue that catastrophe theory showed how qualitative changes could arise from quantitative changes as in Hegel’s dialectical formulation. See Rosser (2000b) for further discussion.

16 A much studied model of the stock market with heterogeneous agents who have evolving strategies was developed at the Santa Fe Institute by Arthur, Holland, LeBaron, Palmer, and Tayler (1997). An example of econophysics modeling of heterogeneous agents in financial markets is Lux and Marchesi (1999).

17 Much of the immediate intellectual response to that event was for many economists to try to explain it using the sensitive dependence on initial conditions idea of chaos theory, which was very much near the peak of its intellectual bubble at that time. Almost nobody bothered to use the Zeeman model, which in retrospect looks much more suitable for explaining the kinds of really big discontinuities one observes in a major stock market crash. One who has used studied the 1987 crash using the Zeeman model is Guastello (1995, pp. 292-297). Rosser (1997) extended the Zeeman model using the five dimensional butterfly catastrophe model to explain the phenomenon observed by Kindleberger (1999), that many historical bubbles experienced a period of gradually declining prices during a “period of distress” after the peak and prior to the main crash. Thus in 1987 the market peaked in August and then gradually declined before plunging on October 19.



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