IS A TRANSDISCIPLINARY PERSPECTIVE ON ECONOMIC COMPLEXIY
POSSIBLE?
J. Barkley Rosser, Jr.
James Madison University
Email: rosserjb@jmu.edu
Website: http://cob.jmu.edu/rosserjb
October, 2009
Codes: A12, B40, C00
Abstract: Marshall’s problem regarding the relationship between economics and physics
and biology is considered within the context of the possibility of a transdisciplinary
approach that would truly combine the various disciplines. While a combined
econophysics is very much an ongoing enterprise, and a possible econobiology may be
emerging along several different lines, a full combination of all three is not in sight
except possibly in the area of global climate-economy modeling. It is argued that
heterogeneous interacting agent forms of complexity are likely to provide the best
methods for achieving such transdisciplinary models.
Acknowledgements: The author acknowledges useful input from Richard H. Day.
1
“When demand and supply are in stable equilibrium, if any accident should move
the scale of production from its equilibrium position, there will be instantly brought into
play forces tending to push it back to that position; just as if a stone hanging by a string is
displaced from its equilibrium position…
But in real life such oscillations are seldom as rhythmical as those of a stone
hanging freely from a string; the comparison would be more exact if the string were
supposed to hang in the troubled waters of a mill-race, whose stream was at one time
allowed to flow freely and at another partially cut off. Nor are these complexities
sufficient to illustrate all the disturbances with which the economist and the merchant
alike are forced to concern themselves.
If the person holding the string swings his hand with movements partly
rhythmical and partly arbitrary, the illustration will not outrun the difficulties of some
very real and practical problems of value.” ---Alfred Marshall, 1920, p. 346.
I. Introduction: A Meditation on Marshall’s Problem
Alfred Marshall is rightly recognized as a supreme formulator of the truly
neoclassical economics that we find still lurking in most economics textbooks, along with
Walras, with this approach arguably culminating later in the work of Paul Samuelson and
then the general equilibrium existence theorem of Arrow and Debreu.1 However, even as
he stands in this position of grand expositor of orthodoxy, the quotation above shows that
Marshall knew better, that he understood that the vision he promulgated had severe limits
when it came to being applied in the real world. While this recognition would be usually
shoved into the background, it provided an essential tension that permeates Marshall’s
work, something that one can find in the work of most of the recognized icons of
1
Colander (1995) has argued that while his contemporary Walras developed explicitly the concept of
general equilibrium, Marshall was well aware of the idea, but avoided developing it openly precisely
because of his awareness of the potential complications and complexities involved. Both he and Walras
were aware of the possibility of multiple equilibria, and in his early years Walras was more aware of these
vicissitudes as well, becoming more “orthodox” after 1900 (Walker, 2006). For a discussion of how
“orthodox economics” is not necessarily identical to “mainstream economics” see Colander et al. (2004),
with the essential idea being that “orthodox” refers to an intellectual framework, whereas “mainstream”
refers to a sociological category, those who are in the leading and dominant positions in the profession.
2
neoclassical orthodoxy if one looks closely enough.2 Thus, Marshall can be seen as a
precursor of modern complexity economics, even if only in dark corners of his work.3
Marshall is also an appropriate starting point for this paper in that he also
attempted to draw into economics influences from other disciplines, most notably physics
and biology. It can be argued that he completely failed at integrating these two into
economics, especially in some combination of the two. The major parts of his standard
theory, reproduced in textbooks, reflects a watered-down version of mid-19th century
physics, as Mirowski (1989) has argued, while in his Preface he declared biology to be
the “Mecca” of economics, even as he arguably failed to follow through on this
declaration with a meaningful effort. This failure would be the touchstone for the critical
coiner of the term “neoclassical,” Thorstein Veblen, who denounced Marshall’s use of
physics as a static and stultifying method when compared with the possible adoption of
Darwinian evolutionary theory that he championed (Veblen, 1898).4
So, we can pose the question of this paper as being “Marshall’s problem.” Is it
possible to integrate other disciplines, especially physics and biology simultaneously, into
economics in a way that both contains its orthodox core as well as providing a way to
understand the limits of that core in a complex world? Such a successful integration
would be transdisciplinary rather than merely multidisciplinary or interdisciplinary.5 Is
2
So, Arrow would be one of the founders and principal supporters of the Santa Fe Institute and Debreu
would contribute to the weakening of general equilibrium theory by the Sonnenschein-Mantel-Debreu
theorem (Debreu, 1974).
3
Marshall’s invention of the concept of quasi-rent also provides the base for an alternative approach to
dynamics as developed by Day (1963, 2004).
4
See Hodgson (1993) for further discussion.
5
The term “transdisciplinary” is used by ecological economists to describe their discipline. Richard
Norgaard in Colander et al (2004, p. 248) argues that “multidisciplinary” refers to separate disciplines
conversing with each other while maintaining fully their mutual distance. “Interdisciplinary,” which came
into fashionable use after multidisciplinary, refers to the establishment of narrowly specialized niche
disciplines that take a few ideas from one discipline and a few ideas from another to create this specialized
3
or can econophysics be transdisciplinary (Rosser, 2006)? What about the much less
developed econobiology? And can these be integrated into a higher level transdiscipline
that can provide a meaningful perspective on economic complexity?6 This is the modern
version of Marshall’s problem.
II. A Collection of Complexities
In order to be able to approach this question we must confront the knotty problem
of the meaning of complexity. Many have despaired of finding a clear or useful definition
of this widely used (and abused) term. We shall adopt a hierarchical view of this,
following Rosser (2009a), seeing three levels of this problem. The lowest level is what
Rosser (1999) labeled “small tent complexity,” which emphasizes the assumption that
agents are heterogeneous in many ways with respect to each other and that they interact
primarily in a local way with their neighbors in some sort of space. This is the sort of
complexity described by Arthur et al. (1997), and has been strongly associated with the
Santa Fe Institute and computer simulations of such heterogeneous agent-based models.7
Economic models adopting this sort of complexity rarely exhibit global equilibria or
global rationality, often exhibiting evolutionary processes of ongoing change and
innovation. Certainly within economics this has been what most people think of when
niche discipline, such as “water economist,” who would draw on parts of hydrology and parts of
economics. Transdisciplinary implies a broader linking and integration across the disciplines at a deeper
level.
6
We shall focus on these two combinations of natural sciences with economics, while recognizing that
other such combinations exist or may exist that we shall not discuss further here, with sociophysics
(Chakrabarti et al., 2006), although this arguably revives an earlier effort that went under different names
(Weidlich and Haag, 1983). We also shall not discuss such well-established transdisciplines within the
social sciences such as political economy, economic psychology, and socio-economics. There is a barely
nascent econochemistry that is barely developed at all (Hartmann and Rössler, 1998; Rosser, 2006).
7
Although he used a chessboard rather than a computer to study his models, it is generally accepted that
the first such efforts were made by Schelling (1971).
4
they think of complexity economics, and it emphasizes that in order to understand
aggregate phenomena, it is advisable to model from the micro level up explicitly with
heterogeneous agents in order to see the emergence of the aggregates, which cannot
simply be imputed directly from the behavior of the individuals. This follows Kirman
(1992) in his critique of representative agent modeling, and is exemplified for
macroeconomic modeling by Delli Gatti et al. (2008).
The second level up is what Rosser (1999) labeled “big tent” complexity, or
dynamic complexity, which embeds the “small tent” complexity within it. This can be
defined, following Day (1994) as referring to systems that do not endogenously converge
on a point, a limit cycle, or a continuous expansion or contraction (although there is some
discussion about whether limit cycles should be included or if all periodic cycles should
be excluded). This broader definition contains what Horgan (1997) dismissively labeled
the “four C’s”: cybernetics, catastrophe theory, chaos theory, and [small tent, or
heterogeneous agent] complexity theory, with him coining the term “chaoplexology” to
combine the last two. He argued that there was such confusion in all this that observers
were ultimately facing “complexity turning into perplexity,” and that each of these four
C’s had been intellectual fads, not worthy of serious longer term consideration.
Rosser (1999) responded by agreeing that indeed all of these suffered going
through fad phases as “intellectual bubbles,” but that this did not mean that each did not
in fact contain a core of useful and reasonable ideas. The overshooting up of prestige for
each was followed by a crash that then tended to overshoot in the opposite direction
sometimes (although this seems to have happened to a lesser degree with the still
5
speading small tent complexity of agent-based modeling).8 Furthermore, Horgan indeed
picked up on something genuine that has been going on, that these four C’s represent a
cumulative intellectual development that has proceeded over a several decade period,
drawing on certain underlying themes, most notably nonlinear dynamics. Rather than a
faded dead end, this development has in fact reached a critical mass or intellectual
bifurcation point, where such ideas are now entering the mainstream, at least in
economics to some extent, if not all the way into the intellectual core of economic
orthodoxy a la Marshall’s standard story as augmented by Walras, Samuelson, and
Arrow-Debreu.9 Whereas in the past economists would (like Marshall) hide in footnotes
oddities such as multiple equilibria that might appear in their models, now they are more
likely to trumpet such discoveries and findings as being of central interest.
Finally, the third level of defining complexity is the level that Rosser (2009a)
labels meta-complexity, where it is indeed recognized that there is a plethora of
definitions of complexity. Horgan (1997, p. 303) provides a list of 45 such categories as
gathered up to that time by Seth Lloyd, although many of these appear to be minor
variations of each other. Even with its great length it would appear not to be complete, as
it does not clearly include either the small tent or broad tent dynamic definitions just
discussed, although the last few are connected and associated with those who have
worked on agent-based modeling at the Santa Fe Institute (self-organization, complex
adaptive systems, edge of chaos). Indeed, there are other meanings that have been used
8
Probably the hardest crash of these was experienced by catastrophe theory, and Horgan used its crash to
denigrate the other three. However, Rosser (2007) provides a defense of the use of catastrophe theory in
economics, and points out that among mathematicians it never experienced either the initial fad/bubble (or
not to the degree it did in other disciplines) and thus did not experience the crash as severely, always
retaining respectability as a branch of broader bifurcation theory (Arnol’d, 1992). See also Puu (2003).
9
That this may be the case has been argued by Blume and Durlauf (2005).
6
by economists that do not fit into any of the 45 listed by Horgan or into the big tent
dynamic definition provided above.10
Now it might seem that this sprawling collection of conceptualizations of
complexity justifies the jibe of Horgan (drawn originally from Francisco Doria) that
complexity became perplexity. However, as noted, many of the definitions are indeed
minor variations on a few themes, with information being perhaps the most widespread.
As argued by Velupillai (2000), Shannon’s (1948) entropic definition of information
provides the original foundation for a series of related definitions of algorithmic and
computational complexity due to Kolmogorov, Solomonoff, Chaitin, and Rissanen.11
These do not fit into the broad tent dynamic definition of Rosser and have been put
forward with enthusiasm recently by various observers (Markose, 2005; Velupillai, 2005)
on the grounds that they are more rigorous in their definition and measure than other
alternatives, and much recent discussion has focused on these and related definitions.
Rosser (2009b) provides a defense of the dynamic definition as being more useful in most
applications and situations than these definitions for economics, while recognizing their
potential ability to provide more exact measures of degrees of complexity.
In any case, for the remainder of this paper we shall mostly focus on the dynamic
definitions of complexity, with the greatest part of this on the small tent version that
emphasizes heterogeneous interacting agent models, even while keeping these broader
views in mind.
One of these is “structural,” as used by Pryor (1995) and Stodder (1995). Rosser (2009b) argues that
these really “complicatedness” rather than “complexity,” noting that these two words come from different
roots in Latin (Israel, 2005). They simply refer to their being many interconnections between different
sectors of the economy, some of them obscure, as in an input-output matrix with many entries. For an
alternative list of ideas of economic complexity, see Warsh (1984).
11
Albin (1982) was the first to apply the computational problems arising from the Gödel incompleteness
and inconsistency theorems of logic to economics. See also Albin with Foley (1998).
10
7
III. Econophysics as a Transdisciplinary Perspective?
Probably the most developed potentially transdisciplinary perspective on
economic complexity is econophysics. This was only neologized in the mid-1990s by H.
Eugene Stanley, with Mantegna and Stanley (2000, viii-ix) defining it as the
“multidisciplinary field…that denotes the activities of physicists who are working on
economic problems to test a variety of new conceptual approaches deriving from the
physical sciences.” While this definition has a peculiarly sociological nature to it (based
on who is doing econophysics almost more than what they are doing), the essential idea
of applying physics theories to economics is clearly the key, with the recently developing
econophysics emphasizing approaches somewhat at variance with the most orthodox
economic theoretical approaches. A particular aspect of physicists predominating in this
new field is the emphasis on starting with data and trying to find models or theories that
might explain the data, while economists tend to assume that their standard theories are
correct and then seek to find them working in data. At their most forceful, some argue
that economic theory is so useless that econophysics models will completely replace it to
the point that students will no longer take Principles of Economics, and will take statistics
and physics courses instead (McCauley, 2004).
Since this appearance in the mid-1990s, arguably inspired at least partly by the
interactions between economists and physicists at the Santa Fe Institute, the most
intensive area of application has been in financial economics (Bouchaud and Cont, 2002;
Farmer and Joshi, 2002; Sornette, 2003), with applications to the distributions of income
and wealth probably the next most common (Levy and Solomon, 1997; Drăgulescu and
8
Yakovenko, 2001; Chatterjee et al. 2005). Other prominent applications have included
the size distribution of cities (Gabaix, 1999) and the size distribution of firms (Axtell,
2001),12 along with a variety of others (Rosser, 2006), although curiously many of the
studies on urban and firm size distributions have been done by economists (e.g. Gabaix
and Axtell).
While other arguments and theories have entered into these efforts, a major theme
and focus has been upon finding and modeling power-law distributions in these data,
which tend to be linear in log-log plots and exhibit kurtosis or “fat tails,” usually ignored
in most standard economics models. Roughly, the apparent stylized facts are that
financial asset returns clearly exhibit such kurtosis, wealth distributions and the upper
ends of income distributions may do so, city sizes almost certainly do so, while there is
some evidence of firm sizes doing so, although this is more controversial. The alternative
for most of these is either the Gaussian distribution or a transformation of it such as the
lognormal or Boltzmann-Gibbs.
While these efforts have moved forward, controversy has broken out over some of
the methods used by some econophysicists, with Gallegati et al. (2006) arguing that many
econophysics studies claim greater degrees of originality than deserved, that many use
insufficiently rigorous statistical techniques, that exaggerated claims of the universality
of empirical findings sometimes made, and that many of the theoretical models put
forward have difficulties or face unacknowledged limits. Rosser (2008) has argued that
while many of these arguments have substance for many econophysics papers in the past,
many of these problems are being corrected, especially as physicists are increasingly
Axtell’s study supported a much earlier one that had been much ignored by economists by Ijiri and
Simon (1977).
12
9
working with economists, although Lux (2009) has documented how econophysicists can
get misled into making embarrassing mistakes if they fall into using overly simplistic
economic theoretical models. Rosser suggests that a model of entropic equilibrium by
Foley (1994) might provide an interesting physics-based alternative theoretical
foundation for the analysis of markets.
However, the question of the relationship between economics and physics is a
deep and complicated one, with mutual influences and feedbacks going back a good two
centuries, with the fact that much of the standard Marshallian framework was influenced
by an earlier and simpler model of physics, as noted by Mirowski (1989). Among the
ironies is that the original discoverer of power-law distributions, now being promulgated
by physicists to explain economic data, was an economist, Vilfredo Pareto (1897). This
would later be reintroduced into dynamic economics by the mathematician Mandelbrot
(1963), although one who was initially influenced by him, Eugene Fama (1963), would
later turn away from his approach and become among the most prominent developers of
the market efficiency hypothesis and conventional financial economics (Fama, 1970).
However, among geographers and urban economists, power-law distributions were used
over a long time (Zipf, 1941). Another curiosity is that prior to its application to
Brownian motion by Einstein (1905), the random walk was applied to the stock market
by Bachelier (1900), with this being forgotten, and that this now-very-conventional
approach to financial economics was reintroduced into economics by a physicist
(Osborne, 1959). Furthermore, the first to apply statistical mechanics models to
economics was an economist (Föllmer, 1974), well before the solid state physicists got
10
into the act two decades later (most econophysicists are solid state physicists). So, the
question of who influenced whom when is a very tangled one.13
IV. Econobiology as a Transdisciplinary Perspective?
It must be stated at the outset that while ecological economics may constitute a
self-conscious transdisciplinary enterprise, the same cannot be said for any nascent
“econobiology,” with nearly as many of the references to this term being negative and
made by econophysicists denying that there can even be a truly scientific econobiology
because of its presumed lack of invariance principles (McCauley, 2004, chap. 9).
Nevertheless, besides ecological economics, there have long been various forms of
evolutionary economics, some more oriented to the biological roots than others, and some
implying or emphasizing complex dynamics or potential complex dynamics.14 Likewise,
there has been a well-established mathematical bioeconomics, due originally to Clark
(1990), which has been more readily open to models of complex dynamics. This latter in
particular looks to be the most serious foundation for a potential econobiology that would
be equivalent to and able to interact with econophysics in some form or other (Rosser,
2001, 2009c).
Following the realization that open access fisheries may exhibit backwardbending supply curves (Copes, 1970), a long line of development has followed along the
lines of Clark and used various dynamic complexity ideas to study the serious problems
of fishery dynamics, including of fishery collapse (Jones and Walters, 1976) and irregular
13
It has been argued that an early conscious advocate of the idea that natural and social sciences should
rely upon common statistical theories was first put forward coherently the physicist Majorana (1942), just
prior to his mysterious disappearance, making him arguably the first true econophysicist.
14
Hodgson (200^) has argued that Darwinian evolution is the supreme complex system.
11
dynamic patterns of fish populations (Conklin and Kolberg, 1994). Such backwardbending situations arise when a fishery gets overfished beyond its maximum sustained
yield level, so that increased fishing effort leads to fewer fish being caught, and price
hikes lead to such increases in fishing effort. More recently, Hommes and Rosser (2001)
have studied complex fishery dynamics within the consistent expectations equilibria
framework due to Grandmont (1998) and Hommes and Sorger (1998), with Foroni et al.
(2003) studying how these fishery dynamics within backward-bending supply curve
situations can generate multiple basins of attraction with fractal basin boundaries.15
Another area of study in complex econobiology has involved forestry (Rosser,
2005). While forestry dynamics tend to be much more slowly moving than fishery
dynamics, the existence of complicated time patterns of benefits from forests, with
animals grazing when they are young through various forms of recreation during middle
and sometimes very late periods, along with various externality factors such as carbon
sequestration and prevention of soil erosion and flooding, to timber harvesting, can serve
as a basis for complex dynamics in optimizing frameworks (Swallow et al. 1990).
Furthermore, complex dynamics can arise because of the predator-prey dynamics
between insects, birds, and trees in forests (Ludwig et al., 1978), with such dynamics
setting up forests for large-scale changes and even collapses in response to apparently
insignificant events far away from them, rather reminiscent of the “butterfly effect” of
chaos theory, although not specifically a matter of chaotic dynamics (Holling, 1988).
This can happen as for example when the draining of a wetland at a crucial location on
the migratory route of birds who eat insects on trees causes them to shift to a different
15
See also Bischi and Kopel (2002).
12
forest for their post-migration location, thus triggering an insect outbreak in the old
location, decimating the forest.
Just as small changes in migratory patterns of birds can lead to catastrophic
collapses of forests, so too can small changes in land management practices lead to
sudden, large changes in the character of lakes, as they go from a more normal
oligotrophic state to an undesirable eutrophic state as a critical level of phosphorous
loading is passed (Carpenter et al., 1999). A detailed study of the nature of the
bifurcations points and related mathematics of these systems has been carried out by
Wagener (2003).16
Yet another example is the possibility of chaotic climatic-economic interactions,
which is arguably not econobiology, per se, although impacts on agriculture are part of
the feedback loops in these models, with complex oscillations as economic changes affect
climatic changes, which in turn lead to economic changes (Chen, 1997; Matsumoto and
Inaba, 2000). But these are certainly complex ecologic-economic systems of the highest
order and significance, with all the difficult policy issues thereby ensuing (Rosser, 2001;
Weitzman, 2007). Arguably of the models we have discussed so far, these may be the
ones with the greatest potential for a genuinely transdisciplinary integration of physics,
biology, and economics, if not precisely a combination of econophysics as it has
developed with some version of econobiology.
The policy issues here involve groups attempting to cooperate in situations
regarding common property resources, which traditionally has been studied using game
theoretic models based on the prisoner’s dilemma (Sethi and Somanathan, 1996). The
search for institutional frameworks that can achieve cooperation in such cases is one of
16
A broader study of critical ecological thresholds of many sorts has been done by Muradian (2001).
13
the largest subjects in all of social science, much less economics or econobiology
(Ostrom, 1990; Bromley, 1991; Rosser and Rosser, 2006). However, considering the
problem from an evolutionary and evolutionary game theoretic stance raises problems of
the evolution of cooperation, and the difficult problem of multi-level evolution (Crow,
1953; Hamilton, 1972; Henrich, 2004), which remains a difficult and controversial topic.
We note at this point that under certain frameworks of heterogeneous interacting and
learning agents, the evolution does not settle down and presents a pattern of evolution
with endlessly changing patterns as agents switch from one strategy to another (Lindgren,
1997).
Which brings us to what is arguably the most controversial element of complex
dynamics in econobiology, the concept of emergence in evolution, which the preceding
discussion of emergence of cooperation among higher level groups can be viewed as a
part of. This is an idea that has been vigorously touted, especially by some at the Santa
Fe Institute as virtually a central key to evolutionary processes (Langton, 1990;
Kaufmann, 1993; Crutchfield, 1994), while being ridiculed as vague and poorly
formulated by many critics, ranging from Horgan (1997, chap. 8) to computable
economists such as Markose (2005) to econophysicists such as McCauley (2004, chap.
9).17 Emergence is an old idea in evolution (Lloyd Morgan, 1923), with roots inspiration
going back to John Stuart Mill (1843) and his “heteropathic laws,” although reductionist
evolutionists such as Dawkins (1989) have long rejected such ideas as retrograde and
fanciful “holism” or “organicism,” supposedly disproven by Williams (1966). However,
the idea has flourished in many forms and contexts, from general systems theory (von
17
See Rosser (2009b) for further discussion. Some of the tougher critics such as McCauley allow that
emergence might be modeled reasonably to some extent using symmetry breaking as argued by Turing
(1952) and Haken (1983).
14
Bertalanffy, 1962) to hierarchical theories of agent-based modeling (Wolfram, 1984) to
mathematical models of flocking and herding (Cucker and Smale, 2007). While many do
not like this idea, it lies at the heart of the idea of algorithmic market forms (markomata)
evolving to higher levels of Chomskyian (1959) hierarchies that has been proposed by
Mirowski (2007) as a new form of integration of biology and economics with
computation, if not necessarily with physics or econophysics.
V. Does Complexity Really Help Explain Anything about Markets?
So, the Mirowski markomata involves a world in which higher level markets
emerge that embed lower level markets, as futures markets embed spot markets, and
options markets embed futures markets, and various derivatives markets embed options
markets, and so on and on and upward and upward, with substantial increases in these
higher-order markets in recent years, The question arises as to whether or not this
evolution toward increasing complexity is a good thing or not, with some officials
(Geithner, 2006) expressing concern even before the difficulties in real estate markets
became clearer in August, 2007 regarding their ability to engage in stabilization policy in
the face of financial crisis for the simple reason that they are unable to discern properly
what is going on in the markets, and which have played out even more dramatically with
the widespread crashes of such markets beginning in September 2008. Of course, a long
literature of conventional wisdom has supported the idea that more assets and more
markets spread risk, thereby reducing volatility, and increasing efficiency and welfare
(Shiller, 2003).
15
While this view is deeply entrenched, doubts have been raised for some time on
both fronts at the purely theoretical level for cases in which markets are incomplete, with
Hart (1975) and Elul (1995) showing that welfare may decrease with an increase in the
number of assets as long as the system is sufficiently far below being complete (in
completeness welfare is maximized in general equilibrium in this standard framework).
Citanna and Schmedders (2005) show that price volatility may increase under the same
circumstances. Branch (2004) finds considerable heterogeneity of expectations
empirically among market traders, and Gerlach et al. (2006) find empirically an increase
in market volatility since the 1970s, a period of increasing numbers of assets and market
depth. Nevertheless, the conventional theoretical literature has been unequivocal that an
ultimate move to complete markets will be welfare improving and stabilizing.
However, this general result of convergence on greater stability and efficiency as
markets approach completeness becomes overturned once agents with heterogeneous
expectations and strategies are allowed to enter the models, as they are certainly present
in the real world (Shiller, 2000).18 Brock, Hommes, and Wagener (2009) present a model
of heterogeneous traders dealing in Arrow securities who vary in their expectations
formation and in their strategies, with some being rational, some exhibiting systematic
bias, and some extrapolating trends. They examine a variety of cases, and find a variety
of outcomes. However, a fairly robust result is that if there are a sufficient number of
traders who extrapolate trends, then increasing the number of hedging instruments may
well increase the volatility of the markets and lower the welfare generated by the market,
despite the best efforts of rational traders in the market. This result harks back to an old
18
For overviews of models of heterogeneous agents in financial economics see Hommes (2006) and of
agent-based models in computational finance see LeBaron (2006).
16
literature that has blamed “trend chasers” and “technical traders” for destabilizing
markets (Baumol, 1957; Zeeman, 1974).
While this is certainly an interesting result, it does not entirely capture the sense
that one gets from the discussions by people such as Geithner. This result involves an
unequivocal increase in volatility as measured by variance with an increase in Arrow
securities, assuming that there are enough trend extrapolaters in the market. However,
much discussion by policymakers seems to suggest that there is a conflict in what is
going on, that indeed much of the time the increase in the number of securities actually
does stabilize the market, reducing volatility and perhaps increasing welfare, while at the
same time the danger of financial fragility has increased, with fears of a “Minsky
moment,” a very large collapse (Minsky, 1972). Such fears heightened after August,
2007, culiminating in the crisis of September 2008. In effect, it would seem that rather
than an unambiguous increase in variance, what may be happening is a reduction of
variance coinciding with an increase in kurtosis, a fattening of the “fat tails.” Such an
outcome would resemble the “stability-resilience tradeoff” observed in ecology by
Holling (1973). Such an outcome might well be derivable from the Brock-HommesWagener model if there is a sufficiently nonlinear responsiveness of the movement in and
out of being trend extrapolaters, which would be consistent with more general results
found in Brock and Hommes (1997), where increases in the willingness to change
strategies tends to destabilize and complexify dynamics.
We shall note one further model in which a real world financial market
phenomenon is explainable within the context of a model with heterogeneous agents.
This is Gallegati, Palestrini, and Rosser (forthcoming) which shows how with
17
heterogeneous agents who learn and face transactions costs and Minskyian financial
constraints, market dynamics can occur that exhibit pattern of a bubble going up,
peaking, declining slowly for a period (the “period of financial distress”), and then
crashing suddenly sometime later. No theoretical model has clearly generated such
patterns,19 even as Kindleberger (2000) has documented that the overwhelming majority
of famous historical bubbles going back to the early 1600s have followed such a pattern
rather than the accelerating up and then crashing from the peak pattern that most
theoretical models generate (or the also rare but not well-modeled, slow move up
followed by a slow move down, which may not be a bubble anyway). Such patterns were
long observed in such famous historical bubbles as the Mississippi Bubble and the South
Sea Bubble, with much discussion about the differences between the traders who got out
at the peak versus the less well-informed, experienced, and so forth traders who were left
“holding the hot potato” as the market slid from the peak before crashing (Rosser, 2000,
chap. 5). These discussions were ruled out in a world where agents were assumed to
homogeneously possess rational expectations, but are allowed in a world of
heterogeneous expectations.
So, allowing for heterogeneous interacting agents, the sine qua non of the “small
tent” complexity, proves to be very helpful in understanding real phenomena observed in
financial markets both historically and currently.
VI. Conclusion
19
Föllmer, Horst, and Kirman (2005) present a model that has some very similar features and outcomes
and also depends on heterogeneous agents.
18
Regarding Marshall’s problem, we have probably failed to solve it, except for the
occasional example such as analyzing global warming where physical, biological, and
economic issues all come into play, or perhaps in situations where an econophysics
model might encounter an ecological principle such as Holling’s stability-resilience
tradeoff. More generally the old conflict between the greater precision and quantitative
rigor of the physics-based models as compared with most biological or evolutionary
models appears to come into play.
However, we have seen that at the lower level of transdisciplinary approaches
such as econophysics or econobiology, these may well be very useful when combined
with various sorts of complexity methods to analyze economic dynamics. A grand
synthetic transdisciplinary perspective on economic complexity is probably beyond our
reach, except in occasional cases, but the transdisciplinary perspective at a more modest
level is alive and well, and promises an interesting research program.
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