Complexity and the Economy Page 6
change will propagate and continue to propagate. In a network of banks, an
individual bank might discover it holds distressed assets. It then comes under pressure to increase its liquidity and calls on its counterparty banks. These in turn come under pressure to increase their liquidity and call on their counterparties, and so the distress cascades across the network (Haldane, 2009). Such events can cause serious damage. They peter out in a low-connection network,
but propagate—or percolate—for long periods as the degree of connection
passes some point and gets large (Watts, 2002).19
This last example brings us to a general property. Generally in complex
systems, phenomena do not appear until some underlying parameter of the
model that depicts the intensity of adjustment or the degree of connection
passes some point and reaches some critical level. The overall behavior then
undergoes a phase transition. In our artificial stock market at low rates of investors’ exploring new forecasts, the market behavior collapses to a rational expectations equilibrium (agents make identical forecasts that produce price
changes that on average validate those forecasts): simple behavior reigns. But if our investors explore at a faster, more realistic rate, the market develops a
“rich psychology” of differing forecasting beliefs and starts to display temporal phenomena: complex behavior reigns. If we tune the rate of exploration
still higher, individual behavior cannot adjust usefully to the rapidly changing behaviors of others, and chaotic behavior reigns. Other studies (e.g. Hommes,
2009; Kopel, 2009; LeBaron et al., 1999) have found similar regime transitions from equilibrium to complexity to chaos, or from equilibrium to complexity to
multiple equilibria (Galla and Farmer, 2012). Such transitions I believe will be general in nonequilibrium models.
We can now begin to see how such phenomena—or order, or structures,
if you like—connect with complexity. Complexity, as I said, is the study of
the consequences of interactions; it studies patterns, or structures, or phe-
nomena, that emerge from interactions among elements—particles, or cells,
or dipoles, or agents, or firms. It’s obvious that interaction takes place in our network example, but in our stock market, interaction is more subtle. If one
of our investors buys or sells, this changes the price, perhaps slightly, and the 19. The literature on networks is large: see for example Albert et al. (2000), Allen and Gale (2000), May et al. (2008), Newman et al. (2006). Networks can be mutually stabilizing (as with banks providing insurance to other banks), but they can also be mutually destabilizing (as when losses cascade across financial institutions). And the topology of the network matters to how swiftly events propagate and to whether connectedness enhances stability or not (Scheffer et al., 2012).
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others may react to this change. In all three examples, changes can propagate through the system.
Complexity studies how such changes play out. Or, to put it another way,
complexity studies the propagation of change through interconnected behav-
ior. When a bank comes under stress, it may pass this change to its connected
neighbors, which may pass it to their neighbors, which may pass it to theirs.
An event occurring at one node will cause a cascade of events: often this cas-
cade or avalanche propagates to affect only one or two further elements, occa-
sionally it affects more, and more rarely it affects many. The mathematical
theory of this—which is very much part of complexity theory—shows that
propagations of events causing further events show characteristic properties
such as power laws (caused by many and frequent small propagations, few
and infrequent large ones), heavy tailed probability distributions (lengthy
propagations though rare appear more frequently than normal distributions
would predict),20 and long correlations (events can and do propagate for long
distances and times). Such features occur in all systems—physical, chemical,
biological, geological—in which events propagate, so it is not surprising that they occur in our economic examples where propagation is important.21 They
also show up tellingly in actual economic data (Brock et al. 1992; LeBaron
et al., 1999).
And we can see something else. If the degree of interaction in such a system
is changed from outside (the probability of events causing further events is
increased, say, or more linkages are added), the system will go from few if any consequences to many, and from that to undying-out consequences. It will
go through a phase change. All these properties are hallmarks of complexity.
We can now say why nonequilibrium connects with complexity.
Nonequilibrium in the economy forces us to study the propagation of the
changes it causes; and complexity is very much the study of such propaga-
tions. It follows that this type of economics properly lies within the purview of complexity.22
One further comment. The phenomena I’ve illustrated appear and disap-
pear very much in distinct historical time or space, so we will not see them
if we insist on equilibrium. And they are localized: they appear in one part of the network or the stock market, possibly to diffuse from there. They operate
typically at all scales—network events can involve just a few individual nodes 20. Their probabilities are proportional to exp(–|propagation-length|) rather than to the exp(–(propagation-length)2) of large normal deviations.
21. The reason these properties do not appear in standard economics is because it assumes that agents react to a given equilibrium price, not to one that fluctuates due to other agents’ behaviors; so random changes individual agents make are independent and can be added together. They therefore result in normal distributions.
22. Hence this form of economics is properly called complexity economics.
comPlexi t y economics [ 15 ]
or they can be felt right across the economy. But usually they take place in between the micro and macro, so we can rightly call them meso- phenomena.23
They are properties of the meso-economy.
It could still be objected that such phenomena make little difference. The
standard equilibrium solution after all lies beneath and still has first-order validity. This is certainly true with our stock market model; no stock will stay at 100 times earnings for long.24 But—and this is an important “but”—the
interesting things in markets happen because of their temporal phenomena,
they happen within departures from equilibrium. That, after all, is where the
money is made. We could similarly say that in an ocean under the undeniable
force of gravity an approximately equilibrium sea level has first-order validity.
And this is certainly true. But, as with markets, in the ocean the interesting things happen not at the equilibrium sea level which is seldom realized, they
happen on the surface where ever-present disturbances cause further distur-
bances. That, after all, is where the boats are.
I have used three fairly well-known phenomena in this section as illustra-
tion. Other phenomena have been noticed and no doubt others remain to be
discovered. Exactly what these might be, what their characteristics are, and
how they might interact are important questions for future work. But most
important, our argument tells us that we need to pay attention to a new level
in the economy, the meso-level, where events can trigger other events at all
scales. The economy has a middle or meso layer, and in this layer
phenomena
arrive, last for a while, and dissipate.
POSITIVE FEEDBACKS
I want to point out a further thing about the mechanisms we’ve been look-
ing at. They arise from self-reinforcing behavior in the interactions. Agents
buy into a stock, or disturb a market slightly, or propagate some change, and
this causes further buying in, or further disturbance, or further propagation
of change. Or as we saw earlier, agents show uncertainty in choice and this
causes further uncertainty, or bring on some novel technology and this calls
for further novel technologies. Such positive feedbacks disturb the status
quo, they cause nonequilibrium. And they cause structures to appear. A small
backup in traffic causes further backup and a structure forms, in this case a
traffic jam. This is where the Brownian motion I alluded to comes in; it brings 23. For earlier uses of “meso” in economics, see Dopfer (2007) and Elsner and
Heinrich (2009).
24. But it is not true in general: many economic situations do not have forces leading to any equilibrium attractor.
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perturbations around which small movements nucleate; positive feedback magnifies them and they “lock in,” in time eventually to dissipate.
Positive feedbacks in fact are very much a defining property of complex
systems—or I should say more accurately, the presence of positive and nega-
tive feedbacks acting together is. If a system contains only negative feedbacks (in economics, diminishing returns) it quickly converges to equilibrium and
shows “dead” behavior. If it contains only positive feedbacks, it runs away and shows explosive behavior. With a mixture of both it shows “interesting” or
“complex” behavior. With positive feedback interactions add to each other
and cause structure, in time to be offset by negative forces and dissipate.
Structures then come and go, some stay to be further built on and some lead
to further structures. The system is “alive.”
These observations add to the earlier literature in economics on positive
feedbacks or increasing returns. Here, if a firm (or product or technology
or geographical region) gets ahead, possibly by small chance events, given
increasing returns it will gain further advantage and get further ahead; it may then subsequently go on to dominate the outcome (Arthur, 1989, 1994b). If N
firms compete there are N possible outcomes, but N need not be small. In the late 1800s, typewriter keyboard layouts “competed” for use, and only the one
we use today became a standard. But a simple calculation shows there were
more than 1054 outcomes possible, and this is a large number by any measure.
The process that increasing returns bring into being is by now well known.
What I would add is that positive feedbacks are present more widely in the
economy than we previously thought: they show up not just with firms or
products, but in small mechanisms and large, in decision behavior, market
behavior, financial behavior, and network dynamics. They act at all scales to
destabilize the economy, even the macro-scale (Keynes’ theory can be seen
as positive feedbacks temporarily locking in one of two possible states: full
employment and unemployment). And they lead to a set of characteristic
properties: multiple attractors, unpredictability, lock-in, possible inefficiencies, and path-dependence. Their counterparts in physics are multiple meta-
stable states, unpredictability, phase- or mode-locking, high-energy ground
states, and non-ergodicity. Once again these are properties we associate with
formal complexity.
THE ECONOMY IN FORMATION
I want to turn now to a very different topic, one that builds on our earlier
issue of disruption by technologies. Until now, we have seen given elements that comprise the economy reacting to the patterns they create and forming
ever different patterns. But this still doesn’t quite capture one fundamen-
tal feature of the economy. The economy continually creates and re-creates
comPlexi t y economics [ 17 ]
itself, and it does this by creating novel elements—often novel technologies and institutions—which produce novel structures as it evolves. How exactly
does this happen? How does the economy form itself and change structurally?
Schumpeter (1908) called this question “the most important of all the phe-
nomena we seek to explain.” Complexity should be able to help here; it is very much about the creation and re-creation of structure.
Let us begin by observing that if we want to look at how the economy con-
structs itself and changes, we need to look at technology and how it constructs itself and changes over time. Technology isn’t the only agent of change in the economy but it is by far the main one (Solow, 1957). The standard story of
economic change equates technologies with production functions and sees
the economy as a container for these. As new industrial technologies enter,
production functions change, output increases and labor or other resources
are released; this provides further wealth that can be invested in further technologies. The economy shifts smoothly from one equilibrium to another and
endogenously grows. This is fine and it fits well with equilibrium economics.
But it puts the main driver, technology, in the background, with prices and
quantities in the foreground. And it sees technologies as formless; they just
somehow arrive, singly and randomly, with no structure to how they build out
or how they change the economy in character over time.
A complexity view would put technologies in the foreground, and prices
and quantities in the back.25 It would recognize that there is considerable
structure to how technologies arise and enter the economy (Arthur, 2009).
In doing this it would focus directly on the collection of technologies present at any time, and ask how this collection evolves: how its members come into
being, how they create and re-create a mutually supporting set, and how this
alters the economy structurally over time.
To start, we can define individual technologies as means to human pur-
poses. These would include industrial processes, machinery, medical pro-
cedures, algorithms, and business processes. And they would also include
organizations, laws, and institutions—these too are means to human pur-
poses. The significant thing about technologies is that they are constructed,
put together, combined—always—from parts, assemblies, sub-assemblies.
These latter are also means to purposes, so novel technologies form by com-
bination from existing technologies.26 The laser printer was constructed from
the existing laser, digital processor, and xerography (the processor directs a highly focused laser beam to “paint” an image on a copier drum). We now have
25. For other complexity approaches to formation see Hildago and Hausmann
(2009), and Lane et al. (2009). On structural change see North (1981).
26. Schumpeter (1912) cites combination as the key driving force of formation (or
“development” as he called it).
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a system where novel elements (technologies) constantly form from existing elements, whose existence may call forth yet further elements.
Next let us define the economy as the set of arrangements and activities by
which a society fulfills its needs. These arrangeme
nts of course are the econo-my’s technologies. This is not a familiar way to look at the economy, but it fits well with the classical economists’ view of the economy as proceeding from
its instruments of production. The economy we can then say emerges from its arrangements, its technologies: it is an expression of its technologies. Seen this way, the economy immediately becomes an ecology of its means of production
(its technologies), one where the technologies in use need to be mutually sup-
porting and economically consistent.
We can add one more observation. Technologies come into being only if
there exists a “demand” for them. Most of this demand comes from the needs
of technologies themselves. The automobile “demands” or calls forth the fur-
ther technologies of oil exploration, oil drilling, oil refining, mass manufacture, gasoline distribution, and car maintenance. At any time then there is an open web of opportunities inviting further technologies and arrangements.
We now have the basic setup. To put it in motion we can ask how the col-
lection builds out. The steps involved yield the following algorithm for the
formation of the economy.
1. A novel technology appears. It is created from particular existing ones, and enters the active collection as a novel element.
2. The novel element becomes available to replace existing technologies and
components in existing technologies.
3. The novel element sets up further “needs” or opportunity niches for sup-
porting technologies and organizational arrangements.
4. If old displaced technologies fade from the collective, their ancillary needs are dropped. The opportunity niches they provide disappear with them,
and the elements that in turn fill these may become inactive.
5. The novel element becomes available as a potential component in further
technologies—further elements.
6. The economy—the pattern of goods and services produced and con-
sumed—readjusts to these steps. Costs and prices (and therefore incen-
tives for novel technologies) change accordingly.