Business Economics: Economies and markets as complex systems: Looking at them this way may provide f

Conventional economic theory follows a mathematical paradigm pioneered by classical physics, embodying smooth, differentiable functions, and dominant equilibria. The real business environment, however, is not so neat; and conventional ways of representing it have severe shortcomings. Complexity theory has important potential for shedding additional light on the behavior of the economy, particularly when impacted by sudden events. This paper outlines basic principles of complexity theory and indicates how they are relevant to the practice of economics in business.

Inspired by the achievements of 19th century physics and thermodynamics, for some 150 years most theoretical work in economics has been anchored by some sort of mathematical framework. Such frameworks are usually characterized by such features as dominant equilibria, smooth curves, easy turning points, non-disruptive changes of state, representative agents, and zero ambushes.

However, business economists must often deal with economies, markets, and companies whose behavior is not only quite messy but may violate one or more of the theory's underlying, traditional assumptions. Abrupt and surprising changes in conditions and prospects due to political events, unplanned inventory accumulation, earnings surprises, financial crises, heterogeneous agents, missed forecasts, organizations that collapse or default, models that miss turning points, and time series that "fall off a cliff" are just some of the problems. A few examples illustrate the potentially serious consequences of reality defying conventional analysis.

On becoming CEO of Citibank in 1984, John Reed faced $13 billion of non-performing loans--mostly to developing countries which, as sovereign nations, were not supposed to go bankrupt. Moreover, the bank's economists failed to anticipate this mess, ignored the factors that triggered it, and-by their subsequent advice-only made things worse. Reed concluded that "a whole new approach to economics might be necessary" and became an early supporter of the Santa Fe Institute, a leading center for the study of a new discipline called "complexity." (Waldrop, 1993, p. 91)

In another example, the path of most U.S. stock-prices indexes through August, 1987 could be described by an ARIMA function. In September, they began to oscillate randomly. Then suddenly in mid October, they plunged briefly into a chaotic mode, only to return to ARIMA patterns, as they gradually recovered their losses over the next fifteen months.

More recently, we have observed unexpected financial crises in Asia, Russia and Mexico; the collapse of Long Term Capital Management; Japan's economic and financial stagnation; the "irrational exuberance" of year 2000's stock-market; and extreme fluctuations in oil prices. September 2001, of course, saw the attack on the World Trade Center and the Pentagon, whose immediate economic effects were unpredictable and whose longer-term effects are highly uncertain.

To some people, these events are just a string of unrelated anomalies, the economist's equivalent of a batting slump. So no fundamental change in thinking is required. However, if we see economies and markets as complex systems and study them within the framework of the new discipline of complexity, the sporadic but persistent recurrence of such events turns out to be quite normal. This paper explains why and makes some suggestions as to how business economists can defend themselves and their organizations against some of the consequences.

A Very Brief Description of Complexity

Many of the themes falling within the purview of complexity have been studied for a long time in fields such as biology, cardiology, chemistry, computer science, demography, economics, electricity, game theory, mathematics, meteorology, and physics. In fact, Adam Smith's "invisible hand" (1776) is a classic example of the unexpected features that complex systems exhibit whenever their participants reach a critical mass and sell-organize, in this case into a decentralized, competitive market.

Yet it was only in the 1970's that investigators from diverse fields began to talk to each other and realize that, despite wide differences in conceptual frameworks and professional jargon, complex systems abound, have common features, and can be fruitfully studied as a group, despite their diverse origins. These systems include biological species, cardiovascular systems, economies, human societies, neural systems, stock markets and weather systems, to name just a few. (1)

Dynamic Systems

Since complex systems constitute one of the most important types of dynamic systems, we must say a few words about the latter before proceeding to the former. Dynamic systems are ubiquitous and range in size from nanomachines to the universe itself. All dynamic systems have common features, such as possible states, initial conditions, evolution rules, and boundary conditions. Here we distinguish between dynamic systems by their processes and by the multiple "tracks" that each system leaves in the sands of time, such as financial statements, GDP data, price series, rock strata, temperature readings, tree rings, and so on. (The literature prefers "orbits" or "trajectories". We prefer "tracks" to emphasize that they contain only limited information about the process that made them.)

The tracks of many dynamic systems, especially nonlinear ones, tend toward a point (such as the low point of a pendulum) or are confined to a well-defined hyperspace, both known as "attractors". Some systems even oscillate between several attractors, while others occasionally "escape" from their attractors, never to return. Thus, nonlinearity can create both bounds to system behavior and unpredictability within these bounds. However, note that attractors, nonlinearity, and specific patterns of system behavior do not always go together.

There are several ways to make the "first cut" in classifying the majority of dynamic systems--for example, difference equations vs. differential equations, linear vs. non-linear, aperiodic vs. periodic. Here we divide them into three groups--sporadic, unimodal, and multimodal--based on multiple criteria.

Sporadic systems are those that produce avalanches, earthquakes, mudslides, volcanic eruptions and such like. They appear to be dormant for long periods, while secretly testing the limits of equilibrium. Then they suddenly spring into action, provoked by external and/or internal forces. The severity of the outburst is inversely related to its frequency by a power function. In such systems, the "edge of chaos" really is an edge.

Unimodal systems have two key features. They can be described in terms of a single algorithm or function, such as an ARIMA function or a set of sine waves, and their tracks trace out a single, persistent, recognizable pattern, such as periodic motion, steady state or a trend. Familiar examples are the clock pendulum and a toy train running around a Christmas tree. Disturbances usually come from outside the system, as when someone accidentally knocks over the train.

Multimodal systems are legion, their tracks even more numerous, and the sources of disturbance are varied. Their most important common characteristic is that they are "chameleon systems". That is, at least one track successively imitates those of two or more unimodal systems. We now describe three important "families" of multimodal systems--the random, the sell-agitating, and the complex.

Random Systems

A random system is one in which each data point in its track is generated in such a way that its value has no causal connection with any other data point, and hence the system's future is inherently unpredictable. A classic example is the record of successive spins of a fair, properly maintained roulette wheel, turning too fast for the players to guess into which slot the ball will fall. Disturbances are usually external, as when a croupier is replaced or a spin is voided.

If we are making consecutive bets on black or red, our cumulative losses or winnings can be globally described by a first-order Markov chain and will exhibit a variety of modes over time. For example, winning and losing streaks can be modeled by an ARIMA function. Frequent alternations between red and black produce random oscillations, and so forth. The cumulative line of base hits in baseball exhibits similar behavior.

Self-Agitating Systems

Sell-agitating systems (misnamed "chaotic" in the literature) can be uniquely characterized as follows:

* They are largely or entirely deterministic. Their tracks are the product of a well-defined, nonlinear process in which the deterministic component dominates any stochastic elements that may be present. Yet the modeling function may have as few as one input and one control parameter.

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* Track behavior is extremely sensitive to initial conditions, measurement error and numerical roundoff. Thus, the tracks of any two systems with close initial values will diverge exponentially.

* Like lions on the Serengeti Plain, sell-agitating systems spend most of their time at a low but visible level of activity, whether patterned and/or random. Changes in the values of input variables generate only modest changes in the values of output variables. Then every so often, these systems abruptly go into a chaotic mode. Changes in the input variables suddenly produce disproportionately large changes in output variables.

* The tracks of sell-agitating systems almost never repeat themselves. So, with time, any non-point attractors will come to look like a bag jammed full of an endless piece of string.

* Given the foregoing, any track of a sell-agitating system quickly becomes unpredictable, which is why meteorologists have such a hard time forecasting the weather more than a few days in advance.

There is no "typical" sell-agitating system. In nature, they are not only more common than periodic systems but come in mind-boggling variety. So two examples must suffice to give their flavor:

* The model, [x.sub.1] = [ax.sub.0] (1-[x.sub.0]), ..., [x.sub.n] = [ax.sub.n-1](1-[x.sub.n-1]), based on the discrete logistic curve ("logistic map"). Similar models are used in marketing studies, animal-population studies, and so on. Note the sole input "[x.sub.0]" and the sole control parameter "a".

* Any weather system that can generate a meteorological disturbance. The very inputs that produce a random and/or patterned sequence of cloudy, rainy, and sunny days may occasionally assume a configuration of values that generate a major storm. Hence the assertion that the flapping of a butterfly wing off Africa can provoke a hurricane in the Gull of Mexico. However, on most days, ten thousand butterflies can flap away all day, and nothing will happen, not even nearby.

Complex Systems

Because complexity is a new discipline, there is no agreement on definitions for "complexity" or "complex systems," or on how to measure the degree of complexity. To keep things simple, we define complexity as the study of complex systems and label "complex" as any dynamic system which meets the following criteria--at least one track exhibits at least four modes; one of these modes is ARIMA, one chaotic, and one random; and all modes are manifest within a time frame of interest to the observer. The more modes, the more "complex" the system.

Complex systems share certain other characteristics:

* Only three conditions are required for their birth: (1) a critical mass of varied participants with some characteristics in common ("agents"), (2) access of these participants to some local information, and (3) a set of rules for their interaction. In other aspects, the participants may be heterogeneous. Both the participants and the rules may be (and often are) simple. Having reached a critical mass, the participants spontaneously self-organize, by a process of mutual accommodation, into a dynamic system of successive hierarchies and do so without any central authority or instructions. Sell-organizing systems are common in nature and often produce complex behavior from just a few ingredients. Among humans, they are more common than realized.

* Once formed, complex systems exhibit surprising properties ("emergent properties") that cannot he deduced from the properties of the participants and/or the reaction rules. In this regard, complex systems differ fundamentally from static objects that are merely complicated, such as computer chips. (Not all surprising properties are emergent. The possibility of a water molecule can be deduced from knowledge of how chemical reactions take place and from the valence of electrons orbiting the atoms of hydrogen and oxygen.)

* The ability to sell-organize depends in part on positive feedback (self-reinforcement)--a tendency for small effects to become magnified when conditions are right, instead of dying away. Increasing returns to scale and positive externalities are important sources of positive feedback.

* As a result, there is no need for strong assumptions about the capacity or rationality of the agents, although neither is prohibited.

* It is of limited use to analyze complex systems by the traditional "reductionist" methods of the natural sciences, since these assume that full knowledge of the parts gives full knowledge of the whole.

* A complex system is likely to spend more time in dis-equilibrium than in equilibrium. Moreover, being in equilibrium may even be a suboptimal state of affairs. It may mean that you are "asleep at the switch" (or stagnating) and are going to be zapped by one of your competitors! Possible examples are the U.S. auto industry at the onset of the Japanese assault on its market share and the Marxist dictatorship of Poland just before the formation of Solidarity.

Complex Adaptive Evolutionary Systems

The most interesting complex systems are also adaptive and evolutionary ("complex adaptive evolutionary" or CAE systems). They develop by co-evolution with their environments and/or other systems. Some relationships will be competitive, others symbiotic and still others both, often in ways more complicated than Darwin imagined. (The interaction of deer, soil, vegetation, weather, and wolves is a good example.)

In the long run at least, this evolution is unpredictable, in both space and time. To be sure, the inherent characteristics of participants (such as factor endowments) and interaction rules (such as the customs, laws, and regulations governing the operation of a particular market) set "the tone" of a system's evolution. However, given occasional chaotic and/or random modes, small differences in initial conditions may give rise to enormously different outcomes. And small chance events later on can cause "lock ins" of geographic location, market positions and/or technological options. Such events can also, like the bumpers in a pinball machine, send the system off in an unexpected direction. Increasing returns, if present, further widen the range of possible futures.

Yet this evolution is not random. Once a system has progressed a way along its "possibility tree," path dependence takes over, and system is unlikely to go back the way it came or "jump" to a far distant branch, although this can happen if multiple equilibria exist. Moreover, quite unintentionally, this evolution may even acquire a clear direction whose persistence, however, is not at all assured.

Given many possible outcomes, one cannot define a long-run optimum or even determine whether one exists. In this evolution, participants play an active role. They do not just respond passively to events. They try to remember their experiences, learn from them, anticipate next moves, define what it means to "get ahead," and then turn whatever happens to their advantage. They are students in the sometimes inhospitable classroom of real life, and respond as much to information as to financial and physical forces. Learning by doing is fundamental.

Successful CAE systems are dynamic but not chaotic. The participants learn to achieve a safe distance from both rigidity and chaos and how to escape from a chaotic mode should they temporarily fall into one. The "state space" in which a successful CAE system spends most of its time is often called "the edge of chaos," which might just as well be called "the zone of fruitful turbulence" because, in the case of CAE systems, it is not an edge at all but resembles a constantly shifting zone of creativity and struggle, fuzzily bounded by chaos on one hand and stagnation on the other. Our hunch is that the more complex the system, the wider this zone, which would explain why living systems have become more complex in the course of biological and cultural evolution.

Metaphorically, the participants in CAE systems are like people in small boats who work the fishing holes along a turbulent river, with rain forest upstream and dangerous rapids downstream. Much of their art consists in staying over the holes without letting dragging anchors, eddy currents, flash floods, or local turbulence carry their boats into backwaters, ground them on the shore, or sweep them into the rapids.

Implications for Economics

Complexity has important implications for economics. First, both economies and securities markets are CAE systems. Economies are complicated, evolving, open, organic, and path-dependent. They are "works in progress" that are never finished. They are more like evolutionary biological systems than like machines. Hence the length, erratic path, and sudden collapse of the most recent U.S. expansion should not have surprised us. Likewise the chronic tendency for securities markets to overshoot and undershoot.

The tracks of securities markets are especially unruly. They can exhibit several modes of behavior in less than a year, as in 1977, 1987, and 2000. This is why most historically validated, profitable trading systems eventually go awry and have to be recalibrated or abandoned, and why the pattern of frequencies in a market price series does not last very long.

In both economies and markets, instability and disequilibrium are normal; stability and equilibrium are not. While equilibria may arise from time to time in specific markets and even become attractors, they tend to be unstable, transitory and not always unique. Non-stagnant economies are even less likely to reach or maintain equilibrium, and they are certainly not "self-righting". So John M. Keynes' key insight, that an economy can stay "off center" with high unemployment indefinitely, remains valid.

Thus, business fluctuations will not go away just because people are selling on the Internet or manipulating interest rates, public sector budgets, and/or tax schedules. Complex systems can and do manifest a great variety of fluctuations, more varied than students of the business cycle have imagined. Moreover, bad sales forecasts by producers of final goods and services still cause wrong-sized inventories all along their supply chains. Thus, explaining or smoothing these fluctuations is a lot more difficult than cycle theorists, fiscalists, monetarists, and policy mavens would have us believe.

Accidents, culture, history, institutions, leadership, policies, programs, and starting points all matter, especially in the case of economic development. Ignorance of such considerations may well explain the failure of most transitions from a Marxist to a decentralized economy, despite a plethora of expert advice from free-market enthusiasts. In the words of W. Brian Arthur, these advisers ignored "embedded structures and understandings." (Colander, 2000, p.62)

Increasing returns to scale are common and significant. They increase the number of possible futures, decrease the possibility that a long-run optimum exists, and increase the influence of chance events on the evolution of a given system.

Given the foregoing, no economic system can get rid of fluctuations entirely. The best we can do is to undertake the economic equivalent of "peak shaving" and provide assistance for the victims. However, it does not appear that we can do as much as we once thought. In the final analysis, we must learn to rollwith the punches, while minimizing their damage.

Complexity makes a better case for decentralized, competitive markets than the usual hyperbole about "free" markets. The latter are not free. It costs money to get in, it costs money to stay there, and it costs money to get out. If you have creditors at bay or a superfund site on the premises, you cannot simply shut the door and walk away. Moreover, the playing field is seldom level. Microsoft has a lot more "freedom" than its competitors.

However, decentralized, competitive markets are very good at generating and processing information and reconciling supply and demand.

In the final analysis, economics and technology are thoroughly intertwined with culture, history, politics, and sociology. Deep down, biological, cultural, and intellectual evolution are different aspects of the same phenomenon. So, in the long run at least, everything interlocks, and no piece of the puzzle can be considered in isolation from the others.

Suggestions for Business Economists

Following are specific suggestions for business economists who must survive in a world of complex systems:

* "Top down" planning based on a "best estimate" forecast is out. The management of uncertainty is in. Planning must be scenario planning, in which most scenarios, if not all, have a less than a fifty percent chance of occurring and some, as a safety precaution, are deliberately made far fetched. For example, one should include an Exxon Valdez type scenario in ones vision of the future. And one must be wary of extrapolations and of the outputs of structural forecasting models. The latter usually insure internal consistency but fall short on accuracy, especially as to turning points.

* Participants in CAE systems responsible for the continuous and multiphased monitoring of reality, should focus on which scenario (if any) appears to be unfolding. Then, as necessary, they should construct alternate scenarios or modify existing ones. And they should keep a weather eye out for "branch jumps" on the possibility tree. Such an experience, while novel, can be traumatic.

* Producers of intermediate goods and services should also monitor, to the extent possible, the sales forecasts of their most important customers.

* Business economists should try to develop novel and sensitive indicators. They should also develop contacts with people in other organizations who sit in good "conning towers."

* While continuing to optimize projects and other capital investments, one should remember that nearly all such optima will turn out to be local and/or temporary. Building flexibility into expansions and new projects is a must, as is reoptimizing from time to time.

* Beyond the short run, it is more important to have "lots of antennas out," to be adaptive, and to be flexible than it is to be efficient.

* Unfortunately, no economic system is very good at dealing with the long run, with strategic considerations, or with drastic technological change. This is where managers who listen to their intuition, the nonprofit sector, the public sector, researchers, and insightful thinkers (such as Peter Drucker) all have important roles to play. In the end, it is not organizations or systems that produce success. Rather, it is the wisdom of people who manage, observe, or study them and the environment in which they operate.

In particular, the ability of participants in CAE systems to make connections, see implications, sense change, and use inductive reasoning is more important than their ability to apply advanced mathematics or use deductive reasoning. Participants in successful systems are opportunistic scenario strategists who try to manage uncertainty while avoiding both chaos and stagnation. On the whole, new-venture types and Adam Smith-type owner/operators tend to make better human antennas than bureaucrats, private or public.

The foregoing implies the need for a considerable degree of subsidiarity in most organizations, that is, for the delegation of operating responsibilities to the lowest level at which it can be effectively exercised. At the same time, the top must encourage full and honest communications from the bottom. Intellectual capital is not only more important than other kinds of capital, it must be spread widely throughout every organization. However, the dispersion of intellectual capital will not work if it is not accompanied by communication and subsidiarity.

The above does not by any means exhaust the useful ideas which complexity has to offer. In particular, see the books by Allison and Kelly (1999) and by Axelrod and Cohen (1999).

Some Words of Warning

As promising as complexity is, it is nonetheless still a young discipline with many basic issues still unresolved, including a lack of consensus on metrics, taxonomy, and terminology; a need to polish theoretical constructs; and a need to perform more empirical verifications.

In addition, the indices that characterize an entire system at one fell swoop require very large sample sizes. Rasband (1989, p. 212) regards 10,000 data points on an attractor as "sufficient" for measuring the degree of complexity of a chaotic system. Serleitis and Gogas (1999) need 144 monthly data points to determine that "North American natural-gas liquid markets are chaotic."

Also, tracks can be misleading, especially when the originating process is poorly understood. For many quarters at a time, the velocity of money is indistinguishable from a first-order Markov chain. Yet we all know there is a rationale behind the ebb and flow of cash balances in payroll accounts and related phenomena. As noted previously, the tracks of sell-agitating systems are easy to confuse with those of random ones.

Those on business front lines, whether short-term traders, strategic planners, utility dispatchers, or just plain-vanilla managers, really don't care about taxonomy. They want to know, "When is the next mode change?" Developing reliable sensors for this purpose is probably one of the most critical tasks faced by complexity.

Modeling is another problem. Adequate models of complex systems are likely to be mathematically intractable, especially nonlinear ones. Yet traditional linearized models generally do a poor job of forecasting turning points and completely fail to anticipate shifts to the chaotic mode. For example, in securities markets, trend-following trading systems produce losses when the market is in a chaotic or a random mode.