Selling Globalization: The Myth of the Global Economy

Michael Veseth

Lynne Rienner Publishers, Inc.

1998

5. Turbulence and Chaos

 

In order to master the unruly torrent of life the learned man meditates, the poet quivers, and the political hero erects the fortress of his will.

—José Ortega y Gasset 1

There are two ways of looking at the landscape of global finance: the perspectives of theory and of practice. As is often the case in economics, the images of theory seem to reveal a wholly different panorama from that which emerges from the viewpoint of practice. Both are true images, yet each is unique. Not surprisingly, we tend to focus on the more understandable and logical scene, which may be a serious mistake.

Exchange rates and the international flows that influence them are determined, in theory, by fundamentals. Fundamentals are the essential characteristics of economic systems that influence real trade and investment behavior. Logically, international flows should respond to changes in their fundamental determinants, making it possible to anticipate generally—if not to predict precisely—financial movements and exchange rate changes.

The pattern of international trade, for example, is determined in part by the prices of the goods that are bought and sold. If higher rates of price inflation in Italy make that country’s goods more expensive than those from other countries on international markets, then it is logical to expect that buyers will purchase fewer Italian goods and therefore fewer Italian lira. This lack of demand tends to depress the prices of both Italian goods and Italian currency, with the process continuing until a fundamental equilibrium is restored. If inflation makes Italian goods more expensive, then the lira must fall to compensate. The fundamental logic is bulletproof.

International capital movements, by the same logic, are influenced by expected real rates of return. If Italian interest rates rise relative to those of other countries and there is no offsetting change in expected prices or risk, then capital should flow to Italy to earn the higher return, with exchange rate and domestic interest rate effects that can be anticipated. The logic is clear.

Although international finance is complicated from the perspective of theory, it is not overly complex. It is complicated because there are a number of fundamental factors that can influence trade and investment decisions, several of which may be changing at the same time. But it is not very complex because each element has its own internal logic, and it is only a matter of time until you see how the pieces add up. Even the problems of currency crisis and speculative attack discussed in Chapter 4 are simple, logical processes.

Looking at international finance from the standpoint of theory, therefore, is like listening to a Bach fugue: lots to listen for, much detail to admire, and some problems to be worked out, but scrutiny is rewarded and the puzzles are solved in the end.

Practice plays a different tune, one that is much more like, say, a Dave Brubeck jazz piece: rhythmically complex, rolling and weaving, solid but ambiguous at times.

The merchants of pure practice are called chartists because they base their understanding of financial movements on what actually has happened, not on what should happen according to a model or equation. The chartists plot market data and analyze the patterns they find, searching for trends, turning points, support levels, and breaking points. Their charts resemble abstract drawings at times. Although theory tells us that the processes that set these prices are logically sound, the result, when it is plotted out, looks decidedly illogical. Sometimes there are no patterns at all. At other times there are patterns, but it is hard to know what they mean. How can logical forces produce such illogical-looking results?

Chaos theory provides a means to reconcile the enormous difference between the theory of international finance and its practice—to understand how the ordered, deterministic processes of the fundamentalists lead to seemingly disordered, prediction-resistant real world patterns of the chartists. Chaos theory, in other words, helps explain how Bach becomes Brubeck.

In this chapter I present a simple introduction to chaos theory and its application to economics in general and international finance in particular. I argue that exchange rates and international capital movements are not just unstable, as we saw in the analysis of currency crises in Chapter 4, but fundamentally chaotic. This is an important observation. Currency crises and speculative attacks don’t happen every day. Several months can go by without even a hint of currency collapse. During these short or long periods of relative stability, it is easy to conclude that global financial markets really are very stable and predictable or are converging toward such a stable state. ₂   But even if currency crises disappeared forever, the existence of chaotic movements in foreign exchange rates would continue to condition foreign trade and investment patterns and limit the globalization process.

The existence of chaotic patterns in international finance is important in several respects. First, it renders accurate long-term forecasting impossible, limiting the essential nature of global investments. Second, it increases the risk associated with even short-term international transactions, thereby limiting and altering the nature of these flows. Third, international financial chaos can lead to the delinking of exchange rates from the real economy, making nonsense of notions of rational global decision making. Finally, and perhaps most important, the turbulence of chaotic financial patterns encourages governments to intervene in financial markets to calm or steady them, which leads to crises and speculative assaults. A vicious cycle of crisis and chaos results, which further discourages the global expansion of economic activity. Chaos in financial markets, therefore, contributes to a wider chaotic condition.

This analysis of international finance using the ideas of chaos theory is thus more than just pretty pictures and interesting images, which are what most of us expect from a study of chaos: It is actually important both as theory and in practice. If international markets exhibit elements of chaos, then the global economy works differently, in fundamental respects, than most people believe, forcing us to reexamine the causes and consequences of the global expansion of economic activity.

 

Chaos Theory: Why You Cannot Stir Things Apart

Chaos theory is more firmly established in popular culture than it is in academic circles, which is unusual for a discipline that is based on sophisticated mathematics. The language of chaos entered the common vernacular in 1987 with James Gleick’s bestselling book, Chaos: Making a New Science. ₃   Since then several interesting books and at least one serious stage play have appeared on the subject. ₄   Of the 186 books with chaos in the title at Collins Library at the University of Puget Sound, for example, 114 were published after 1987, in the post-Gleick era. Most are about chaos theory in the sense in which I use it here—the science of complex dynamics—although there are a few works of literature mixed in that use the term in its classical sense: chaos as the formless disorder from which life sprang in Greek mythology. Book titles include Adventures in Chaos, The Collapse of Chaos, Chaos and Complexity, Chaos in Wonderland, Coping with Chaos, and many more. Like Gleick’s book, most chaos books have pictures of startling beauty, often in color. This distinguishes them from other books on the shelf, especially the academic books. The pictures are visual representations of computer simulations of chaotic processes.

Pictures are important in chaos theory, I think, because chaos is easier to recognize than it is to define clearly. Although there is no single standard definition of chaos, I think the important ideas are perhaps best captured in Stephen H. Kellert’s description of chaos theory as “the qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems.” ₅   The essential elements of chaos as I use the concept are these:

Unstable aperiodic behavior. The outcomes of chaotic systems are not regular patterns that exhibit smooth cycles or neat equilibria. Rather, a key characteristic of chaotic systems is the seeming randomness or unpredictability of the patterns and flows generated. In a nonchaotic system, a close study of the past eventually yields insights that allow us to anticipate the future. In a chaotic system, by contrast, the future is full of surprises and does not repeat the past in any periodic or regular way. Past is not prologue in chaos. Alfredo Medio notes that

For nonchaotic systems, therefore, after a certain time, listening to the ‘news’ becomes totally uninformative. For a chaotic system, however, no matter how long we accumulate data on the past positions of the system, we cannot accurately predict its transition from the present position to the next one (or to any of the future ones). In this case, we can only make probabilistic forecasts, if any at all. For chaotic systems, therefore, coarse-grained past, however long, does not determine uniquely and completely coarse-grained future. In other words, the ‘news’ will continue indefinitely to be a source of additional information to the system. ₆

Deterministic systems. The paradox—and a defining element—of chaotic systems is that they seem random, but they are not. The causes are rational and logical; the effects are seemingly random. Disorder arises from order, which may be specified by a set of equations that determine the behavior of the system. If the equations are known, behavior can be simulated or anticipated. But it is hard to “work backwards” and infer from the aperiodic observations the underlying deterministic system. Thomasina Coverly, the math prodigy in Tom Stoppard’s play Arcadia, makes the point this way:

If you could stop every atom in its position and direction, and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra, you could write the formula for all the future; and although nobody can be so clever as to do it, the formula must exist just as if it could. ₇

Dynamical systems. The key is that the deterministic system is dynamical, not static. It is not a system of equations to be solved simultaneously for equilibrium but rather a description of a movement through time, in which each instant’s condition is related to the moment before and determines the condition of the next moment. In some applications, the most important contribution of chaos theory is that it shifts the focus from static to dynamical analysis. Most economic analysis, for example, is static because this allows us to work on systems of ordinary equations that can be solved generally using what Thomasina Coverly would call “good English algebra.” Dynamical systems, on the other hand, require the use of difference equations, or differential equations, which have solutions but often cannot be solved in a general sense. (Numerical analysis can be used to find solutions to specific cases.)

Nonlinear systems. Not all dynamical systems are chaotic. Chaos occurs when the systems are nonlinear, and for this reason the term nonlinear dynamics is often applied to what I call chaos theory. In a linear system, patterns of behavior are very regular. Actions respond to their stimuli in a constant direction at a constant rate and display the same behavior going forward and backward. Linear systems are convenient for theory because they are so well behaved. The world is generally nonlinear, however. As stimuli increase, actions increase and decrease and at varying rates of acceleration and deceleration. Nature does not always work the same going forward and backward. Thomasina discovered that “When you stir your rice pudding, Septimus, the spoonful of jam spreads itself round making red trails like the picture of a meteor in my astronomical atlas. But if you stir backward, the jam will not come together again. Indeed, the pudding does not notice and continues to turn pink just as before.... You cannot stir things apart.” ₈

A linear system may provide a workable description of nonlinear behavior within a very local region, but the resemblance breaks down over time in a dynamical system and as the focus of attention shifts from local to global. Thus, it may be reasonable for an aeronautical engineer to test an airplane wing with a constant wind of two hundred kilometers per hour from the north to learn about certain narrow aspects of design and performance, but it would be nonsense to infer from this experiment the wing’s actual behavior in the real world and complex or changing airflow patterns. ₉

Qualitative study. This is controversial. Although much analysis of chaos is quantitative in nature, my focus is really qualitative, and I have chosen my definition of chaos accordingly. In this study I am not interested in being able to make exact predictions of how international financial variables change when they are in a state of chaos, although it would be useful and potentially profitable to be able to do so! ₁₀   Rather I am concerned with understanding how fundamental relationships change over time and the consequences of these changes. This is qualitative, not quantitative, analysis. Quantitative analysis of chaotic systems is important, but for reasons that I discuss later in this chapter, I think it is of relatively limited utility in economics.

The definition of chaos as the qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems suits my purposes because it effectively describes the nature of this study (qualitative), the character of international financial markets (dynamic, deterministic, and nonlinear), and the observed outcomes (aperiodic behavior). Other commonly cited properties of chaos, which may also be present in international financial markets, are these:

Sensitive dependence on initial conditions. One common feature of chaotic systems is that small changes in parameters ultimately cause enormous changes in outcome or behavior, as the tiny initial differences are magnified and transformed by the nonlinear dynamical processes at work. It is not very difficult to understand how sensitive dependence works. The accumulation of compound interest is a nonlinear dynamical process. Compound interest accumulates over time (dynamical) and rises exponentially (nonlinear). It makes little difference in the short run if the interest rate on a 1-year $1 bank deposit is 7 percent or 8 percent. The difference is small in proportionate terms and insignificant in absolute amounts. If we allow interest to accumulate and compound over 100 years, however, the difference is significant and the outcome is very sensitive to the initial interest rate. At 8 percent, the original $1 deposit compounds and accumulates to a total of nearly $3,000, whereas at 7 percent the total is only about $1,100. The total here is sensitive to initial conditions, with the difference rising as the interval of time lengthens. In chaotic systems, sensitive dependence suggests that small differences in starting points or pathways can create both quantitative and qualitative differences. I make little use of the feature of sensitive dependence of initial conditions in this chapter, but I will have something more to say about it in Chapter 7.

Presence of strange attractors. A final property often cited is the presence of strange attractors, which is not a very descriptive name. It means that there is a tendency for chaotic patterns to veer suddenly from one local range of observed values (an attractor) to another and perhaps back again at unpredictable intervals. The property of strange attractors is related critically to the notion of unstable aperiodic behavior discussed earlier.

In Gleick’s book, the hero is the economist Brian W. Arthur, who has applied principles of chaos theory with skill and imagination to a number of problems, including population growth and patterns of technological change. Brian Arthur did not invent chaos theory, however. The French mathematician and physicist Henri Poincaré (1854–1912) usually receives credit for the discovery of the concept of systematic chaos. Edward N. Lorenz writes that Poincaré

raises the possibility that what we generally regard as chance, or randomness, may in many circumstances be something that has of necessity followed from some earlier condition, even though we may be unaware that it has done so. He notes that in some cases we might be completely unable to detect the relevant antecedent conditions, while in others we might observe it fairly accurately, but not perfectly. In the later case the uncertainty might amplify and eventually become dominant. Is he not describing chaotic behavior? ₁₁

Although Poincaré posed the problems of chaos, he lacked the technology to explore them fully. In particular, he lacked the computing abilities we take for granted today that allow us to make thousands of calculations in a moment and so to explore dynamical processes more fully. Thus chaos theory waited almost half a century for its time to come.

The U.S. meteorologist Edward N. Lorenz is one of several contemporary scientists who helped create the modern science of chaos and popularize the study of chaos theory. ₁₂   His most famous paper is called “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” ₁₃   In it he argued that the earth’s atmosphere is a complex space and it is not unreasonable to believe that small causes can have large effects—the butterfly effect.

The Lorenz Attractor is a cool picture that, by coincidence, actually looks a lot like a butterfly. It shows patterns of atmospheric convection modeled by simulating the flow of fluid in a box that is heated from the bottom. This process is nonlinear and dynamical. The outcome, illustrated by the Lorenz Attractor, is unstable and aperiodic. The two strange attractors are the most obvious strange visual evidence of instability; atmospheric conditions do not stay put but instead swing about wildly. The movements between and within each attractor are aperiodic. As Poincaré said of this sort of condition, “La prédiction devient impossible...” ₁₄

The important thing to remember here is this. The world is broadly characterized by the existence of nonlinear dynamical processes. They are all around us, and we are in them. Most such systems have produced chaotic behavior at some level and in some form. Because chaotic behavior is as natural as the spread of jam in your rice pudding, it is natural to take it for granted. This can be a serious mistake. Visions of globalization that fail to take into account the chaotic behavior of global financial markets risk overstating the degree of globalization that is possible and risk understating the persistent influence of local factors in the global economy.

Chaos theory is now widely applied in many fields, with uneven results. Perhaps physicists seeking to analyze turbulent fluid dynamics flows have done the best work. ₁₅   Inevitably, however, the thought of order flowing out of disorder reminds people of economics. ₁₆

 

Economics and Chaos Theory

There is little doubt that economics and finance give us examples of chaos and unpredictable behavior (in a technical sense). But it is difficult to say more, because we do not have here the kind of carefully controlled system with which physicists like to experiment. Outside events, which economists call shocks, cannot be neglected. Earnest efforts have been made to analyze financial data (which are known with much better precision than economic data) in the hope of isolating a moderately complicated dynamical system. Such hopes, in my opinion, have failed. We are left therefore with the tantalizing situation that we see time evolutions similar in some sense to those of chaotic physical systems, but sufficiently different that we cannot analyze them at this time. ₁₇

It hasn’t been easy to apply chaos theory to economics. Paul Krugman has commented that economics is hard, much harder than physics (or at least classical Newtonian physics), but not nearly so difficult as sociology. Classical physics is easy, he says, because it is just math, and math always works the same way. Sociology is hard, however, because it is just people, and people hardly ever behave the same way twice. Krugman’s point is that the farther we move from deterministic systems governed by mathematical laws that can be tested by reproducible experiment and the closer we get to bunches of people milling around in the town square or trading in a currency pit, the harder it is to make precise statements and draw meaningful conclusions. ₁₈   This observation applies with special force to the case of chaos theory.

Although the practice of economics is rich in experiences that can perhaps best be understood in terms of nonlinear dynamics, the theory of economic science is not so well developed as to provide a sound foundation for such analysis. There are reasons for this, which I discuss in Chapter 7. The Economics Research Program at the Santa Fe Institute is one of the leading centers for the application of chaos theory to economics. The following is a list of working papers produced from 1993 to June 1996 ₁₉   :

• Aggregate Fluctuations from Independent Sectoral Shocks: Self-Organized Criticality in a Model of Production and Inventory Dynamics
• Pathways to Randomness: Emergent Nonlinearity and Chaos in Economics and Finance
• The Santa Fe Art Market
• Common Knowledge
• Contrarians and Volatility Clustering
• Self-Organized Markets in a Decentralized Economy
• Inductive Reasoning, Bounded Rationality, and the Bar Problem
• Economies with Interacting Agents
• Choice and Action
• Rational Routes to Randomness
• Faster Valuation of Financial Derivatives
• A Strategic Game with Secured Lending
• Connectivity and Financial Network Shutdown
• When Optimization Isn’t Optimal: Aggregations and Information Contagion
• A Comparison of Political Institutions in a Tiebout Model
• Clustered Volatility in Multiagent Dynamics
• Breeding Competitive Strategies
• Neighborhood Feedbacks, Endogenous Stratification, and Income Inequality
• Nonlinear Times Series, Complexity Theory, and Finance
• Discrete Choice with Social Interactions
• Foresight, Complexity, and Strategy
• Time and Money
• Asset Price Behavior in Complex Environments
• Identification of Anonymous Endogenous Interactions
• Evolution of Trading Structures
• How the Economy Organizes Itself in Space: A Survey of the New Economic Geography
• Population Games

What these papers have in common is their focus on dynamical processes in complex environments. Apart from this, however, they are seemingly unrelated in terms of form and content. In my reading of the literature, some of the more successful theoretical applications have used chaotic dynamics to explore economic cycles, such as inventory and business cycles. The most ambitious applications in practice are attempts to discover and understand patterns of chaotic behavior in time series of economic data. ₂₀   The relative lack of observations and the high level of noise in these data make this task difficult, however, at least as compared with problems in the physical sciences.

Although economists seek the same sort of deep understanding of social phenomena that physicists have of natural behavior, the built-in constraints of social science limit what can be accomplished. It is unlikely, therefore, that chaos theory will be useful to economists in the same way that it is useful to a physicist studying fluid dynamics or the flow of air over a wing and seeking a more precise understanding of these phenomena. Chaos theory may turn out to be a weak quantitative tool in economics, but it could be a strong one to expand qualitative understanding. Chaos theory may also turn out to be a robust quantitative tool—it is just too soon to tell. In fact, I think it is too soon to know what specific contribution chaos theory will make to our understanding of the economy. In this regard, chaos theory today is in about the same place that game theory was a generation ago.

William J. Baumol and Jess Benhabib have argued that the most important contribution of chaos theory to economics currently is its ability to broaden our vision, “revealing sources of uncertainty, and enriching the list of recognized possible developments.” ₂₁   Chaos theory suggests that unstable fluctuations may be at least as common or easy to produce as other sorts of economic behavior and that the seemingly random need not, in fact, be random. This information can be used, Baumol and Benhabib suggest, to disprove certain elements of conventional wisdom in theory and practice and to provide useful caveats to otherwise broad generalizations and accepted practices. ₂₂

An example illustrates this point. Economists generally believe that free trade results in an efficient use of resources and that it therefore maximizes welfare. They generally favor programs of economic integration, such as the North American Free Trade Agreement (NAFTA) or the European Union, therefore, because of their expansion of free trade’s domain. The benefits of increased efficiency, however, may be offset by unexpected stability problems: “... the complicated system obtained by coupling together various local economies is not unlikely to have a complicated, chaotic time evolution rather than settling down to a convenient equilibrium.... Legislators and government officials are thus faced with the possibility that their decisions, intended to produce a better equilibrium, will in fact lead to wild and unpredictable fluctuations.” ₂₃

This statement does not, of course, prove that economic integration leads to chaos, or even provide conditions such that chaos appears or does not appear. What it does do—and I think this is very useful—is increase the dimension of our analytical domain and challenge us to think clearly about the complex relationships we study. Globalization might be chaotic, and it is a mistake to plunge headfirst into the global pool without first considering this possibility.

International financial markets have proved to be one of the most successful areas in which to apply chaos theory to economics. These financial markets serve as the nexus for complex patterns of nonlinear relationships, making them an obvious hunting ground for chaos. They generate relatively large volumes of accurate data, especially on exchange rates, making it possible to actually test for chaos in some cases.

There is strong evidence that international financial markets are chaotic in the sense discussed here. Chaos is produced by three sets of interactions, which are discussed in the next three sections. Chaos is created by the interaction of fundamental analysis with chartists, by cascades of market information or “news” over time, and by the interaction of political and economic forces in these markets.

 

Chaos in Theory and Practice

The interdisciplinary team of Paul De Grauwe, Hans Dewachter, and Mark Embrechts has produced some of the best analysis of the chaotic behavior of international financial markets. ₂₄   De Grauwe has found that relatively simple models of foreign exchange behavior can produce chaotic patterns of exchange rate movements under reasonable conditions. Their work suggests strongly that foreign exchange markets are chaotic, at least at times.

Suppose that there are two types of participants in foreign exchange markets: chartists and fundamentalists. Chartists base their expectations of future exchange rates on the movements of the past. They base their actions on the information contained in their charts and do not explicitly take into account information, or “news,” about economic variables that affect the underlying goods, services, and asset markets that are the foundation of the nonspeculative demand and supply of foreign exchange. Chartists add an element of positive feedback into the exchange markets. Chartists who observe an upward trend in a currency’s value, for example, extrapolate this movement into the future and, by purchasing the currency in hopes of gain, give the trend momentum.

The fundamentalists use a model of the equilibrium exchange rate as the basis for forming expectations and determining their market behavior. Their model reflects the fundamental economic variables, such as interest rates, inflation rates, and money supply data that condition exchange market behavior. Fundamental indicators are used to forecast exchange rate equilibria. If the current exchange rate is different from the forecast equilibrium rate, fundamentalists expect the actual rate to move toward the forecast rate, and they will act to profit from this movement. Thus, if the actual rate is above the expected rate, fundamentalists will expect the currency to depreciate and will sell it short. This action tends to drive down the currency value toward a new equilibrium. Fundamentalists are assumed in this model to use different specific models such that their forecasts of the equilibrium exchange rate are normally distributed around the true rate.

Fundamentalists are sensitive to news about economic conditions. When fundamental economic conditions change, their estimates of the equilibrium rate also change, perhaps radically, and they make market bets under the assumption that the exchange rate will move toward the forecast rate. Their market bets tend to drive the exchange rate toward its new fundamental equilibrium.

Chartists and fundamentalists thus present two distinct types of behavior. Chartists are backward looking in their analysis, and their behavior tends to be momentum preserving (an appreciating exchange rate continues to appreciate, given the chartist model). They may, for example, base their forecasts on moving averages of past exchange rates. One important factor that affects chartist behavior is the degree to which they look backward. That is, how many hours, days, weeks, or months of prior activity do they consider in making forecasts? If long-term trends are followed, then short-term swings in chartist activity will be few. Chartist activity is more likely to change in the short run if the time series used to guide forecasts is also relatively short.

Fundamentalists are forward-looking and base their forecasts on expectations of equilibrium exchange rates, assuming that the actual exchange rate will move over time toward the equilibrium rate. Their actions tend to preserve the equilibrium in the sense that if the exchange rate is at equilibrium, their market bets do not move it away and if the exchange rate is away from equilibrium, their market bets tend to move it toward equilibrium. The sensitivity of fundamentalists to news about economic variables means that they are a source of change in the exchange market, and perhaps a sharp one at times.

One important factor that affects fundamentalist behavior is their estimate of the speed of adjustment of the foreign exchange market. That is, if a currency is overvalued by 10 percent, how long does it take for the market exchange rate to depreciate by this amount? A day or week or month or year? If adjustment to fundamental equilibrium is thought to be fast, then fundamentalist market bets will be large because short-term profits will be large and the profit window small. If, on the other hand, the market is thought to have considerable momentum, making adjustment to the fundamental equilibrium slow, then fundamentalist actions will be more modest.

In De Grauwe’s model, chartists and fundamentalists are assumed to base their actions on their own methods and not attempt to anticipate the movements of the other group; the only way the two groups interact is through the market. Chartist actions, for example, may induce fundamentalist reactions by moving the exchange rate away from the expected equilibrium rate, these reactions may feed back into chartist responses, and so on.

The simple model just described was stated mathematically by De Grauwe. Computer simulations were then performed under a variety of assumptions about the degree to which chartists look backward and the fundamentalists’ expectations of market adjustment. Many different dynamical patterns were found. Simulated price movements were especially stable when the chartists’ time frame was short, so that the amount of “momentum” chartists induced to the market was small relative to the stabilizing force of the fundamentalists. Under some circumstances, the exchange rate developed patterns of stable cycles or limit cycles.

Most interesting for us, however, is the fact that a chaotic pattern of exchange rate movements developed in almost half of the simulations. Chaos was most frequent when the time frame on which chartists based their action was quite long. Because chartist actions were based on long-term trends, their actions provided a strong force of momentum, which produces chaos when mixed with the behaviors of fundamentalists.

Two aspects of the De Grauwe chaos are worth noting. First, chaos is produced even in the absence of news that changes fundamentalist behavior: Under some circumstances, chaos is inherent in the dynamics of the exchange market and is not produced by shocks of changed expectations of the type discussed in Chapter 4. This fact forces us to realize that crises and chaos are two different factors in the foreign exchange markets, not the same behavior interpreted in different ways.

Second, De Grauwe points out that the type of chaotic patterns this simple model generates are not especially realistic. Chaos took the form of unpredictable variation from an apparently constant mean. This type of chaos is, literally, like noise in a circuit. It would represent a problem for international traders or investors, but a problem that could reasonably be minimized using forward rates or other hedging techniques. Real world exchange rates tend to display patterns of seemingly random cycles that appear to be embedded within longer cyclical patterns, which themselves appear unpredictable, creating a sort of fractal landscape.

The simple De Grauwe model, therefore, under certain conditions produces chaotic price movements in foreign exchange markets. But these movements are of a sort that is not typical of real world foreign exchange markets. The simple model, however, is very simple. De Grauwe improves the model by making the behavior of fundamentalists more realistic. ₂₅   Following standard exchange rate modeling practice, De Grauwe introduces three equilibrium conditions that guide fundamentalist analysis.

• A money market equilibrium condition holds that adjustments in real incomes, price levels, and interest rates ensure that money supply equals money demand in each country.

• An open interest parity condition holds that interest rates and exchange rates adjust over time so as to eliminate covered interest arbitrage. Exchange rates and the forward premium or discount adjust to offset differences in interest rates among countries.

• A goods market equilibrium holds that exchange rates and price levels adjust so that the law of one price (level) holds in international trade. Exchange rates adjust to offset differences in inflation rates between two countries. This is also called the Purchasing Power Parity (PPP) condition.

Further, De Grauwe assumes some degree of “interest rate smoothing” by monetary authorities. The central bank is assumed to “lean against the wind” and expand money supplies in the face of rising interest rates, for example. With this reasonable addition, the model includes several forces that preserve market momentum, other forces that seek fundamental equilibrium, and sources of news that can alter expectations and market behavior. The resulting system is fairly complex, but De Grauwe models it and performs simulations for different parameter values.

The complex exchange rate model, including interest rate smoothing, is never stable in the simulations that De Grauwe reports, although stable cycles and limit cycles appear under some sets of assumptions. ₂₆   Chaotic patterns appear even more frequently than before, however, and a qualitative change occurs. Under the assumptions of interest rate smoothing, the exchange rate takes on a realistic pattern of short- and medium-term variation embedded in similar longer-term exchange rate swings. In other words, the simulation patterns actually look like actual movements in exchange rates. This property tends to increase as the degree of interest rate smoothing or monetary intervention increases. De Grauwe finds, as well, that the complex model simulations display statistical properties consistent with actual exchange rate experience. ₂₇

Several properties of the complex model are interesting. Chaos tends to be a qualitative feature of the exchange rate system when it is present, for example. If fundamentalists have high confidence in their model’s ability to predict equilibrium exchange rates, the degree of market variation is reduced, but the essential chaotic pattern remains. Chaos, therefore, cannot be eliminated through better estimation techniques. Indeed, the chaotic movements of exchange rates, according to De Grauwe, systematically obscure the underlying fundamental relationships, making the successful construction of models difficult. ₂₈

De Grauwe’s complex model shows that the interaction of chartists, fundamentalists, and interest rate smoothing monetary authorities produces chaotic exchange rate patterns that are similar to actual exchange rate patterns. This is not the same as showing that actual exchange rates are in fact chaotic. For this, more evidence is needed.

 

Information Cascades and Market Turbulence

A recent study by a Swiss-German team of physicists reported in scientific journal Nature provided evidence of chaotic foreign exchange markets. ₂₉   Ghashghaie, Breymann, Peinke, Talkner, and Dodge obtained access to an enormous database of exchange market information: 1,472,241 bid-ask quotes that represented all activity in the U.S. dollar–German deutschmark foreign exchange market from October 1, 1992, to September 30, 1993. This deep but narrow database allowed them to perform the sort of complex empirical analysis that social scientists rarely experience.

The physicists were interested in turbulent flows. Turbulence is one of the tough problems of natural science that drove the early inquiries into chaos theory, including Edward Lorenz’s “butterfly” research. Gleick wrote that “turbulence was a problem with a pedigree. The great physicists all thought about it, formally or informally. A smooth flow breaks up into whorls and eddies. Wild patterns disrupt the boundary between fluid and solid. Energy drains rapidly from the large-scale motions to the small. Why?” ₃₀

The answer—not so much to why this happens, but how—is that as more energy is released to a nonlinear deterministic system (for example, the water tap in your bathtub or the atmosphere of the planet Earth), a pattern of bifurcation occurs, and increasing numbers of strange attractors are created. Turbulence and chaos are the result.

One of the signature characteristics of turbulence in nature is a cascading effect that breaks big flows into progressively smaller ones, releasing energy in the process:

A flow of energy from large to small scales is one of the main characteristics of fully homogeneous isotropic turbulence in three spatial dimensions. It provides a mechanism for dissipating large amounts of energy in a viscous fluid. Energy is pumped into the system at large scales of the order of, say, metres (by a moving car or a flying aeroplane) or kilometres (by meteorological events), transferred to smaller scales through a hierarchy of eddies of decreasing sizes, and dissipated at the smallest scale—on the order of millimetres in the above examples. ₃₁

Ghashghaie and his colleagues analyzed data from the dollar-deutschmark market using the same statistical techniques they would have used on fluid dynamics data. They found cascading effects over time and exactly paralleled the cascading behavior of fluids over three-dimensional space. That is, foreign exchange prices displayed the same turbulent patterns of activity over time that fluid flows show in space.

Other parallels between fluid dynamics and exchange markets appeared. In particular, they found that “an important aspect of turbulent flows is their intermittent behavior, that is, the typical occurrence of laminar periods which are interrupted by turbulent bursts. In the foreign exchange markets this corresponds to clusters of high and low volatility.” ₃₂   This pattern of uneven instability was, of course, a property noted earlier by De Grauwe and is found in both turbulent fluids and foreign exchange markets.

If fluid turbulence dissipates energy, then what force drives the foreign exchange cascades? Ghashghaie and his colleagues suggested that information—news—is a source of energy and the force dissipated in foreign exchange markets. They speculated that the turbulence they observed was caused by the behaviors of long-term and short-term trades. They posited that long-term traders, who watch foreign exchange markets only from time to time, influence the behavior of short-term traders, who constantly monitor market behavior. Turbulence results as the new information that long-term traders bring to the market dissipates over time to the short-term traders. Their analysis therefore draws parallels between fluid dynamics and exchange market dynamics, as noted in Table 5.1.

Table 5.1: Correspondence Between Fully Developed Three-Dimensional Turbulence and Foreign Exchange Markets
Dynamic System	Hydrodynamic Turbulence	Foreign Exchange Markets
Force	Energy	Information
Turbulent domain	Spatial distance	Time delay
Dynamic characteristics	Laminar periods interrupted by turbulent bursts (intermittency)	Clusters of high and low volatility
Cascade type	Energy cascade in space hierarchy	Information cascade in time hierarchy
Source: S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, and Y. Dodge, “Turbulent Cascades in Foreign Exchange Markets,” Nature 381 (27 June 1996), p. 769.

One way to understand the logic of the information cascade model is to think of it in terms of De Grauwe’s model of interaction between chartists and fundamentalists. Suppose that the fundamentalists are the long-term traders who enter foreign exchange markets only when they receive “news” or fundamental information that causes them to alter their expectations of the true equilibrium foreign exchange rate. As the news arrives, the actions of the fundamentalists drive information into the market through changes in market prices. Chartists react to the changing prices directly (and do not, by assumption, pay any attention to the changing news itself, nor do they attempt to anticipate the reactions of fundamentalists).

Suppose that the chartists adopt varying strategies, some using long-term charts, others medium-term trend analysis, and still others relying on very short time horizons, a real characteristic of different groups of speculators. Then the short-horizon chartists will react quickly to the fundamentalist information impulse, as their estimate of the future exchange rate trend is very sensitive to recent data. Chartists with medium- and long-term analytical horizons will react and change their expectations more slowly.

The fundamental news thus cascades through the exchange market, flowing from fundamentalists to short-horizon, medium-horizon, and long-horizon chartists. Turbulence and chaos are produced as the new information is dissipated throughout the market.

De Grauwe found that realistic chaotic patterns were most common in the complex model with interest rate smoothing by the monetary authority. There is no direct analog to interest rate smoothing in the Nature study on turbulent cascades. However, we might usefully consider interest rate smoothing as the equivalent of friction in fluid dynamics, which inhibits flow, making fluid viscous. Viscosity in nature increases the rate of energy dissipation and hastens the onset of turbulence. In the same way, De Grauwe found that interest rate smoothing hastens the onset of chaos of the sort found in both foreign exchange markets and fluid dynamics.

Understanding the problems of modeling turbulent flows, the physicists are pessimistic about the possibility of understanding foreign exchange market turbulence in any deeply systematic way. They conclude that “it is unlikely that there is a set of a few partial differential equations (like Navier Stokes equations in hydrodynamics) which might serve as a model of foreign exchange market dynamics.” ₃₃   But, as we have seen, De Grauwe and his team have developed a model of foreign exchange behavior that produces chaotic patterns in theory that are qualitatively similar to those experienced in practice. A precise quantitative understanding of exchange rate chaos may still be beyond the horizon, but I think we are very close to a qualitative understanding of what is going on in these markets.

The case for chaotic foreign exchange markets, therefore, seems quite strong. Economics is harder than physics, however, and the empirical analysis of chaos in foreign exchange markets requires more discussion. But I think we should first consider the part of chaos that seems to be as obvious in practice as it is invisible in the theories presented here: politics.

 

Political Economy Chaos

The models of foreign exchange chaos that I’ve presented so far have focused on finding chaos within the natural forces of the market. The market agents whose interaction produced chaos came right out of the standard economic toolbox: individuals, both self-interested and profit-seeking, taking independent action without organization or coordination. The only deviation from this pattern was the added assumption De Grauwe made in the complex model of the interest rate–damping monetary authority, whose actions made the mix viscous and introduced shocks whenever “news” broke.

It seems to me that the real world of exchange rates contains not only these elements but also others that contribute to the chaos we have observed. ₃₄   In particular, the actions of states and the motives of politics cannot be ignored. We saw in Chapter 4 that central bank policies were a potent ingredient in the mixture that sometimes explodes in currency crises. De Grauwe’s complex model showed that monetary policies that seek to reduce interest rate fluctuations also increase the chaotic domain, although they are not necessary for foreign exchange chaos to occur.

States interact with the foreign exchange markets in several ways—some are systematic, others discretionary, and some appear almost random and might be chaotic themselves. Among the many ways states get into the act are these:

• Monetary policy. Central banks dampen interest rates and introduce news into markets, but they can also affect foreign exchange markets in other ways. Monetary authorities may target interest rates, as De Grauwe suggested, but they can also adopt systematic policies that instead target money supplies, nominal gross domestic product, or a price level. Monetary policy can be systematic, as these would be, or it can be discretionary. The possibility of monetary policy that responds to changing political winds is important in what I have to say later in this section.

• Fiscal policy. Tax and spending policies can have many indirect effects of international markets. Perhaps the clearest link lies in deficits and public debt policy. The timing, amount, and type of public debt, the credibility of debt policy, and the expectations of future debt patterns can have important international effects as well as the obvious domestic ones. ₃₅  

• Direct intervention policy. Monetary and fiscal policies affect foreign exchange markets indirectly, but government officials also intervene directly in exchange markets, buying and selling currency for a variety of reasons. Intervention may be coordinated, as in some cases discussed later, or unilateral. It may be guided by clear policy or a discretionary response to political needs.

• Currency target zone policy. Government authorities may attempt to coordinate domestic policies and international direct intervention policies to support a target zone regime. De Grauwe simulated a target zone system under the assumption that it would make fundamentalists more confident in their models’ abilities to forecast equilibrium exchange rates. He found that the range over which the simulated exchange rate varied was diminished but that chaos still appeared, albeit on the smaller scale. He did not attempt to model the currency crises associated with target zones.
  Not all nations belong to a given target zone regime, however, so a multispeed system is necessarily created. The deutschmark, for example, may be very stable relative to the French franc, moderately stable relative to the Italian lira and Portuguese escudo, and freely floating relative to the U.S. dollar. The fact that nations may participate in several different overlapping currency policy groups (or have unilateral but not necessarily reciprocal policies with respect to different currencies that create such an overlapping pattern) creates a complex system.

• Pegged exchange rate policy. Many soft currency countries attempt to fix their exchange rates against the currency of their major trading partner nation. This again creates the possibility of interesting dynamic patterns, as the strategies of floating, pegging, and setting targets interact.

It is not difficult to imagine real world scenarios in which the policy actions of states play an important part in creating a chaotic pattern in international financial markets. In fact, when the possibilities are considered, it is a wonder that anyone would ever think that exchange markets are anything other than chaos! Here are some thumbnail sketches of potentially chaotic policy scenarios.

State-state dynamic interaction. De Grauwe’s private sector chartists and fundamentalists may have analogs among states. The European monetary system crisis of 1992–1993 showed that states do not all have the same policy goals for political reasons, even when they may have committed to coordinating economic policies. Suppose that one nation acts like a fundamentalist or perhaps a reverse fundamentalist. Suppose it seeks to attain certain domestic policy goals that are consistent with a particular exchange rate and that it intervenes in exchange markets whenever the actual exchange rate varies significantly from the one consistent with its domestic policy goals. Japan in the mid-1990s might be an example of a reverse fundamentalist. The need to promote domestic recovery from their deep recession caused Japanese officials to intervene when the yen appreciated above the range consistent with domestic policy goals. The motives for intervention to achieve domestic goals and the motives of private sector fundamentalist speculators distinctly differ, but their market behavior is qualitatively the same. Both “intervene” to push or pull exchange rates toward the target, or forecast, rate.

Other nations may be more like the chartists. These nations may be more concerned about the stability of the exchange rate than its actual level. Content to allow the market to choose the range within which its exchange rate trades, a government may adopt a stability policy of damping the exchange rate, intervening to prevent large short-term swings in what is viewed as a market-determined path. Although the motives of such a government would be much different from those of the speculating chartists, their market actions would be qualitatively the same.

Trend-smoothing policies are not the same as pegging rates or establishing a target zone. A nation may be content with the market pattern of systematic appreciation or depreciation of its currency but may still make a habit of intervening for stability’s sake whenever the exchange rate moves by more than a percent or so in a given period. The potential effect of sudden exchange rate changes on domestic financial markets is such that trend-smoothing policies could be used even by governments philosophically committed to market-based policies.

As you can now imagine, if chaos can be produced when chartists and fundamentalists interact, it can also result when reverse-fundamentalist states intervene in exchange markets along with trend-smoothing states. Chaos is probably even more likely when we put all four groups together. If this analysis holds, we are faced with the irony that nations seeking stability in domestic and international affairs could, through their dynamic interaction, add to the chaos of international financial markets.

Political business cycle dynamic effects. William Nordhaus introduced the idea of the political business cycle more than twenty years ago. ₃₆   This idea is based on the fact that economic well-being is an important factor in elections, especially national leadership elections. A leader or party is much more likely to be returned to power if the economy is growing than if it is not. Since politicians have at least some influence or control over economic policy, it is logical to suppose that they use it to improve reelection prospects. Thus, we have the political business cycle, timed to correspond with the incumbent’s term in office, “starting with relative austerity in early years and ending with the potlatch right before elections.” ₃₇

The political business cycle, superimposed over other cycles in the economy, may tend to dampen existing economic patterns, or it may exacerbate them. Or, as Kazuyuki Sasakura has suggested, the combination could produce a chaotic domestic economic pattern. ₃₈   Sasakura assumed that fiscal policy is influenced by pressure groups and that this pressure varies nonlinearly. First, the pre-election potlatch stimulus is assumed to be greater than the post-election austerity because of nonlinearities in the politics of fiscal policy. (For an elected official, it is better to give to voters than to take from them.) Second, the political pressure to stimulate the economy also varies nonlinearly. When national output is near the economy’s potential output, political pressure to stimulate spending and create jobs is small. As the output gap grows, political pressure grows stronger at an exponential rate. The pressure on fiscal policy is thus nonlinear and asymmetric and interacts with the underlying business cycle of the economy, with which it is not generally fully synchronized. (The period of business cycles in the United States, for example, is not obviously the four years of the presidential election cycle.)

Sasakura modeled this system under reasonable mathematical assumptions and discovered that chaotic output movements were possible. That is, the political business cycle can interact with the underlying business cycle to form patterns that are not explosively unstable but are still unpredictably chaotic. Interestingly, his model generates simulated chaotic patterns even when the political response to pressure groups, in terms of actual fiscal action, is relatively small. Sasakura found this result interesting in the particular but fascinating in terms of what it might mean for economics in general: “Economists believe that a stable economic system can be analyzed only linearizing it around the equilibrium. Then, is it not astonishing that chaos may emerge from such a stable system with a fairly small periodic external force?” ₃₉

Although Sasakura is content to keep his analysis on the level of domestic economic effects, it seems reasonable to speculate that chaotic output patterns by individual nations could also create chaotic patterns in international trade and finance linkages between and among nations. This may be especially true when nations experience political cycles of different types, periods, and magnitudes.

Asynchronous political business cycles. The political election cycles of major nations are not coordinated, and pressure group influence varies considerably. This alone might be enough to generate chaotic output patterns even if global markets were perfectly integrated, creating an underlying global business cycle. In fact, however, economic integration is incomplete, so nations experience business cycles of different types, periods, and magnitudes. These many business and political cycles flow into global markets. Here, we must seriously consider the possibility that chaos breeds chaos.

J-curve policy nonlinear feedback effects. Political economy chaos may be even more likely than Sasakura’s analysis suggests because of the possibility of nonlinear J-curve feedback effects. Indeed, chaotic domestic and international economic patterns are highly likely under these circumstances. Here is one scenario.

The high levels of public debt that many industrial countries have accumulated tend to limit the extent of fiscal policy responses to domestic political pressure. Suppose, however, that exchange rate policy is used instead to address domestic political-economic needs. That is, instead of fiscal expansion, a policy of currency depreciation is adopted to boost output and create jobs in the run-up to a national election.

National output does respond in most cases to currency depreciation, since a lower foreign exchange value makes exports cheaper to foreign buyers and increases the cost of imports at home. The domestic effect transmitted through the current account, however, displays the nonlinear pattern known as the J curve. In the short run, exchange rate changes affect prices before they affect output, so that the value of net exports actually falls, temporarily depressing national income. Imports are more expensive in terms of domestic currency, for example, but the quantity of imports purchased tends to be relatively sticky in the short run for a variety of reasons, such as the existence of long-term purchase agreements, uncertainty about future price and exchange rate behavior, and the costs of searching for equally reliable domestic suppliers. In the short run, then, it is possible that even more is spent on imports when the value of a currency falls, as the increased cost of each unit imported exceeds the effects of lower import quantities.

In the long run, however, contracts do run out, uncertainty diminishes, and search costs become economic. Decreased import quantities make up for higher import prices, and net exports increase, causing output, income, and employment to also rise. This creates the J-curve effect. Depreciation causes net exports to fall in the short run and then stabilize and eventually increase over time. All else being equal, the J-curve pattern of net exports is duplicated by national income.

The nonlinearity of the J-curve effect creates a potentially chaos-causing political business cycle dynamic. Pressure groups lobby for currency depreciation (and other policies to stimulate job creation) in response to the gap between current and potential output levels. Suppose that the pressure these groups exert is asymmetric and nonlinear, as was argued earlier. Now assume a J-curve effect, so that the response to currency depreciation is also asymmetric and nonlinear, which then feeds back into the pressure group equation.

Once again, the dynamic interaction contains all the elements we normally associate with chaos. Even more, however, in this scenario the international financial markets are directly affected and then feed back into the domestic political markets. Here, too, we have the well-known J-curve effect acting as a nonlinear element, making a chaotic pattern even more likely.

Turbulent vicious cycle effects. Finally, I’d like to suggest the possibility of turbulent vicious cycles. Assume that chartists and fundamentalists interact in ways that produce chaos or some weaker form of instability in foreign exchange rates. Now suppose that the very existence of exchange rate chaos creates enough instability in international economic interactions that states make the political decision to establish target zones for currencies. These target zones, as we saw in Chapter 4, are prone to speculative attacks that produce currency crises and the resulting huge swings in exchange values. These larger swings, I would argue, tend to draw even more chartists and fundamentalists into the market by increasing the sizes of speculative gains and losses. ₄₀   This effect in turn adds to chaos, causes greater policy efforts to stabilize, and thus produces more crises. The vicious cycle of chaos, crisis, and chaos continues, with both market actions and policy efforts increasing.

This discussion of political economy chaos has been more anecdotal than analytical. It has drawn on the qualitative properties of chaos as well as recent research to suggest that political factors affect international markets and, by their nature, tend to make chaos a more likely circumstance. But are foreign exchange markets chaotic? It is time to examine the evidence.

 

Evidence of Global Financial Chaos

My reading of the evidence about chaos in foreign exchange markets is that direct evidence of chaotic price movements exists but tends to be relatively narrow or weak; there are some technical reasons for this lack of robust evidence, which I will explain. On the other hand, various attempts to prove that foreign exchange rates are not chaotic are also unsuccessful. Despite many tries, it has been impossible to clearly refute the random walk hypothesis, which supposes that actual exchange rate movements are unpredictable. I do not believe that this is proof of chaos, but I do think it is evidence of chaos—enough evidence for me to take the chaos hypothesis seriously. ₄₁

Some of the evidence for chaotic exchange rate behavior is strong but narrow. One example is the findings of Ghashghaie and his colleagues as reported in Nature. The temporal cascading behavior they found for the dollar-deutschmark exchange rate from 1992–1993, based on almost one and a half million observations, is remarkable. But this evidence is narrow in three important ways. First, it is based on only a single exchange rate, which may not reflect behaviors in other markets. Second, it is based on a relatively narrow time frame, which by itself means that the observed behavior may not be typical of broader market patterns. Third, this particular period was one that might well be regarded as atypical in any case, since it includes parts of the EMS crisis discussed in Chapter 4. If you are looking for exchange rate turbulence, you are likely to find it during a currency crisis. So it would be better if we had the same sort of massive data bank and detailed analysis from some other more “normal” time period.

Thus, although I think it is fair to say that the dollar-deutschmark market was turbulent and presumably chaotic during 1992–1993, I am unwilling to draw broader conclusions based on this study alone. Broader analysis is needed.

De Grauwe, Dewachter, and Embrechts provided such evidence, but it is weak. They obtained daily exchange rate data for the period January 4, 1971, through December 30, 1990, for the deutschmark-dollar, pound sterling–dollar, and Japanese yen–dollar rates. Their study thus has the broad scope we are looking for, but there is a catch. Although for an economist this represents a fairly deep data pool, it is still not really enough. The empirical techniques for identifying chaos that have been developed by physicists require considerable data to ensure validity, perhaps twenty thousand observations. ₄₂   The lack of a data pool that is both broad and deep thus weakens the study, but this is a problem that is almost impossible to avoid in economics. That’s one reason why economics is so hard.

De Grauwe reported that “Our results are mixed. There are some indications for the occurrence of chaos in the yen/dollar and pound/dollar markets. We did not find evidence of chaotic behaviour in the mark/dollar market. Thus, although we find some evidence for chaos, it cannot be said that it is conclusive.” ₄₃   Their conclusions are reported in Table 5.2.

Table 5.2  Evidence of Chaotic Foreign Exchange Rates, 1971–1990
Currency	Period	Funding
Deutschmark-dollar Pound sterling–dollar Japanese yen–dollar	1971–1972 1971–1972 1971–1972	Inconclusive Speculative Chaotic
Deutschmark-dollar Pound sterling–dollar Japanese yen–dollar	1973–1981 1973–1981 1973–1981	Nonchaotic Chaotic Inconclusive
Deutschmark-dollar Pound sterling–dollar Japanese yen–dollar	1982–1990 1982–1990 1982–1990	Random walk Random walk Random walk
Deutschmark-dollar Pound sterling–dollar Japanese yen–dollar	1973–1990 1973–1990 1973–1990	Inconclusive Chaotic Possibly chaotic
Source: Paul De Grauwe, Hans Dewachter, and Mark Embrechts, Exchange Rate Theory: Chaotic Models of Foreign Exchange Markets (Oxford, UK: Blackwell Publishers, 1993), p. 217.

De Grauwe used these data to test for the existence of nonlinearities and found them strongly indicated in the daily and weekly variations in exchange rates: “The existence of nonlinearities in the exchange rate return does not prove that chaos exists. Other nonlinear structures than chaotic ones could be driving the exchange rate. However,... there are some theoretical reasons to believe that exchange rates can behave in a chaotic manner.” ₄₄   Although De Grauwe’s study is not “conclusive evidence” of chaos, it does give “credibility to the view that chaotic processes are important in the foreign exchange markets.” ₄₅

Although the analysis of chaotic movements in exchange rates is still in its infancy, economists have pretty thoroughly studied foreign exchange markets in testing the PPP (purchasing power parity) theory and the efficient markets hypothesis. These studies shed some indirect light on the question of exchange rate chaos.

The PPP theory is one of the most logical “fundamental” theories. It is an application of the law of one price across international borders with different currencies. If inflation in A causes its currency to purchase fewer traded goods such as wheat at home, then the law of one price argues that A’s currency should depreciate so that it also purchases less wheat abroad. If the currency fails to adjust in this way, then the price of wheat (in terms of A’s currency) is different at home and abroad and arbitrage profits exist, which induces behavior that drives prices and exchange rates back to parity. This process takes time and is complicated by the fact that the world has many currencies and many goods; however, the logic still holds.

In a recent survey of the PPP literature, Kenneth Rogoff commented that “While few empirically literate economists take PPP seriously as a short-term proposition, most instinctively believe in some variant of purchasing power parity as an anchor for long-run real exchange rates. Warm, fuzzy feelings about PPP are not, of course, a substitute for hard evidence.” ₄₆   The evidence about PPP that Rogoff reported, however, does little to reinforce warm fuzzy feelings.

Recent studies have shown that major exchange rates do tend to converge to their PPP levels in the long run but that the speed of convergence is very slow, only about 15 percent per year. This finding is in fact very encouraging for PPP theorists, since most past studies failed to find any PPP component in the long pattern of exchange rate movements, which could not be distinguished statistically from a random walk! Still, this leaves a puzzle, as Rogoff noted. Only a fraction of the variation in exchange rates can be explained by PPP factors. What accounts for the rest?

Another fundamental theory of exchange rates behavior is market efficiency (or the efficient markets hypothesis). Mark Taylor noted that “In an efficient speculative market, prices should fully reflect information available to market participants and it should be impossible for a trader to earn excess returns to speculation. Academic interest in foreign exchange market efficiency can be traced to arguments concerning the information content of financial market prices and the implications for social efficiency.” ₄₇

Exchange rates should adjust, therefore, to eliminate speculative profits as new information is absorbed and dissipated throughout the market. Some studies have found evidence of this tendency in the exchange rates of major currencies, but “Notwithstanding this, however, it remains true that time series for the major nominal exchange rates over the recent float are extremely hard to distinguish from random walks.” ₄₈

There is fairly strong evidence then, broad and deep, that even if exchange rate movements are not actually chaotic, neither do they follow the logical equilibrium patterns suggested by PPP or efficient markets theories, especially in the short run. It is difficult generally to dismiss the possibility that exchange rates are following a random walk.

Finally, we have De Grauwe’s simulations of the interactions of fundamentalists and chartists in a system that includes interest rate damping by monetary authorities. These simulations produce chaos under many circumstances and generate patterns of exchange rate movement that are qualitatively similar to real world conditions. These simulations, combined with the empirical evidence cited above, strengthen the case for currency chaos.

The studies that seek to find chaotic behavior in real world exchange rates are either deep but not broad or broad but not deep. In neither case can they provide proof, only indicators for further study. They do, however, add credibility to the case for periods of chaotic exchange rate movements. The simulations generate chaotic behavior that mimics actual foreign exchange movements on a qualitative, if not a quantitative, level. Thus, to reinforce this point, although proof of exchange rate chaos is illusive, I think the possibility of chaos needs to be taken seriously.

Currencies are subject to crises definitely, and to chaos probably, and they follow patterns that are at least random and perhaps turbulent. What are the consequences of these conclusions?

 

Globalization and Financial Chaos

Markets aren’t supposed to behave the way the foreign exchange markets behave. Markets are supposed to be flexible but stable. They should provide just the right foundation on which to build lasting structures in an age of rapid change.

Markets matter, economists believe, and their stability and flexibility are necessary to coordinate the actions of thousands of firms and millions of consumers. If markets are global, as is the current vogue, the stakes are higher: millions of firms, billions of workers and consumers, trillions of dollars. Our understanding of markets and their effects is fundamentally wrong if a thing so big, technologically advanced, and seemingly efficient as the foreign exchange market doesn’t work as it should.

One way to understand this is to assume that the financial markets really do work properly and that the problems actually lie elsewhere. For example, when the evidence shows that the foreign exchange market responds only minimally to the basic principle of the law of one price, as expressed in the PPP principle, you can keep faith in international financial markets by pointing an accusative finger at international trade. According to Mark Taylor,

One is left with a conclusion that would certainly make the godfather of purchasing power parity, Gustav Cassel, roll over in his grave. It is simply this: International goods markets, though becoming more integrated all the time, remain quite segmented, with large trading frictions across a broad range of goods. These frictions may be due to transportation costs, threatened tariff barriers, information costs, or lack of labor mobility. As a consequence of various adjustment costs, there is a large buffer within which exchange rates can move without producing an immediate proportional response in relative domestic prices. International goods markets are highly integrated, but not yet nearly as integrated as domestic goods markets. This is not an entirely comfortable conclusion, but for now there is no really satisfactory alternative explanation to the purchasing power parity puzzle. ₄₉

Taylor is right in thinking that global integration is incomplete and that tariffs and such are part of the problem. But is he correct in thinking that this is the whole problem? He sees a one-way relationship: Incomplete globalization causes exchange market errors. Isn’t it also possible for the arrow of causation to point the other direction? (Or both directions?) It seems even more likely that breakdowns in the financial markets are at the root of the problem and represent a built-in barrier to globalization.

Paul Krugman, ever the iconoclast, argued that the problem lies in international financial markets themselves:

This is a highly controversial (although of course correct) position. In questioning the reliability of international financial markets I am challenging both the cherished views of economists and the preconceptions of most lay observers. It is one thing to question the functioning of global markets for goods and services, which are not very different in appearance today from what they were in the past; however, most people imagine that—at least in the case of financial markets—borders either have disappeared or are about to. After all, computers and satellite transmission have created financial markets that almost never sleep and that can transfer billions of dollars across the world in seconds. Surely whatever imperfectness there is in the linkages between countries lies in the dull traditional world of freighters and longshoremen, not in the glittering world of international finance. ₅₀

I think that Krugman’s analysis is incomplete. In addition to the currency crises he sees, there is also built-in chaos, at least at times and perhaps as a persistent phenomenon. This matters greatly when we think about solutions, but not so much when the focus is on the consequences for global markets. Instability, chaotic or crisis-driven, has its own effects. Krugman argued that these effects are invisible to us because we have become used to them and because, in our thinking about global markets, we have been conditioned to ignore them. He writes that

Over the past few years, and especially since the dollar began declining, we have imperceptibly become accustomed to living in the world in which exchange rates move by huge amounts but the changes have only small effects on anything else . . . .

In fact, exchange-rate fluctuations of the size we have seen recently are possible only because they have so little effect. If changes in the relative cost of producing manufactured goods in different countries were quickly reflected in changes in the actual locations of production, large swings in the dollar would produce trade-balance changes that would themselves place limits on those swings. If exchange-rate changes were passed through rapidly into domestic prices, the kind of exchange-rate movements we have seen would either lead to massive differences in inflation... or would be met by non-accommodating monetary policy.... It is only because there seems to be some kind of delinking of exchange rates and the real economy that exchange rates can be as volatile as they have been. That is, exchange rates can move so much precisely because they seem to matter so little. ₅₁

Exchange rates matter so little because markets aren’t really global, except for a few exceptions. They are increasingly multilocal in nature. Exchange rate instability breaks down the logic of global economic activity (except in a few cases in which other factors are at work), and erects barriers to the spread of the single global market. Paradoxically, as attempts to expand global markets increase and more weight is attached to exchange rate movements, more chaos is released into financial markets, making exchange rates even less stable and further delinking exchange rates.

The bottom line of turbulence in international financial markets, therefore, is that we must thoroughly rethink globalization as the driving force of the era. Rather, we need to think seriously about the consequences of a world in which global financial markets present natural barriers to economic integration instead of smooth channels to it.

Reconsidering globalization is necessary, but it isn’t easy. The idea of globalization serves many interests that are threatened in one way or another by doubts about the efficient spread of worldwide markets. In the next two chapters I examine the intellectual and political stakes in the globalization debate.

 

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Endnotes

Note 1: José Ortega y Gasset, Meditations on Quixote, “Preliminary Meditation” (1914).  Back.

Note 2: I wrote this paragraph on December 19, 1996, during a period of such stability—or so thought the New York Times, which included an article on currency stability on its first business page of that date. The Times worried that stability would cost jobs in the parts of the finance industry that hedge against or speculate on volatile foreign exchange rates. In my view, the Times’s concern about stability was misplaced. Although currencies in the yen-dollar-mark groupings were relatively stable during the period in question, the Thai baht had recently experienced a major speculative attack. The rumors of the death of currency crises are premature, as the subsequent Asian currency crisis of 1997 has proved.  Back.

Note 3: James Gleick, Chaos: Making a New Science (New York: Viking, 1987).  Back.

Note 4: The play is Tom Stoppard, Arcadia (London: Faber and Faber, 1993).  Back.

Note 5: Stephen H. Kellert, In the Wake of Chaos (Chicago: University of Chicago Press, 1993), p. 2. Italics in the original.  Back.

Note 6: Alfredo Medio, Chaotic Dynamics: Theory and Applications to Economics (Cambridge, UK: Cambridge University Press, 1992), pp. 5-6.  Back.

Note 7: Stoppard, Arcadia, p. 5.  Back.

Note 8: Stoppard, Arcadia, pp. 4-5.  Back.

Note 9: The need to solve problems such as airflow turbulence was partly responsible for the development of both supercomputers and the formal analysis of nonlinear dynamics.  Back.

Note 10: Some of the funding for chaos research has come from the banking and financial industry in the hopes that chaos theory will prove able to unlock the mystery of seemingly random financial market movements and allow more profitable investment or speculation. So far, this hope has gone unfulfilled.  Back.

Note 11: Edward N. Lorenz, The Essence of Chaos (Seattle: University of Washington Press, 1993), pp. 118-119.  Back.

Note 12: Other important contributors include M. Feigenbaum, B. Mandlebrot, and D. Ruelle. (This list makes no attempt to be complete.)  Back.

Note 13: This paper was presented at the meetings of the American Association for the Advancement of Science in 1972 and is reprinted in Lorenz, The Essence of Chaos, pp. 181-184.  Back.

Note 14: “Prediction becomes impossible...” Quoted in Lorenz, The Essence of Chaos, p. 118.  Back.

Note 15: The works of David Ruelle and Steve Smale are notable here.  Back.

Note 16: Economics is also the only social science with mathematical and empirical frameworks adequate to even attempt the analysis of chaotic behavior.  Back.

Note 17: David Ruelle, Chance and Chaos (Princeton, NJ: Princeton University Press, 1991), p. 85.  Back.

Note 18: It seems to me that Heisenburg’s uncertainty principles also apply with special force to the social sciences.  Back.

Note 19: For a current list of working papers, send e-mail to wp@santafe.edu.  Back.

Note 20: A good example of early work that illustrates this point is William A. Brock, “Nonlinearity and Complex Dynamics in Economics and Finance,” in The Economy as an Evolving Complex System: Santa Fe Institute Studies in the Sciences of Complexity. Vol. 5, ed. P. W. Anderson, K. Arrow, and D. Pines (Redwood City, CA: Addison-Wesley, 1988), pp. 77-97.  Back.

Note 21: William J. Baumol and Jess Benhabib, “Chaos: Significance, Mechanism, and Economic Analysis,” Journal of Economic Perspectives 3:1 (winter 1989), p. 80.  Back.

Note 22: Ibid., p. 80.  Back.

Note 23: Ruelle, Chance and Chaos, pp. 84-85.  Back.

Note 24: Paul De Grauwe, Hans Dewachter, and Mark Embrechts, Exchange Rate Theory: Chaotic Models of Foreign Exchange Markets (Oxford, UK: Blackwell Publishers, 1993). De Grauwe is an economics professor at Katholieke Universiteit, Belgium, and a member of Belgium’s parliament. Embrechts is a professor of nuclear engineering and engineering physics. Dewachter works at the National Fund for Scientific Research Belgium at Katholieke Universiteit, Belgium. In this section, text references to De Grauwe will refer to the work of this team.  Back.

Note 25: See De Grauwe et al., Exchange Rate Theory, Chapter 5.  Back.

Note 26: Ibid., p. 138.  Back.

Note 27: In particular, the forward exchange rate is a biased estimator of the spot rate in De Grauwe’s simulations, just as it is in the real world.  Back.

Note 28: Very short-term (one period ahead) forecasting is possible, however.  Back.

Note 29: S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, and Y. Dodge, “Turbulent Cascades in Foreign Exchange Markets,” Nature 381 (27 June 1996), pp. 767-770.  Back.

Note 30: James Gleick, Chaos: Making a New Science (New York: Viking, 1987), p. 121.  Back.

Note 31: Ghashghaie et al., “Turbulent Cascades in Foreign Exchange Markets,” p. 768.  Back.

Note 32: Ibid., p. 769.  Back.

Note 33: Ibid., p. 769.  Back.

Note 34: One additional element not discussed here is the presence of speculators with market power who act strategically. I am thinking of hedge fund managers, such as George Soros, who played an important role in creating currency crises (see Chapter 4).  Back.

Note 35: See the discussion of Mexico in Chapter 4.  Back.

Note 36: William Nordhaus, “The Political Business Cycle,” Review of Economics Studies 43 (1975), pp. 169-190.  Back.

Note 37: Ibid., p. 187.  Back.

Note 38: Kazuyuki Sasakura, “Political Economics Chaos?” Journal of Behavior and Organization 27 (1995), pp. 213-221.  Back.

Note 39: Ibid., p. 220.  Back.

Note 40: This conclusion assumes that speculators weigh potential gains more heavily than potential losses in choosing to enter markets.  Back.

Note 41: If this standard of evidence seems low, and it is, I must say it is not untypical of the standards that economists and other social scientists often must apply.  Back.

Note 42: De Grauwe et al., Exchange Rate Theory, p. 216.  Back.

Note 43: Ibid., p. 242.  Back.

Note 44: Ibid., p. 242.  Back.

Note 45: Ibid., p. 255.  Back.

Note 46: Kenneth Rogoff, “The Purchasing Power Parity Puzzle,” Journal of Economic Literature 34 (June 1996), p. 647.  Back.

Note 47: Mark P. Taylor, “The Economics of Exchange Rates,” Journal of Economic Literature 32 (March 1995), p. 14.  Back.

Note 48: Ibid., p. 14  Back.

Note 49: Rogoff, “The Purchasing Power Parity Puzzle,” pp. 664-665.  Back.

Note 50: Paul Krugman, Exchange Rate Instability (Cambridge, MA: MIT Press, 1989), pp. 76-77.  Back.

Note 51: Ibid., pp. 39-40.  Back.