THE dismal science is trying to brighten itself up with fashionable ideas from elsewhere. Economists are cautiously importing concepts from the new science of chaos and trying to apply them at home. This sounds an odd thing to do, but chaos is not what it used to be.
By "chaotic" behavior, scientists now mean patterns and events that are apparently random, but which are in fact causally determined (and so are sometimes confusingly called deterministically chaotic"). They are thus predictable, at least in theory. In practice, chaotic events are unpredictable, because they are "non-linear" effects of many causes. This means that minute changes in the causes can lead to surprisingly large changes in the effect. One well-worn example is the weather. The beating of a butterfly's wings could affect the future weather thousands of miles away. But it is clearly impossible to monitor each butterfly (or all the other determining factors), so the distant weather remains a surprise.
Astronomers, biologists and physicists use chaos theory to help explain how planets move, how populations grow and how fluids mix. Some economists now think that some of the things that appear partly random-such as exchange rates-may really be chaotically determined. And some of the things they would like to forecast with certainty-such as a firm's profit-may be forever unpredictable.
Much of the chaotic work in economics consists of constructing hypothetical models that produce chaotic behavior, and then seeing how closely these models fit reality. Consider an example from Dr William Baumol and Dr Jess Benhabib of New York University. Suppose a firm's profit depends on the amount of advertising it does. At first an increase in advertising raises profit. But eventually-when the cost of more advertising surpasses the extra revenue it brings in-this strategy will bring profit down. Thus the relationship between advertising and profit is nonlinear: a small change (such as just a bit more advertising) can have a surprisingly big effect. Finally, suppose the amount spent on advertising next year entirely depends on this year's profit.
Feed in such assumptions and this sort of model can do strange things. If the effect of advertising on profit is small, the firm makes little money the first year, does not advertise much in the second year, makes even less money that year, advertises still less, and so on until it makes no money at all. If the effect of advertising on profits exceeds a certain critical level, the annual profit starts to cycle, moving from, say, $100 to $200, back to $100 and so on. This is known as a two-period cycle. Increase the effect of advertising still more and the cycle will increase from two to four periods (eg, profits move from $100 to 10 to $75 to $25 to $100 and so on). This "period doubling" continues as the effect of advertising on profits is increased, until eventually the cycles become infinitely long and so the level of profit appears to vary randomly.
A recent and more sophisticated example of economic chaos was presented in London to the Centre for Economic Policy Research, by Dr Paul de Grauwe and Dr Kris Vansanten of the University of Leuven. They assumed that today's exchange rate will influence tomorrow's, because lots of currency dealers rely on past prices to predict the future. They then argued that exchange rates are also influenced by trade balances, because dealers will sell a country's currency when its trade deficit deteriorates. And the exchange rate itself, by affecting import and export prices, will also influence the trade balance. Finally they assumed that a fall in the exchange rate would at first worsen the trade balance, since import prices rise, but after a while it would improve it, as the volume of imports falls.
The model was fine-tuned until movements of the exchange rate became chaotic. Armed with the behavior of this hypothetical model, the authors concluded that exchange rates can move when there is no economic news, because they are adjusting slowly to events in the past. This makes short-term forecasts difficult. And attempts to forecast exchange rates in the long run must also break down, according to the model. A small change in the model used for forecasting, or in the information put into it, would radically change the predictions. This implies that small changes in government economic policy can have large effects on the exchange rate much later-and not necessarily the intended ones.
Such work shows how chaos could reign in an economy, not that it actually does so. Several economists, including Dr William Brock of the University of Wisconsin, have developed techniques for distinguishing between numbers that look random, but are determined by chaotic equations, and those which truly are random. This should reveal chaos, if it is there.
The commonest way to spot simple chaotic (ie, non-random) numbers uses graphs. With truly random data, the position of economic data-points on a graph should be unrelated. Take the example of the relationship between profit and advertising. Imagine plotting today's profit on the x-axis and next year's profit on the Y-axis. If today's profit is $140, and next year's is $220, you have one coordinate (140, 220). Do the same for all previous profit levels, and if the profits are truly random, there should be no discernible pattern. The co-ordinates should fall all over the graph. But with chaotic numbers a pattern will emerge. In the advertising example, all the co-ordinates will fall on a hill-shaped curve.
In practice, chaotic models might well be more complicated-advertising depends a bit on last year's profit, a bit on that of the year before and so on. So a statistician might plot this year's profit on the x-axis, last year's on the Y-axis, the year before's on the z-axis, (and so on, for as many dimensions as he likes, giving co-ordinates such as 140, 220, 80, 60). If the co-ordinates all fall in a pattern that can be expressed by a series of non-linear equations then deterministic chaos is present. If not, there is pure randomness.
There is a snag: chaos and genuine randomness are likely to go together. This is known as noisy chaos. This means that it is only possibly to say how likely it is that there is chaos, not that it definitely exists. Generally, the more coherent the pattern produced by the co-ordinates, the more likely there is to be chaos, and not just randomness.
So far the application of these techniques to stockmarket returns, variations in GDP and exchange rates has not revealed any significant chaotically deterministic patterns in the data. Indeed, if any obviously deterministic patterns were found, investors could use them to predict prices-and, as soon as they used chaotic models to buy and sell stocks, they would upset any deterministic relationships that their model had discovered.
Although there is so far no hard evidence of economic chaos, reading about it has made economists more open-minded about some things. They are receptive to the idea that small changes can feed on themselves and have large overall effects. And even if the mathematical elegance of chaos theory still eludes them, some of its implications still apply. Traditional models portrayed the economy as essentially stable, only fluctuating around some point of equilibrium because of external, random events. Many newer models are more sophisticated. The economy is seen as inherently variable, sensitive to changes in policy, and hard to control. To non-economists, this will not come as news.
Money and mayhem. (chaotic behavior in systems)THE dismal science is trying to brighten itself up with fashionable ideas from elsewhere. Economists are cautiously importing concepts from the new science of chaos and trying to apply them at home. This sounds an odd thing to do, but chaos is not what it used to be.
By "chaotic" behavior, scientists now mean patterns and events that are apparently random, but which are in fact causally determined (and so are sometimes confusingly called deterministically chaotic"). They are thus predictable, at least in theory. In practice, chaotic events are unpredictable, because they are "non-linear" effects of many causes. This means that minute changes in the causes can lead to surprisingly large changes in the effect. One well-worn example is the weather. The beating of a butterfly's wings could affect the future weather thousands of miles away. But it is clearly impossible to monitor each butterfly (or all the other determining factors), so the distant weather remains a surprise.
Astronomers, biologists and physicists use chaos theory to help explain how planets move, how populations grow and how fluids mix. Some economists now think that some of the things that appear partly random-such as exchange rates-may really be chaotically determined. And some of the things they would like to forecast with certainty-such as a firm's profit-may be forever unpredictable.
Much of the chaotic work in economics consists of constructing hypothetical models that produce chaotic behavior, and then seeing how closely these models fit reality. Consider an example from Dr William Baumol and Dr Jess Benhabib of New York University. Suppose a firm's profit depends on the amount of advertising it does. At first an increase in advertising raises profit. But eventually-when the cost of more advertising surpasses the extra revenue it brings in-this strategy will bring profit down. Thus the relationship between advertising and profit is nonlinear: a small change (such as just a bit more advertising) can have a surprisingly big effect. Finally, suppose the amount spent on advertising next year entirely depends on this year's profit.
Feed in such assumptions and this sort of model can do strange things. If the effect of advertising on profit is small, the firm makes little money the first year, does not advertise much in the second year, makes even less money that year, advertises still less, and so on until it makes no money at all. If the effect of advertising on profits exceeds a certain critical level, the annual profit starts to cycle, moving from, say, $100 to $200, back to $100 and so on. This is known as a two-period cycle. Increase the effect of advertising still more and the cycle will increase from two to four periods (eg, profits move from $100 to 10 to $75 to $25 to $100 and so on). This "period doubling" continues as the effect of advertising on profits is increased, until eventually the cycles become infinitely long and so the level of profit appears to vary randomly.
A recent and more sophisticated example of economic chaos was presented in London to the Centre for Economic Policy Research, by Dr Paul de Grauwe and Dr Kris Vansanten of the University of Leuven. They assumed that today's exchange rate will influence tomorrow's, because lots of currency dealers rely on past prices to predict the future. They then argued that exchange rates are also influenced by trade balances, because dealers will sell a country's currency when its trade deficit deteriorates. And the exchange rate itself, by affecting import and export prices, will also influence the trade balance. Finally they assumed that a fall in the exchange rate would at first worsen the trade balance, since import prices rise, but after a while it would improve it, as the volume of imports falls.
The model was fine-tuned until movements of the exchange rate became chaotic. Armed with the behavior of this hypothetical model, the authors concluded that exchange rates can move when there is no economic news, because they are adjusting slowly to events in the past. This makes short-term forecasts difficult. And attempts to forecast exchange rates in the long run must also break down, according to the model. A small change in the model used for forecasting, or in the information put into it, would radically change the predictions. This implies that small changes in government economic policy can have large effects on the exchange rate much later-and not necessarily the intended ones.
Such work shows how chaos could reign in an economy, not that it actually does so. Several economists, including Dr William Brock of the University of Wisconsin, have developed techniques for distinguishing between numbers that look random, but are determined by chaotic equations, and those which truly are random. This should reveal chaos, if it is there.
The commonest way to spot simple chaotic (ie, non-random) numbers uses graphs. With truly random data, the position of economic data-points on a graph should be unrelated. Take the example of the relationship between profit and advertising. Imagine plotting today's profit on the x-axis and next year's profit on the Y-axis. If today's profit is $140, and next year's is $220, you have one coordinate (140, 220). Do the same for all previous profit levels, and if the profits are truly random, there should be no discernible pattern. The co-ordinates should fall all over the graph. But with chaotic numbers a pattern will emerge. In the advertising example, all the co-ordinates will fall on a hill-shaped curve.
In practice, chaotic models might well be more complicated-advertising depends a bit on last year's profit, a bit on that of the year before and so on. So a statistician might plot this year's profit on the x-axis, last year's on the Y-axis, the year before's on the z-axis, (and so on, for as many dimensions as he likes, giving co-ordinates such as 140, 220, 80, 60). If the co-ordinates all fall in a pattern that can be expressed by a series of non-linear equations then deterministic chaos is present. If not, there is pure randomness.
There is a snag: chaos and genuine randomness are likely to go together. This is known as noisy chaos. This means that it is only possibly to say how likely it is that there is chaos, not that it definitely exists. Generally, the more coherent the pattern produced by the co-ordinates, the more likely there is to be chaos, and not just randomness.
So far the application of these techniques to stockmarket returns, variations in GDP and exchange rates has not revealed any significant chaotically deterministic patterns in the data. Indeed, if any obviously deterministic patterns were found, investors could use them to predict prices-and, as soon as they used chaotic models to buy and sell stocks, they would upset any deterministic relationships that their model had discovered.
Although there is so far no hard evidence of economic chaos, reading about it has made economists more open-minded about some things. They are receptive to the idea that small changes can feed on themselves and have large overall effects. And even if the mathematical elegance of chaos theory still eludes them, some of its implications still apply. Traditional models portrayed the economy as essentially stable, only fluctuating around some point of equilibrium because of external, random events. Many newer models are more sophisticated. The economy is seen as inherently variable, sensitive to changes in policy, and hard to control. To non-economists, this will not come as news.
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