The Future of Everything: The Science of Prediction

by David Orrell

  When the stock price crossed the four-figure barrier, the company directors, either spooked or sated, began to sell their shares. The price stabilized, then wobbled, then started to sink, as investors began to suspect they had been the victims of a giant scam. By the end of September, the price had collapsed to £135. As Jonathan Swift wrote:

  Subscribers here by thousands float

  And jostle one another down

  Each paddling in his leaky boat

  And here they fish for gold, and drown.2

  Parliament was recalled to discuss the crisis. The bishop of Rochester called the scheme a “pestilence,” while Lord Molesworth suggested that the perpetrators be tied in sacks and thrown into the Thames. Robert Walpole was more contained, arguing that there would be time later to punish those responsible. “If the city of London were on fire, all wise men would aid in extinguishing the flames, and preventing the spread of the conflagration before they inquired after the incendiaries,” he remarked.

  As they argued, the company treasurer Robert Knight put on a disguise, boarded a specially chartered boat, and slipped across the Channel to France. The former chancellor of the exchequer, John Aislabie, who was the company’s main advocate in the government, stayed to face the music and was escorted, Martha Stewart–fashion, to the Tower of London.

  As a response to the crisis, which had caused a record number of bankruptcies at every level of society, Parliament passed the Bubble Act in 1721. It forbade the founding of joint-stock companies without a royal charter—but it didn’t manage to ban bubbles, or the occasional “irrational exuberance” of investors (as Alan Greenspan later described it). When the NASDAQ soared to new heights at the turn of the millennium, how many of its listed companies were engaged in an “undertaking of great advantage, but nobody to know what it is”? And could a trained scientist have predicted such rises and falls? Isaac Newton, who lost a large part of his fortune in the South Sea bubble, didn’t think so. As he said in 1721, “I can calculate the motions of heavenly bodies, but not the madness of people.”

  Nonetheless, the gleaming skyscrapers of financial centres like London, New York, and Tokyo are full of professional prognosticators who make good money forecasting the future state of the economy. Is it therefore possible to build a dynamical model of the economy—a kind of global capital model—which is capable of forecasting economic storms? Given enough data and a large enough computer, can we predict the circulation of money just as we predict the orbit of Mars?

  MAKING DOUGH

  As Vilhem Bjerknes pointed out, the accuracy of a dynamical model depends on two things: the initial condition and the model itself. To know where the economy is going, we must first know its current state. In 1662, a London draper named John Graunt tried to do for his city what Tycho Brahe and other astronomers had done for the heavens: determine its population. His work Natural and Political Observations Made upon the Bills of Mortality compiled lists of births and deaths in London between 1604 and 1661. Many of the deaths were attributed either to lung disease, which Graunt associated with pollution from the burning of coal, or to outbreaks of the plague, like the one that forced the young Newton to leave Cambridge for the countryside.3

  Graunt’s book can be seen as the beginning of the fields of sampling and demographics. The aim of sampling is to obtain estimates using a limited amount of information. Graunt used birth records to infer the number of women of child-bearing age. He then extrapolated to the total population, obtaining an estimate of 384,000 souls.

  All measurements of the physical world contain a degree of uncertainty and error. To determine the average rainfall in a particular region, for example, we cannot count all the water that falls; instead, we’ll make use of a few randomly located rain-collection devices, each of which will give us a different reading. The average of these should be a good indicator of the region as a whole, provided the rainfall is reasonably uniform. When Tycho Brahe tried to measure the location of a distant star, this too was subject to error because of atmospheric distortions and because his measurements were done by eye. His sextant would give one answer one day, a slightly different answer the next. The “true” answer in such a situation is never known, so Tycho and other astronomers would take the average over different measurements. The sampling was done not over different stars, but over different measurement events.

  Similarly, when pollsters want to estimate the average yearly income for a certain area, they ask a relatively small sample of people. So long as those selected are representative of the population as a whole, their responses can be used to make a statistical prediction of the likely average.

  Given that all measurements are subject to uncertainty and error, how can we ever be sure that the answer we obtain is good enough? This question was addressed by mathematicians such as Jakob Bernoulli. Part of the famously talented Bernoulli clan, which was later studied by Galton as an example of inherited eminence, he imagined a jar containing a large number of white and black pebbles in a certain proportion to one another. We pull out one pebble, and it is black. The next is white. Then a black, and another black. Then three whites in a row. How many pebbles do we need to examine to make a good estimate of the true proportions? The answer was provided by Bernoulli’s law of large numbers, which showed that as more pebbles are sampled, their ratio will converge to the correct solution. In other words, sampling works for pebbles, so long as the sample is large enough.

  Bernoulli believed that this result could be generalized beyond pebbles. He wrote, “If, instead of the jar, for instance, we take the atmosphere or the human body, which conceal within themselves a multitude of the most varied processes or diseases, just as the jar conceals the pebbles, then for these also we shall be able to determine by observation how much more frequently one event will occur than another.”4 Until then, the laws of probability had been limited to games of chance, where the odds of holding a face card or rolling two sixes, could be computed exactly. Using the techniques of sampling, it seemed, scientists could make probabilistic estimates of anything they wanted.

  Sampling methods were put on a still firmer basis by de Moivre’s discovery of the bell curve, or normal distribution. His 1718 work, The Doctrine of Chances, which was dedicated to his London friend Isaac Newton, showed how, under certain conditions, a sample of random measurements will fall into the bell-shaped distribution, which peaks at the average value. As mentioned in the previous chapter, one of the most enthusiastic supporters of the normal distribution was Francis Galton, who described it as “the supreme law of Unreason” because events that appear random turn out to be governed by a simple mathematical rule.5 The mean (or average) and standard deviation of the curve can be used to determine the margin of error of a measurement or the expected range of a quantity based on a sample. Because mortality statistics tend to cluster according to a normal distribution, it was soon also used by insurance companies to determine life expectancies, and therefore to price annuities.

  Galton’s work on inheritance drew on the research of the Belgian scientist Lambert Quetelet, who in his 1835 Treatise on Man and the Development of his Faculties, turned normal into a kind of character: l’homme moyen, or the average man. He claimed that “the greater the number of people observed, the more do peculiarities, whether physical or moral, become effaced, and allow the general facts to predominate, by which society exists and is preserved.”6 Perhaps this inspired Galton to make his composite photographs of convicts’ faces. It also seemed to put the social sciences on a footing similar to that of the physical sciences, which had made great strides by realizing that it is not necessary to model each particle in detail. The temperature of a gas is a function of the average motion of its individual molecules, so in a way it’s a measure of the “average molecule.” Perhaps a crowd of people could be similarly described by one average person, which would certainly make analysis easier.

  Of course, while molecules of air are identical and don’t interact except by collidi
ng, the same is not true of people. As the economist André Orléan observed, our “beliefs, interpretations and justifications evolve and transform themselves continuously.”7 If someone knocks on your door, says she is doing a survey, and asks how much money you earn in a year, you may tell her to go away, participate but lie because you are concerned that she is a tax officer in disguise, or say what you think is the truth but be wrong. If she asks how you feel about the economy, the answer may reveal your own strongly held opinions, but equally it may reflect a discussion you had the previous night or something you saw on a recent TV show. It will also depend on the exact way the question is asked. Just as in physics there is an uncertainty principle that states that the presence of the observer affects the outcome of an experiment, there is a corresponding demographic principle that says any answer is subjective and is affected by the questioner, and even by the language used. This is why politicians spend so much time arguing over how questions should be worded in referendums. Even exit polls are prone to error, as we saw in the 2004 U.S. election, when exit polls at first had John Kerry winning over George Bush.

  In measuring the economy, about the only thing that can be counted on is money. An individual can count how much he earns; a company’s accountants can count how much it has produced; and a government’s accountants can count how much it has taxed. (Most societies undervalue things like trees because it is easy to calculate how much they’re worth when cut into pieces but much harder when they’re left intact. And trees don’t have accountants. This bias may change, to a degree, as economists try to invent costs for such “services.”8) Even counting money, however, is not straightforward. Governments constantly revise important data, such as unemployment figures and gross national product, and creative accounting techniques, like those used to value Internet companies in the 1990s, distort company accounts.

  WHAT’S IT WORTH?

  Demographics and accounting can give some insight into the current state of the economy, but to know where it is headed, we need to understand the dynamics of society, and in particular of money. Are there simple laws that underpin economics, like an analogue of Newton’s laws of motion for the movement of capital?

  Such laws would obviously depend on the idea of value. Just as air flows from areas of high pressure to areas of low pressure, money flows through the economy, seeking out investments that are undervalued. The English philosopher Jeremy Bentham associated value with an object’s utility—the property that brings benefit to the owner.9 His follower, the economist William Stanley Jevons, noted that the utility of an agricultural commodity such as wheat depends on the amount available, which in turn is closely linked to the weather. If a harvest is ruined by drought, then bakers and others compete for the scarce resource, driving up the price. Jevons, who also produced meteorological works (including the first scientific study of the climate of Australia), believed that the weather was affected by sunspots. He therefore developed a model of the boom/bust business cycle based on the sunspot cycle. His hope was that economics would become “a science as exact as many of the physical sciences; as exact, for instance, as meteorology is likely to be for a very long time to come.”10

  The desire to maximize utility is a kind of force that drives the economy. Again, though, there’s an important difference between utility and a physical property such as mass: the former is a dynamic quantity that for each person depends on her subjective expectations for the future. Financial transactions are based not just on present value but also on future value. In a market economy, where prices are not set by the state, future value is subject to a number of factors.

  First, the value of an asset depends on its prospects for future growth. You don’t spend the asking price on a house if you suspect that in five years’ time its value will be diminished. Similarly, assets such as stocks can be redeemed only if the seller finds a buyer, which can be tricky if the company’s market evaporates overnight.

  An asset’s valuation must also take into account its risk, which is related to its tendency to fluctuate. Suppose that instead of yeasts,figure 5.6 (see page 210) showed the historical returns from two assets, known as Regular and Mutant, over forty years. Since most people like to avoid unnecessary risk, if only so they can sleep at night, an asset that fluctuates greatly in price, like Mutant, is worth less than one that’s relatively stable. The volatility, usually denoted by σ, can be calculated from the standard deviation of the price fluctuations—assuming, of course, that these follow a normal distribution and the volatility does not change with time.

  Finally, the value of money will also change, because of inflation and interest rates. If a stock pays a dividend of one dollar in a year’s time, and if inflation is zero and interest rates are 3 percent, then the “present value” of that dividend is ninety-seven cents (that’s how much you’d have to invest to receive a dollar in a year’s time). In economics, time really is money.

  Calculating the present value of an asset is clearly a challenge. In the case of a stock, you have to estimate the company’s rate of growth, its volatility, any dividends, and the interest-rate environment— not just for now but into the future. Since none of these can be known by an investor who is less than clairvoyant, it means that the present value is at best a well-educated guess. Bonds at least pay you back, but only at some future date, by which time the value of money has changed. Even fixed interest-cash deposits are subject to the effects of inflation.

  Assets that have limited functional use and do not earn interest, such as gold or diamonds, are considered valuable in part because of their beauty but mostly because of their scarcity. Galileo wrote, in Dialogue Concerning the Two Chief World Systems, “What greater stupidity can be imagined than that of calling jewels, silver, and gold ‘precious,’ and earth and soil ‘base’? People who do this ought to remember that if there were as great a scarcity of soil as of jewels or precious metals, there would not be a prince who would not spend a bushel of diamonds and rubies and a cartload of gold just to have enough earth to plant a jasmine in a little pot, or to sow an orange seed and watch it sprout, grow, and produce its handsome leaves, its fragrant flowers, and fine fruit.”11 Adam Smith echoed him a century and a half later. “Nothing is more useful than water: but it will purchase scarce any thing; scarce any thing can be had in exchange for it,” he wrote. “A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it.”12 Since the perceived scarcity depends on demand, it too is subject to the whims of the market.Value is therefore not a solid, intrinsic property, but is a fluid quality that changes with circumstances. The value of a bar of gold is determined not by its weight but by what the gold market will bear. Value in the end is decided by people, in a social process that depends on complex relationships in the marketplace. It is subjective rather than objective, moving rather than fixed. Indeed, we often seem more sensitive to changes in price than to the price itself (just watch what happens whenever the cost of gas spikes).

  Because of this variability, it would seem that the economy could never reach equilibrium. Nonetheless, economists in the late nineteenth century reasoned that if the market were somehow to settle on a fixed price for each asset, which everyone agreed reflected its underlying “true” worth, then the future expectations of investors would align perfectly with the present. Furthermore, any small perturbation would be damped out by the negative feedback of Adam Smith’s invisible hand: the self-interest of “the butcher, the brewer, or the baker.” If the price of wheat was too high, then more producers would enter the market, driving the price back down. Fluctuations in prices would die out. Just as a molecule of gas has a known mass, every asset or object would have a fixed intrinsic value.

  Of course, there will always be a constant flow of external shocks, new pieces of information that impact prices. In 2004, for example, North American bakeries had to deal with record cocoa prices caused by violence in the Ivory Coast; a rise in
the cost per kilo for vanilla, owing in part to cyclones in Madagascar; high sugar prices caused by damage to crops in the Caribbean and the U.S.; expensive eggs because of avian flu; record oil prices, which affect transportation costs; and so on.13 All of these factors would affect a bakery’s bottom line, so the market would adjust its predictions about its performance. (Businesses often insulate themselves against such fluctuations by purchasing futures contracts, which allow them to obtain resources in the future at a fixed price.)

  These ideas were the foundations for the theory of competitive, or general, equilibrium. It assumed that individual players in the market have fixed preferences or tastes, act rationally to maximize their utility, can calculate utility correctly by looking into the future, and are highly competitive (so that negative feedback mechanisms correct any small perturbations to prices and drive them back into equilibrium). These assumptions meant that the economy could be modelled and predicted as if it were a complicated machine.

  PREDICTING THE PREDICTORS

  The equilibrium theory saw the homme moyen as a stable, tranquil, emotionally dead person, a mere cog in the machine who would be utterly predictable if it weren’t for the rest of the world, with its constant stream of random and disturbing news. Every time a news flash arrives, the homme moyen responds by fiddling the control knobs on his portfolio. He can always account for his actions later with a cause-and-effect explanation. Louis Bachelier, however, took the idea of randomness a step further. A doctoral student of Henri Poincaré, the discoverer of chaos, Bachelier chose as his thesis subject the chaos that took place at the Paris Exchange, or Bourse, a building modelled after a Greek temple. In his 1900 dissertation, he argued that new information is unpredictable— which is why we call it news—and so is the reaction of investors to that information.14