Is the basic inequality in wealth distribution repeated in country after country the result of the talentsor lack thereofof a country's citizens? Not according to a new study. According to this excerpt from a Harvard Business Review article, the disparity "appears to be something akin to a law of economic life that emerges naturally as an organizational feature of a network."

by Mark Buchanan

The economic world is full of patterns, many of which exert a profound influence over society and business. One of the most controversial is the distribution of wealth. You might expect the balance between the rich and the poor to vary widely from country to country. Different nations, after all, have different resources and produce different kinds of products. Some rely on agriculture, others on heavy industry, still others on high technology. And their peoples have different backgrounds, skills, and levels of education. But in 1897, an Italian engineer-turned-economist named Vilfredo Pareto discovered a pattern in the distribution of wealth that appears to be every bit as universal as the laws of thermodynamics or chemistry.

Suppose that in the United States or Cuba or Thailandor any other country for that matteryou count the number of people worth, say, $10,000. Then you count the number of people at many other levels of wealth, both large and small, and you plot the results on a graph. You would find, as Pareto did, many individuals at the lowest end of the scale and fewer and fewer as you progress along the graph toward higher levels of wealth. But when Pareto studied the numbers more closely, he discovered that they dwindled in a very special way toward the wealthy end of the curve: Each time you double the amount of wealth, the number of people falls by a constant factor. The factor varies from country to country, but the pattern remains essentially the same.

Pareto's distribution has, from a mathematical standpoint, stubbornly defied explanation.  Mark Buchanan

Unlike a standard bell curve distribution, in which great deviations from the average are very rare, Pareto's so-called fat-tailed distribution starts very high at the low end, has no bulge in the middle at all, and falls off relatively slowly at the high end, indicating that some number of extremely wealthy people hold the lion's share of a country's riches. In the United States, for example, something like 80% of the wealth is held by only 20% of the people. But this particular 80-20 split is not really the point; in some other country, the precise numbers might be 90-20 or 95-10 or something else. The important point is that the distribution (at the wealthy end, at least) follows a strikingly simple mathematical curve illustrating that a small fraction of people always owns a large fraction of the wealth.

What causes this pattern? Is there some kind of regularity in human behavior or culture that supersedes national variations? Is there some devilish conspiracy among the rich? Not surprisingly, given the strong emotions stirred by matters of wealth and its disparity, economists have flocked to such questions. Of the central issues in economics, John Kenneth Galbraith wrote in his History of Economics, the first is "how equitable or inequitable is the income distribution. The explanation and rationalization of the resulting inequality has commanded some of the greatest, or in any case some of the most ingenious, talent in the economics profession." Despite all the attention, however, Pareto's distribution has, from a mathematical standpoint, stubbornly defied explanation.

Finding out why one individual is richer than another is, of course, relatively straightforward. One has only to delve into the details of inheritance and education, inherent ability and desire to make money, circumstance, and plain old luck. The sons or daughters of doctors or bankers frequently become doctors or bankers themselves, while children born into inner-city poverty often remain mired in hardship, unable to escape their environment. But Pareto's distribution isn't about individuals. It captures a pattern that emerges at the level of large groups, leaving individual histories aside. It is, it might be posited, a network effect.

As scientists have discovered, many of the overarching organizational features of networks depend only weakly or not at all on the actions or character of their individual members. Physicists, to take just one example, have long known that, in some cases, they can build strikingly accurate models of complex molecular systems using only a few very crude assumptions. It turns out that the details of individual atoms have little influence over the behavior of the entire network. In principle, the same might be true of wealth. Perhaps Pareto's distribution reflects less about people and their characteristics than it does about the deeper, impersonal laws of network organization.

Webs of wealth

To find out, let's forget for the moment about creativity and risk taking, the distribution of intelligence, and all the other factors that might influence an individual's destiny. Instead, let's focus on the flow of wealth in an economy. Think of an economy as a network of interacting people. At any given time, each person has a certain amount of wealth, and over the days and weeks, that amount will change in one of two fundamental ways. Your employer pays you for your work; you sell your car; you build a patio; you take a vacation in Italy. Such transactions transfer wealth from one person to another along the links in the network. But suppose you purchase a house or a piece of land, and, sadly, its value falls. Or you invest in stocks and, as in the 1990s, the market soars, showering on you a pile of totally new wealth. In such cases, wealth is not merely transferred but actually created or destroyed. Very basically, then, a person's wealth can go up or down either through transactions with others or by earning returns (positive or negative) on investments.

This is hardly news, of course, but it implies that two factors control the basic dynamics in the web of wealth. As people earn salaries, pay rent, buy food, and so on, wealth should flow through the network in a more or less regular way, like water through a network of pipes. Meanwhile, owing to investments, overall wealth should generally increase slowly, even as individuals' wealth randomly kicks up or down as their investments go particularly well or especially poorly.

The finding suggests that the basic inequality in wealth distribution seen in most societies may have little to do with differences in the backgrounds and talents of their citizens.  Mark Buchanan

Obviously, this picture leaves out almost every detail of reality except the most basic. And yet it is intriguing to wonder if these two simple factors might imply something about how wealth ends up being distributed. A couple of years ago, physicists Jean-Philippe Bouchaud and Marc Mézard of the University of Paris took a large step toward answering this question by bringing into the picture one other "obvious" factthat the value of wealth is relative. A multimillionaire, for example, will not ordinarily sweat losing a few thousand dollars in the stock market, but the same loss would likely be catastrophic for a single parent trying to raise her son while putting herself through college. The value of money depends on how much one already has, and consequently wealthy people tend to invest more than the less wealthy.

With these commonplace observations, Bouchaud and Mézard formulated a set of equations that could follow wealth as it shifts from person to person, as each person receives random gains or losses from his investments, and as those who accumulate more wealth invest relatively more. Equations in hand for a network of 1,000 people, the two physicists set to work with a computer to create an economic model. Not knowing precisely how to link people together into a network of transactions, they tried various alternatives. Unsure of how precisely to set the balance between interpersonal transactions and investment returns, they tried shifting it first one way and then the other. But no matter what they did, the model always produced the same basic shape of wealth distributionprecisely the same shape as Pareto's distribution. This happened even when every person in the model started out with exactly the same amount of money. And it happened when every person was endowed with identical money-making skills.

The finding suggests that the basic inequality in wealth distribution seen in most societies may have little to do with differences in the backgrounds and talents of their citizens. Rather, the disparity appears to be something akin to a law of economic life that emerges naturally as an organizational feature of a network.

Shades of inequality

Bouchaud and Mézard's discovery suggests that the temptation to find complex explanations behind the distribution of wealth may be seriously misguided. What makes wealth fall into the pockets of a few appears to be quite simple. On the one hand, transactions between people tend to spread wealth around. If one person becomes dramatically wealthy, she may start a business, build a house, and consume more products, and in each case wealth will tend to flow out to others in the network. Conversely, if a person becomes terribly poor, he will tend to purchase fewer products, and less wealth will flow through links going away from him. Overall, the flow of funds along links in the network should act to wash away wealth disparities.

But it seems that this washing out effect never manages to gain the upper hand, for the random returns on investment drive a counterbalancing rich-get-richer phenomenon. Even if everyone starts out equal, differences in investment luck will cause some people to start to accumulate more wealth than others. Those who are lucky will tend to invest more and so have a chance to make greater gains still. Hence, a string of positive returns builds a person's wealth not merely by addition but by multiplication, as each subsequent gain grows ever bigger. This is enough, even in a world of equals where returns on investment are entirely random, to stir up huge wealth disparities in the population.

That doesn't mean that inequities in wealth can't be mitigated. In a Pareto distribution, the factor by which the number of people declines as wealth increases remains constant in any particular country, but the factor itself is different in different countries. So, while there is always a disparity between the rich and the poor, there are differences in degree from country to country. And, socially speaking, there's a world of difference between an 80-20 distribution and 90-5.

Bouchaud and Mézard's network model can track those degrees of inequality and show how Pareto's distribution can be influenced. Specifically, the two researchers found that the greater the volume of money flowing through the economy and the more often it changes hands, the greater the equality. Conversely, the more volatile investment returns are, the richer the rich tend to get.