The Rich Really Do Get Richer!

Antoun Nabhan anabhan@attglobal.net
Mon, 29 Apr 2002 16:28:24 -0700


Well, we all knew that it was easiest to make money once you already had a 
fair bit. What's interesting is that, according to this model, the 
distribution of wealth doesn't really depend on whether "all men are 
created equal" with respect to their wealth-generating ability.

<http://hbswk.hbs.edu/pubitem.jhtml?id=2906&sid=0&pid=0&t=finance>

Wealth Distribution and the Role of Networks
HBSWK Pub. Date: Apr 29, 2002


It's an old question still in search of an answer. Why does inequality in 
wealth distribution repeat itself so consistently from country to country? 
New research suggests that network effects may be more in play here than 
the backgrounds and talents of citizens. It also suggests we may reach a 
tipping point where just a few citizens control most of the wealth. Should 
public policy play a role?


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.

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.

· · · ·

Excerpted with permission from "Wealth Happens," Harvard Business Review, 
Vol. 80, No. 4, April 2002.

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