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The surprising message of the statistics of wealth distribution.
The academic researchers who study inequality are forever arguing about where that tipping point lies, and how much inequality is too much. Many observers wonder if we’ve begun to tip already, pointing to the surprisingly strong support enjoyed by the avowed socialist Bernie Sanders in the recent United States presidential election.
But what no one can deny is that in many countries around the globe, inequality has reached eye-popping extremes. In the U.S., for example, the top 1 percent of the population holds 42 percent of the national wealth. And the top 100 individuals now have an average wealth roughly 45,000 times the national average.
Where do such massive differences in wealth come from? The positive narrative surrounding inequality might chalk them up to the talent and effort of high earners. Social critics will also cite the many ways that talent and effort can be frustrated by prejudices based on class, race, or gender. Both sets of factors are obviously relevant—but mainly at the lower and middle levels of the wealth spectrum, where people’s standings are largely affected by salaries and consumption. They cannot possibly be the whole story at the high end, where people’s wealth is primarily determined by capital gains or losses on investments. If the ratio of 50,000 were to hold for other traits, it would imply individuals who are 53 miles tall, have IQs of 5 million points, and live to be 4 million years old. Nobody is that much better than the typical run of humanity.
Could the differences between the very rich and the hugely rich—the differences that amplify moderate inequality into extreme inequality—be the result of pure, dumb luck?
This turns out to be a very difficult question to answer just by looking at individuals. We all know stories of ambitious and talented people like Steve Jobs or Bill Gates, who grew companies and created great wealth. But for each one of these superstars, there may have been many more people who were equally ambitious and talented, yet did not succeed. Maybe the string of investment and managerial decisions that made one person’s company successful, and that seem so very wise in retrospect, were actually just the entrepreneurial equivalent of flipping a coin 20 times and getting all heads. The chances of that happening are about 1 in 1 million, so if enough people try it, someone is bound to get lucky and look like a coin-flipping genius—purely by chance.
The distribution of wealth at the highest end of the scale is quite consistent with pure luck.
However, that coin-flip analogy does suggest a better way to differentiate between talent and luck: Instead of looking at specific individuals, look at the way wealth is distributed over the whole population at the high end of the wealth spectrum.
To illustrate the basic idea, suppose that we are flipping coins and trying to figure out whether they are fair or biased. This is tricky with only a single coin. If we flip it 20 times and get 14 heads versus 6 tails, we might be a little suspicious that it’s biased. But we could not be completely sure: The chance of a fair coin yielding 14 heads or more is still about 6 percent, and unlikely events do sometimes come to pass. A much better approach would be to perform the same 20-flip experiment with thousands of identical coins: If we still see lots of them coming up with an overabundance of heads, then something is definitely fishy.
I have applied this idea to the world of investments and the distribution of wealth by imagining the following investment game.1 A large number of investors all start with $100,000. Every year, each investor flips a coin that determines his or her rate of return for that year: Half the time it will come up heads and yield a return of 30 percent, and on the rest of the tosses it will come up tails and yield a loss of 10 percent. The numbers are chosen to give an average annual return of 10 percent, plus or minus 20 percent, which is typical of investments in the real stock market, but the overall conclusions do not depend on these specific numbers.
After playing this game for 20 years, the typical investor will toss about 10 heads and 10 tails, ending up with something like $480,683. But a few lucky investors who happen to toss 20 heads in a row will have wealth of $19 million. Likewise, a few very unlucky investors will toss 20 tails and end up with only $12,158. As the game continues, however, individuals will rise and fall, growing richer or poorer according to the whim of the coin flips. To make the game more realistic, assume that if investors’ wealth declines below some level they have to drop out of the game, and are replaced by newly rich players emerging from the middle class. Eventually, the game will reach a kind of equilibrium—one in which the number of players going up is always balanced by the number going down, so that the overall distribution of wealth reaches a steady state and doesn’t change anymore…