By Josep Colomer.
Thomas Piketty’s best-selling Capital in the Twenty-First Century is rich and innovative in data, although the author’s management of some sources is now being discussed. Another matter is that his findings could be illuminated by previous work that he may have overlooked. Some light could possibly be cast over the issue of wealth distribution, for instance, from the tradition of literature on “rank-size distributions”. According to the so-called “Zipf’s law” (for the American linguist George K. Zipf, who popularized the idea in the 1940s), remarkable regularities can be observed in the distribution of disparate resources, whether population in cities, frequency of word usage –and also wealth among individuals and groups, which is Piketty’s topic.
Zipf’s basic formula is:
Sk = S1/ks
which means that the size of the k-th unit in rank equals the size of the first unit divided by k (raised to power s). A simplified formula makes s=1, which would mean that in a population divided in groups of equal number of individuals the share of wealth in the hands of the second wealthiest group would be half the first, the share of the third group would be one third of the first, and so on. The higher the value of s, the more unequal the distribution; the formula can, thus, be adjusted for empirical data in order to fit the basic values and confirm (or not) a regularity.
Let’s assume that a certain population can be divided in ten deciles. Zipf’s cumulative distribution looks like the Figure above. The data presented by Piketty would fit the cumulative distribution derived from s=2 rather well. This means that the top 10 percent of the population would accumulate about 62 percent of total wealth. But even more interesting is that the top 20 percent would get about 81 percent.
The latter values are extremely close to those postulated by Italian economist Vilfredo Pareto, who observed in early 20th century that 20 percent of the population owned 80 percent of the land in Italy (and viceversa, of course: the remaining 80 percent of the population owned 20 percent of the land). Pareto’s “80:20 law”, which could be considered, in retrospect, a case of Zipf’s law, has been used to understand many phenomena. [For instance, as a personal aside, in working with a research team I noted that we had written 80 percent of a paper in a certain, relatively brief amount of time, but that to complete the remaining 20 percent (which required an apparently minor effort at searching for a few new data, filling gaps, drawing Tables and Figures, footnoting, referencing, and above all, solving a few disagreements) was taking much longer].
Piketty’s main point is that the distribution of wealth in a few most developed countries has become more unequal in the last twenty years. But his data show that it’s still significantly less unequal than it was one hundred years ago, when Pareto presented his findings on the distribution of income and wealth among the population. Piketty does not mention Zipf and discusses only the so-called Pareto’s coefficients to compare the income of different fractions of the population, but he doesn’t mention the 80:20 law.
