ABSTRACT
How can one account for the observed shape of income distributions? In practice, a very complicated stochastic process is involved. The set of, say, all U.S. incomes in 1979 will be a random perturbation of the set of incomes in 1978. Some new individuals will have entered the market, some will have left. Those present in both years will typically have different incomes. The myriad contributory causes of these changes in the income-earning population and in the incomes of individuals defy enumeration. If a tractable model is to be obtained, it must necessarily ignore most of the possible causative agents and (over-) simplify the manner in which the remaining ones affect the income distribution. Similar observations apply to wealth distributions. We will chiefly speak of income distributions, but many of the models obtained apply, not surprisingly, almost as well to wealth distributions. The invariably heavy-tailed nature of income and wealth distributions was a matter of observational common knowledge in the nineteenth century. Pareto’s two models (1.2.1, 1.2.2) constitute, essentially, selection of parametric families of distributions which seem to fit the upper tails of the observed distribution in a satisfactory manner. Their law-like statement and their remarkable resilience to matters such as how we measure wealth, what population we use, etc., have certainly affected subsequent modeling efforts. Models which lead to Paretian tail behavior have been popular and reasonable in the light of observational studies. Pareto’s suggested laws will not be included in our list of models. In the final section of this chapter we will list several families of distributions which have been proposed as candidates for fitting or graduating income distributions, usually with little indication as to why the fit should be good. The two Pareto laws will appear in this list. The title, “model,” in this chapter, will be reserved for stochastic mechanisms which mirror, to some extent, socio-economic forces which affect income and which lead to delineation of at least some properties of resulting income distributions. The line is not always easy to draw. Authors frequently supply post-hoc economic interpretations of their parameters. If they had written their paper the other way around, maybe they could have qualified as “models.” Gibrat will be included in the list of modelers, although his law of proportional effect is, perhaps, more of an axiom than a model. He does provide a convenient starting point.
