Notes on Thick-Tailed Distributions of Wealth

One of the best-known empirical regularities in economics is the 'Law of Pareto', according to which the upper tails of the distributions of income and wealth are described by the relationship, , for income and wealth levels (x) greater than some value x0 and ? < 2. However, despite its ubiquity across economies and time, the matter of why this 'law' holds remains an open question. Is there, as Mandelbrot has suggested, simply a base "prime mover" that gives rise to scalable distributions, not only for income and wealth, but also to a large number of other economic, social, and natural phenomena? If so, then the question of "why" is, by definition, not answerable. On the other hand, if thick upper tails can somehow emerge through processes that do not assume a Pareto prime mover, then the question is not only potentially answerable, but is also of a great deal of interest. Examining the possibility of this is the purpose of the present notes. Three scenarios involving highly stylized, artificial economies (all of which can be given a Darwinian interpretation) are simulated under varying assumptions regarding heritability, distribution of talents, and stability of tastes. Simulations with the first two scenarios make it pretty clear that talent differentials and pure randomness of tastes cannot suffice to produce wealth distributions with sufficient thickness to be interesting. However, things change in the third scenario, in which there is an allowance for preference stability, in the sense that once an agent experiences a good, that good is consumed with a non-zero probability in subsequent periods (so long, of course, as the agent remains "alive"). What the results with the third scenario show is that, with strong preference stability and substantial productivity differences amongst agents, thick-tailed distributions of wealth can emerge that have certain Pareto features and are log-log translatable.

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