Abstract
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
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Notes
- 1.
I am grateful to Teodosio Perez-Amaral and Barbara Sands for comments on this chapter and to the Cardon Chair Endowment in the Department of Agricultural and Resource Economics at the University of Arizona for financial assistance.
- 2.
Simulations (on a standard PC with Pentium III chip) for 10 periods for Section 21.3.1 take about 8 min for 5,000 agents and 40 min for 10,000 agents. For Section 21.3.3, the time required is about 10 min for 1,000 agents, an hour for 5,000 agents, and more than 10 h for 10,000 agents. All coding and simulations have been done in SAS.
- 3.
So striking, in fact, that it is useful to report a variation on the parameters in column (8), in which z and q are kept at 4 and 1, respectively, but pz is reduced to 0.2. The result (for the simulation undertaken) is an increase in P(0) to 0.423, and a reduction in P(≥10) to 0.172. The point to note is that the latter remains high in relation to simulations in which q is less than 1.
- 4.
The graphs in these figures are for different realizations than those shown in Table 21.6. In the captions of the figures, npds refers to the number of periods in the simulations. Graphs have been constructed in Excel.
- 5.
If a period is interpreted as a year, then periods of 2–400 should represent a plausible length of “history” for the distribution of wealth to reach an asymptotic form. The small size of the economy (1,000 agents) is not thought to be a problem because of the results presented in 21.4, which show the distribution to be reasonably independent of the number of agents.
- 6.
The point of this exercise is that, as discussed by Mandelbrot in his 1963 JPE paper, an implication of a distribution with an infinite variance is for sample variances to behave erratically as a function of increasing sample size, with no tendency to reach an asymptote.
- 7.
Also, as has been suggested to me by Barbara Sands, another interesting exercise would be to eliminate the restriction that agents with negative wealth are removed the instant that their wealth turns negative. Allowing them to continue living, at least for a few periods, might give rise to the “lower hump” that is characteristic of real-world income and wealth distributions.
- 8.
See Chapters 5 and 20.
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Taylor, L.D. (2010). Notes on Thick-Tailed Distributions of Wealth. In: Consumer Demand in the United States. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0510-9_21
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DOI: https://doi.org/10.1007/978-1-4419-0510-9_21
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