A Test of the Stable Paretian Hypothesis for the Distribution of Income

Mandelbrot has recently proposed that the distribution of income might be described by a class of mathematical processes called Stable Paretian functions. These functions have many of the desirable properties of Gaussian distributions but they have infinite variance, which has implications for making projections. Since Mandelbrot’s hypothesis applies only to very high income families, his ideas are of interest to the Army because children in high income families have a low propensity to enlist in the military, so an increasingly affluent population could have an effect on Army recruiting. This paper concludes that the distribution of income cannot be adequately described by either lognormal or Stable Paretian distributions. So, forecasters of the distribution of income do not need to deal with infinite variances, and may assume only that the underlying distributions are stationary.