I’m starting to see a lot more references in research to the economist Vilfredo Pareto. He’s noteworthy for a great number of things, but his 2016 resurgence seems to be due mainly to his (still) accurate mathematical description, in 1909, of the way wealth and income are distributed in society. This topic is of course once again a hot button political issue, but also as central banks endeavor to counteract structurally slowing growth, the impact of wealth and income inequality on economic performance is also now a focus. By varying a single assumption, Pareto’s distribution can illustrate broad degrees of inequality, from complete parity at one extreme, to complete concentration at the other, where one theoretical individual holds 100% of society’s income or wealth. It’s especially good at depicting very top-heavy income stratification. The existence of this mathematical tool allows for measurement of the degree of inequality observed in actual data, the trends therein, and an ability to model how inequality affects economic growth. The results can be striking, as illustrated by the punchy title of a recent academic paper on this topic: “When does inequality freeze an economy?”
One mathematical characteristic of Pareto-distributed income is that once inequality is sufficiently high, it’s possible to increase the mean individual income in an economy while actually decreasing the median individual income. Since GDP is just the sum of an economy’s total income, growth in mean income will result in growth in GDP. However, if median income is shrinking at the same time, the prosperity and standard of living for a majority of individuals will still be declining. This is occurring in the United States. Economists broadly understand that while US GDP has been generally increasing in real terms over the past decade (and by extension, average real income), the median real income has been consistently declining. The resurgence of mathematical focus on the specific properties of the Pareto distribution suggest that this decline may be structural, in that the current magnitude of income inequality is now sufficient to perpetuate a declining real median income in the current policy framework, even as GDP grows.
Secondly, the five researchers who authored the recent paper with the eye-catching title seem to have successfully modeled the evolution of an economy whose wealth is distributed in Pareto fashion. In case you doubted that the rich get richer and the poor get poorer, their results lend analytical weight to that view. The analysis constructs a model economy with a large number of individuals, assigning each a certain amount of wealth and cash holdings according to a Pareto distribution, and simulates the agents engaging in random trading of a set of durable goods with a range of prices. Any transaction that is affordable at the individual level occurs, and those that are unaffordable do not. Three outcomes precipitate: 1) cash tends to migrate – through many, many transactions – toward the economic agents who began the simulation with higher wealth, 2) inequality intensifies, and 3) economic activity slows as wealth inequality increases. The policy implications are stark: injecting cash into economic agents who are already capital-rich, say, via a policy which purchases bonds from bank balance sheets, would not stimulate economic activity. Rather, cash transfers to those who are capital-poor would be most stimulative, and even that would still result in increased inequality over time, notwithstanding a temporary lift to living standards.
The implications of these outcomes appear to add yet another structural headwind to real global growth that monetary policy cannot fix (at least not in an obvious way). Lackluster growth in our working age population, increasing childcare costs restraining labor participation, and increasing old-age dependency ratios are slowing our potential growth rates all over the world, and monetary policymakers are powerless to change these facts. If the extent of our income inequality is now high enough that mathematically what growth there is accrues to the top, and the inequality-driven impulse to growth is negative, that is an unwelcome conclusion indeed.
 Jerico, Joao Pedro; Landes, Francois P.; Marsili, Matteo; Castillo, Isaac Perez; and Volatpi, Valerio. When does inequality freeze an economy? arXiv:1602.07300v2. http://arxiv.org/pdf/1602.07300v2.pdf