This paper presents findings from a census of more than 79,000 stock-keeping units (SKUs) in 37 consumer packaged goods categories totaling $55 billion in annual revenue. It shows that, in 86% of product categories, the relationship between market share and retail distribution is increasing and...

The rise of the super-rich has attracted much political and academic attention in recent years. However, to date there have been few attempts to explain the cross-national variation in the recent rise of very top incomes. Drawing on the World Top Incomes Database, we study the income share of...

We describe a simple method to obtain kindred stationary densities of random Markov processes with respect to an Ito transformation function. As applied to income and wealth densities, they are akin to one another because they share the income growth and income volatility shape parameters. The...

Aphorisms that "Rising tides raise all boats" or that material advances of the rich eventually "Trickle Down" to the poor are really maxims regarding the nature of stochastic processes that underlay the income/wellbeing paths of groups of individuals. This paper looks at the implications for the...

To illustrate that the mathematical form of P. K. Clark's distribution of lognormal-normal increments, with a minor bug fix, is the same as the symmetric lognormal cascade distribution that I studied in 2008-9, although the two were derived from very different stochastic assumptions

This paper examines the long-run trends in per-capita income across the US states (1929-2005). Our analysis advocates and implements a Vector Error Correction Model (VECM), in order to investigate whether disparities in per-capita income embody a stable long-run relation. The empirical...