Measures of physical mixing evaluate the economic mobility of the typical individual

Abstract

Measures of economic mobility represent aggregate values for how individual wealth changes over time. As such, these measures may not describe the feasibility of a typical individual to change their wealth. To address this limitation, we introduce mixing, a concept from statistical physics, as a relevant phenomenon for quantifying how individuals move across the wealth distribution. We display the relationship between mixing and mobility both theoretically and using data. By studying the properties of an established model of wealth dynamics, we show that some individuals can move across the distribution when wealth is a non-mixing observable. Only in the mixing case every individual is able to move across the whole wealth distribution. There is also a direct equivalence between measures of mixing and the magnitude of the standard measures of economic mobility, but the opposite is not true. We then describe an empirical method for estimating the mixing properties of wealth dynamics in practice. We use this method to present a pedagogical application using the USA longitudinal data. This, approach, even though limited in data availability, leads to results suggesting that wealth in the USA is either non-mixing or that it takes a very long time for the individuals to mix within the distribution. These results showcase how mixing can be used in tandem with measures of mobility for drawing conclusions about the extent of mobility across the whole distribution.