Abilities, Mobilities, And The Beta Wealth Distribution

Abstract

This paper studies the stationary distribution of wealth by using a basic economic model encompassing saving, investment, occupational choice, an imperfect credit market, entrepreneurial abilities, and intergenerational wealth mobilities. It implies that persistent wealth inequality depends on the probability of intergenerational upward mobility relative to the downward mobility probability. The model predicts substitutability between the probabilities that workers' children and entrepreneurs' children have sufficient wealth to become entrepreneurs in achieving the same degree of persistent wealth inequality. It also implies workers' children can have sufficient entrepreneurial wealth with greater or less probability than entrepreneurs' children depending on an explicit mobility measure. A wealth variant of the Great Gatsby Curve is shown to require a restriction on the downward mobility probability. The model also shows that the two kinds of entrepreneurial skills (endowed and environmental-historical abilities) are net substitutes rather than complements in preserving a given measure of stationary wealth inequality. Conditions are given on environmental-historical and endowed abilities that allow different probabilities of passing the wealth test for different types of agents, though no structural relationship between them was built into the model. We obtain insights into how the interest rate affects mobility probabilities and persistent inequality. Finally, the model is solved to obtain a closed Beta form for the distribution of wealth. Its shape is given by the mobility probabilities and subsumes the Pareto wealth distribution as a special case. Empirical illustrations inclue comparisons of the quantile estimates of our Beta stationary wealth density with the generalized Pareto distribution.