Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the U.S.

Abstract

We construct a tractable neoclassical growth model that generates Pareto's law of income distribution and Zipf's law of the firm size distribution from idiosyncratic, firm-level productivity shocks. Executives and entrepreneurs invest in risk-free assets as well as their own firms' risky stocks, through which their wealth and income depend on firm-level shocks. By using the model, we evaluate how changes in tax rates can account for the evolution of top incomes in the U.S. The model matches the decline in the Pareto exponent of the income distribution and the trend of the top 1% income share in recent decades.JEL Codes: D31, L11, O40

The Dynamics of Inequality

“…15 For instance, it is messy to define a reflecting barrier in the presence of jumps. 16 See, for example, Champernowne (1953), Simon (1955), Nirei (2009), Toda and Walsh (2015), Aoki and Nirei (2015), Kim (2015), Jones andKim (2014), andLuttmer (2015) for models with similar reduced forms. Some of these are derived from individual optimization, but others are not.…”

“…We also build on Luttmer (2011), who studied a related framework applied to firm dynamics and argued that persistent heterogeneity in mean firm growth rates is needed to account for the relatively young age of very large firms at a given point in time (a statement about the stationary distribution rather than transition dynamics as in our paper). Aoki and Nirei (2015) presented a related and more complex economic model with entrepreneurs and workers that are subject to different income growth rates, and Jones and Kim (2014) examined a model with different types of entrepreneurs.…”

“…All of these papers focus on the income or wealth distribution at a given point in time by studying stationary distributions, and none of them analyze transition dynamics. Aoki and Nirei (2015) are a notable exception; they examined the dynamics of the income distribution and asked whether tax changes can account for the rise in top income inequality observed in the United States. Our paper differs from theirs in that we obtain a number of analytic results providing a tight characterization of transition dynamics in random growth models, whereas their analysis of transition dynamics is purely numerical.…”

Determinants of Wealth Inequality and Mobility in General Equilibrium

“…The model is cast in continuous time, which boosts the analytical discussion. This toolbox -in particular the Fokker-Planck equations available in this framework providing the cross-sectional distribution -has been successfully employed recently in order to analyze issues of inequality (Aoki and Nirei (2017), Cao and Luo (2017), Nuño and Moll (2018)). The model features an overlapping generations structure with uncertain life time and a bequest motive in the presence of annuity markets.…”

Heterogeneity and Persistence in Returns to Wealth

“…In a world where individuals have identical access to a menu of instruments differing by risk, liquidity and other features, including private businesses, as in Quadrini (2000), Cagetti and De Nardi (2009;2006) and Aoki and Nirei (2015), the portfolio return is: r (10), we add the interaction of time dummies and the individual risky assets share ω j i(g)t . If individuals have identical access to a menu of financial instruments, such controls would absorb all the existing variation in returns.…”