Zipf’s Law, Pareto’s Law, and the Evolution of Top Incomes in the U.S.
This paper presents a tractable dynamic general equilibrium model of income and firm-size distributions. The size and value of firms result from idiosyncratic, firm-level productivity shocks. CEOs can invest in their own firms’ risky stocks or in risk-free assets, implying that the CEO’s asset and income also depend on firm-level productivity shocks. We analytically show that this model generates the Pareto distribution of top income earners and Zipf’s law of firms in the steady state. Using the model, we evaluate how changes in tax rates can account for the recent evolution of top incomes in the U.S. The model matches the decline in the Pareto exponent of income distribution and the trend of the top 1% income share in the U.S. in recent decades. In the model, the lower marginal income tax for CEOs strengthens their incentive to increase the share of their firms’ risky stocks in their own asset portfolios. This leads to both higher dispersion and concentration of income in the top income group.
For the last three decades, there has been a secular trend of concentration of income among the top earners in the U.S. economy. According to Alvaredo et al. (2013), the top 1% income share, the share of total income going to the richest top 1% of the population, declined from around 18% to 8% after the 1930s, but the trend was reversed during the 1970s. Since then, the income share of the top 1% has grown and had reached 18% by 2010, on par with the prewar level.