The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents

Abstract

We study the dynamics of the distribution of wealth in an overlapping generation economy with finitely lived agents and intergenerational transmission of wealth. Financial markets are incomplete, exposing agents to both labor and capital income risk. We show that the stationary wealth distribution is a Pareto distribution in the right tail and that it is capital income risk, rather than labor income, that drives the properties of the right tail of the wealth distribution. We also study analytically the dependence of the distribution of wealth—of wealth inequality in particular—on various fiscal policy instruments like capital income taxes and estate taxes, and on different degrees of social mobility. We show that capital income and estate taxes can significantly reduce wealth inequality, as do institutions favoring social mobility. Finally, we calibrate the economy to match the Lorenz curve of the wealth distribution of the U.S. economy.

Incomplete market dynamics and cross-sectional distributions

“…My results on the cross-sectional distributions build on and extend those of Gabaix (1999) and Benhabib et al (2011Benhabib et al ( , 2014. Benhabib, Bisin, and Zhu derive the power law in an equilibrium model with optimizing agents, which is closest to my results.…”

“…She derives a secondorder ordinary differential equation that the stationary distribution satisfies, but neither explicitly solve it nor refer to the power law. Benhabib et al (2011) study an overlapping generations model with inheritance. Since between generations the wealth is subject to idiosyncratic investment risk and estate tax, and each generation receives lump-sum transfers (e.g., present value of labor income), the wealth of dynasties obeys the so-called Kesten (1973) process, X t+1 = M t+1 X t + Q t+1 .…”

Wealth Distribution with Random Discount Factors

“…Another common approach in generating wealth inequality is to assume that agents have heterogeneous but nonstochastic discount factors (Krueger et al, 2016;McKay and Reis, 2016;McKay, 2017), although this type of models do not generate Pareto tails without further assumptions. Benhabib et al (2011) provide the first rigorous proof that idiosyncratic investment risk can generate Pareto tails. They consider an overlapping generations model in which households face idiosyncratic rates of return on wealth and earnings at birth (which remain constant in their lifetime).…”

Partial differential equation models in macroeconomics

“…For example, Benhabib et al [31] and in particular Benhabib et al [33] develop models of the wealth distribution whose mathematical structure is quite similar to the one presented here. Similarly, Jones [45] applies the same insights into the question why the top of the income distribution (the infamous 'one percent') can be well described by a power law.…”

“…This has motivated the study of richer models of individual heterogeneity and wealth accumulation. Examples include models in which individuals have access to different returns to their savings [31,33], for instance because they run private enterprises in a world with imperfect capital markets [34][35][36], and models in which individuals have different preferences for current and future consumption [37]. A close interplay between numerical solutions of calibrated models and data is a central theme in the macroeconomic literature reviewed in this paper (and which we do not discuss in more detail due to space limitations).…”