The Distribution of Wealth in the Blanchard–yaari Model

Abstract

We study the dynamics of the distribution of wealth in an economy with infinitely lived agents, intergenerational transmission of wealth, and redistributive fiscal policy. We show that wealth accumulation with idiosyncratic investment risk and uncertain lifetimes can generate a double Pareto wealth distribution.

Incomplete market dynamics and cross-sectional distributions

“…Benhabib et al (2014) derive the double Pareto distribution in an economy with optimizing agents subject to idiosyncratic investment risk, which is similar to my results. Although they have features absent in my model (bequest, fiscal policies, etc.…”

“…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.…”

“…Although these assumptions may be plausible for human capital, which is not transferable across agents and disappear upon death, they may not be appropriate for physical capital. We may easily enrich the model by introducing life insurances, bequest, estate tax, and redistributions as in Benhabib et al (2014), but the basic structure of the model (homotheticity and individual units obeying multiplicative processes that are i.i.d. conditional on aggregate shock) is preserved.…”

“…By introducing birth and death in a mechanistic model with geometric Brownian motion, Reed (2001) showed that we can get the double Pareto distribution, whose tails satisfy the power law exactly. Benhabib et al (2014) do the same with optimizing agents in a partial equilibrium model. But the real world is certainly more complicated than the i.i.d.…”

A Note on the Size Distribution of Consumption: More Double Pareto Than Lognormal

“…A property that holds for the lognormal can often be generalized for dPlN. Second, Benhabib et al (2014) and Toda (2014) have theoretically shown that the size distribution of consumption should be approximately lognormal within age cohorts and double Pareto or dPlN in the entire cross-section. Therefore if we find that consumption is dPlN, we have an indirect evidence suggesting that the consumption dynamics obeys the generative mechanism of dPlN.…”