Kindred Distributions: An Application to Wealth and Income Densities

16 Pages Posted: 19 Jun 2015

See all articles by Murray Brown

Murray Brown

SUNY at Buffalo, College of Arts & Sciences, Department of Economics

Shin-Hwan Chiang

York University - Department of Economics

Date Written: June 12, 2015

Abstract

We describe a simple method to obtain kindred stationary densities of random Markov processes with respect to an Ito transformation function. As applied to income and wealth densities, they are akin to one another because they share the income growth and income volatility shape parameters. The procedure first assumes a linear infinitesimal drift and a quadratic infinitesimal variance, which together with the stationary Kolmogorov forward equation gives rise to a power law income distribution. To find a kindred distribution we assume that the rate of change of wealth is a function of savings from income and the returns from accumulated wealth. Applying the Ito transformation, we then obtain an explicit wealth-income density, which turns out to be another power law density with an augmented exponential term. It shares certain shape parameters with the income density. Another objective of the paper is to learn how volatility affects the specific wealth-income prediction in Piketty-Zucman (2014).

Keywords: Uncertainty, Wealth-Income Distributions, Diffusion Processes

JEL Classification: D8, D31, C22

Suggested Citation

Brown, Murray and Chiang, Shin-Hwan, Kindred Distributions: An Application to Wealth and Income Densities (June 12, 2015). Available at SSRN: https://ssrn.com/abstract=2617812 or http://dx.doi.org/10.2139/ssrn.2617812

Murray Brown (Contact Author)

SUNY at Buffalo, College of Arts & Sciences, Department of Economics ( email )

Fronczak Hall
Buffalo, NY 14260
United States
716-838-1941 (Phone)
716-645-2127 (Fax)

Shin-Hwan Chiang

York University - Department of Economics ( email )

4700 Keele St.
Toronto, Ontario M3J 1P3
Canada
416-736-5083 (Phone)

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