Population Aging and Income Inequality in a Semi-Endogenous Growth Model

This paper asks how population aging changes the distribution of income and wealth, using a continuous-time overlapping-generations (“perpetual youth”) model in which persistent growth in per capita income is sustained by external increasing returns to aggregate capital — a semi-endogenous growth setting in which the long-run growth rate is tied to the rate of population change. The authors show analytically that the stationary distributions of effective wealth, financial assets and income are all Pareto, with a shape parameter whose reciprocal — the paper’s inequality index — equals the growth rate of individual wealth (the net rate of return on capital minus the discount rate minus per capita income growth) multiplied by the degree of population aging, measured as 1/(b+m) where b is the birth rate and m the mortality rate. Because population aging raises the share of older, wealthier households, it accelerates capital accumulation and lowers the steady-state return on capital, which pulls inequality down, while simultaneously raising 1/(b+m), which pushes it up; the paper is explicit that “the sign of the right-hand side of the above equation is analytically indeterminate,” so which force wins is a quantitative question. Under a baseline calibration with capital share α = 0.35, external effect γ = 0.3, discount rate ρ = 0.02 and depreciation δ = 0.075 — chosen to give per capita growth of 1.74% at a birth rate of 2% — numerical experiments show the inequality index rising monotonically with the mortality rate and falling monotonically with the birth rate, so aging driven by longer life expectancy lowers inequality while aging driven by a falling birth rate raises it. The asymmetry arises because a change in the birth rate alters the steady-state growth rate of per capita income in this semi-endogenous growth setting, whereas a change in the mortality rate does not.

Kazuo Mino | Macro Paper Warehouse

Population Aging and Income Inequality in a Semi-Endogenous Growth Model