The Variance of Population Characteristics in Stable Populations, with Applications to the Distribution of Income

Stable population theory has recently been used to analyse the effects of changes in fertility and mortality on economic variables such as income per head. In this paper more general results are derived to describe the effects of changing vital rates on the variance and higher moments of the distribution of some age-dependent variable. Simple analytical expressions are derived which decompose the effects of changes in age structure into the effects on inter-cohort and intra-cohort variance. The results are easily applied to standard measures of the distribution of income. By combining the analytical results with actual age profiles of income and income variance from the United States and Brazil it is observed that both the magnitude and direction of the effects of population growth on measured inequality are sensitive to the specific age profiles used. The most surprising result is that the Brazilian age profiles suggest that higher growth rates may actually reduce measured inequality, although the effect is relatively small.