Life Expectancy and Lost Life Expectancy

James W. Vaupel, Max Planck Institute for Demographic Research
Zhen Zhang, Max Planck Institute for Demographic Research

Consider e†(y) = ∫eo(x,y)f(x,y)dx, where eo(x,y) is remaining life expectancy at age x in year y and f(x,y) is the life table distribution of deaths. e† can be interpreted as remaining life expectancy lost due to death. It is correlated with the standard deviation of the distribution of lifespans and is a measure of the homogeneity of a population’s life chances. If e† is small, then most people die at roughly the same age. Our paper explores the properties of e†, from a mathematical perspective and also in terms of empirical data. In particular we investigate the relationship between e† and life expectancy at birth and at various older ages. Our most interesting and important finding is that the population with the longest life expectancy in the world in some year is generally also the population with the lowest value of e† in that year.