The concept of the Equivalent Length of Life for quantifying differences in age-at-death distributions across countries

Life expectancy, that is the mean age at death in a life table, is the most common measure used to describe and compare mortality distributions. Alternatives to life expectancy that have been proposed so far have also referred to only a single parameter of the mortality distribution. We propose to study mortality distributions by applying Silber’s concept of the Equivalent Length of Life (ELL), which enables comparisons based on up to three parameters of age-at-death distributions: life expectancy, dispersion and skewness. The method, and our decomposition, is used to study convergence/divergence of life-table age-at-death distributions across 35 developed countries of the Human Mortality Database in 1970–2010 and to assess the contribution of the three moments of the distribution to the total differences between countries and trends in the contribution. We observed a divergence of age-at-death distributions across the study countries from 1970 to 2005, followed by a convergence. Differences in life expectancies contributed the most to inequalities between the countries in life-table age-at-death distributions and the observed changes over time for both sexes. An additional important contribution resulted from the growing negative covariance between life expectancy and dispersion of ages at death, indicating that the largest increase in life expectancy occurred in the countries where variation in ages at death was lowest, especially among women. For men, including the skewness parameter resulted in lower differences between countries. The ELL and its decomposition thus have clear added value for studying differences between countries and convergence/divergence of age-at-death distributions.