The Average Uneven Mortality Index: Building on the "e-dagger" Measure of Lifespan Inequality

Ugofilippo Basellini , Max Planck Institute for demographic Research
Marco Bonetti, Bocconi University
Andrea Nigri, Sapienza, University of Rome

BACKGROUND. In recent years, lifespan inequality has become an important indicator of population health. Uncovering the statistical properties of lifespan inequality measures can provide novel insights on the study of mortality. METHODS. We revisit the e† measure of lifespan inequality, introduced in Vaupel and Canudas-Romo (2003). Leveraging a result first noted in Schmertmann (2020), we derive an upper bound for e†. This finding motivates us to introduce the ``Average Uneven Mortality" (AUM) index, a normalized version of the e† measure that can be meaningfully compared across countries and over time. RESULTS. The use of the AUM index is illustrated through an application to observed period and cohort death rates from the Human Mortality Database. We explore the behavior of the index across age and over time, and we study its relationship with life expectancy. The AUM index at birth declined over time until the 1950s, when it reverted its trend; also, the index generally increases with age. CONTRIBUTION. We elaborate on Vaupel and Canudas-Romo’s e† measure, deriving its upper bound. We exploit this result to introduce a novel mortality indicator, which provides a new perspective on the historical evolution of lifespan inequality. We also develop novel routines to compute e† and the standard deviation of lifetimes from death rates, which are possibly more precise than available software, particularly for calculations involving older ages.

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 Presented in Session P2. Health, Mortality, Ageing - Aperitivo