How lifespan and life years lost equate to unity

Annette Baudisch and José Manuel Aburto
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Annette Baudisch: Syddansk Universitet
José Manuel Aburto: London School of Hygiene and Tropical Medicine

Demographic Research, 2024, vol. 50, issue 24, 643-666

Abstract: Background: Life expectancy at birth (e0), life years lost at death (e†), and lifetable entropy (H) are key indicators that capture average lifespan and lifespan variation. Expressions and relationships among these summary measures form the basis to analytically derive a range of formal demographic relationships, that build on each other and together help create new insights. Even though many elegant relationships are known, new ones are still to be discovered. Results: The sum of life expectancy and life years lost at death, scaled by the level and rate parameters a and b of the Gompertz mortality model, equals one. This plain relationship has mathematical beauty and connects key demographic measures. It directly implies further relationships, and allows connecting existing ones. It can be interpreted as a pace–shape decomposition of lifespan. Contribution: We contribute a useful relationship to complement analytical tools for studying life expectancy and lifespan variation. It can reveal macro-level regularities that may aid development of novel forecasting methods in the future. It could also support more comparative research across species by quantifying the relative impact of the environment on species’ life histories. We also propose the ratio a/b as a potential metric to signal major trend changes in mortality improvements.

Keywords: life expectancy; life years lost; life table entropy; lifespan variation (search for similar items in EconPapers)
JEL-codes: J1 Z0 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:dem:demres:v:50:y:2024:i:24

DOI: 10.4054/DemRes.2024.50.24

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