The threshold age of the lifetable entropy

José Manuel Aburto, James W. Vaupel, Jesús-Adrián Alvarez and Francisco Villavicencio
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José Manuel Aburto: London School of Hygiene and Tropical Medicine
James W. Vaupel: Syddansk Universitet
Jesús-Adrián Alvarez: Syddansk Universitet
Francisco Villavicencio: Universitat de Barcelona

Demographic Research, 2019, vol. 41, issue 4, 83-102

Abstract: Background: Indicators of relative variation of lifespans are markers of inequality at the population level and of uncertainty at the time of death at the individual level. In particular, the lifetable entropy H represents the elasticity of life expectancy to a change in mortality. However, it is unknown how this measure changes over time and whether a threshold age exists, as it does for other lifespan variation indicators. Results: The time derivative of H can be decomposed into changes in life disparity e† and life expectancy at birth eo. Likewise, changes over time in H are a weighted average of age-specific rates of mortality improvements. These weights reflect the sensitivity of H and show how mortality improvements can increase (or decrease) the relative inequality of lifespans. Further, we prove that in the assumption that mortality is reduced at all ages, H, as well as e†, has a threshold age below which saving lives reduces entropy, whereas improvements above that age increase entropy. Contribution: We give a formal expression for changes of H over time and provide a formal proof of the existence of a unique threshold age that separates reductions and increases in lifespan variation as a result age-specific mortality improvements.

Keywords: lifespan variation; pace of aging; mathematical demography; mortality (search for similar items in EconPapers)
JEL-codes: J1 Z0 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

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Persistent link: https://EconPapers.repec.org/RePEc:dem:demres:v:41:y:2019:i:4

DOI: 10.4054/DemRes.2019.41.4

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