The impact of proportional changes in age-specific mortality on life expectancy when the mortality rate is a log-linear function of age

Michael Væth, Henrik Stovring () and Mette Vinther Skriver
Additional contact information
Michael Væth: Aarhus University
Mette Vinther Skriver: Aarhus University

Demographic Research, 2018, vol. 39, issue 23, 671-684

Abstract: Background: Demographers and epidemiologists have investigated the dependence of life expectancy on proportional changes in the age-specific mortality. Objective: To develop an approach that allows estimation of change in life expectancy from proportional changes in age-specific mortality and to identify aspects of the death rate that influence the accuracy of the estimation. Results: We obtain an exact expression for the first derivative of the life expectancy with respect to the proportional change in age-specific mortality when the age-specific death rate is log-linear in age. We use the result to establish bounds for the change in life expectancy following a proportional change of the mortality. The result shows that the change in life expectancy is approximately linear in the logarithm of the proportional change of the mortality. In populations with low infant mortality, the slope of this linear relationship is essentially equal to minus the inverse of the slope of the log-linear age dependence of the death rate. Contribution: In a wide range of mortality scenarios, the relationship between change in life expectancy and the logarithm of the proportional change of the mortality allows accurate approximation of a difference in life expectancy from a ratio of death rates.

Keywords: life expectancy; force of mortality; Gompertz distribution (search for similar items in EconPapers)
JEL-codes: J1 Z0 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.demographic-research.org/volumes/vol39/23/39-23.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:dem:demres:v:39:y:2018:i:23

DOI: 10.4054/DemRes.2018.39.23

Access Statistics for this article

More articles in Demographic Research from Max Planck Institute for Demographic Research, Rostock, Germany
Bibliographic data for series maintained by Editorial Office ().