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

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Listed:
  • Michael Væth

    (Aarhus University)

  • Mette Vinther Skriver

    (Aarhus University)

  • Henrik Støvring

    (Aarhus University)

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.

Suggested Citation

  • Michael Væth & Mette Vinther Skriver & Henrik Støvring, 2018. "The impact of proportional changes in age-specific mortality on life expectancy when the mortality rate is a log-linear function of age," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 39(23), pages 671-684.
    • Handle: RePEc:dem:demres:v:39:y:2018:i:23
    DOI: 10.4054/DemRes.2018.39.23
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    References listed on IDEAS

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    1. Tomasz Wrycza & Annette Baudisch, 2012. "How life expectancy varies with perturbations in age-specific mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 27(13), pages 365-376.
    2. Simon Broadbent, 1958. "Simple Mortality Rates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 7(2), pages 86-95, June.
    3. James Vaupel & Vladimir Romo, 2003. "Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday," Demography, Springer;Population Association of America (PAA), vol. 40(2), pages 201-216, May.
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    Cited by:

    1. Qi Cui & Vladimir Canudas-Romo & Heather Booth, 2019. "The Mechanism Underlying Change in the Sex Gap in Life Expectancy at Birth: An Extended Decomposition," Demography, Springer;Population Association of America (PAA), vol. 56(6), pages 2307-2321, December.

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    More about this item

    Keywords

    life expectancy; force of mortality; Gompertz distribution;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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