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The difference between alternative averages

Author

Listed:
  • James W. Vaupel

    (Syddansk Universitet)

  • Zhen Zhang

    (Fudan University)

Abstract

Background: Demographers have long been interested in how compositional change, e.g., change in age structure, affects population averages. Objective: We want to deepen understanding of how compositional change affects population averages. Results: The difference between two averages of a variable, calculated using alternative weighting functions, equals the covariance between the variable and the ratio of the weighting functions, divided by the average of the ratio. We compare weighted and unweighted averages and also provide examples of use of the relationship in analyses of fertility and mortality. Comments: Other uses of covariances in formal demography are worth exploring.

Suggested Citation

  • James W. Vaupel & Zhen Zhang, 2012. "The difference between alternative averages," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 27(15), pages 419-428.
    • Handle: RePEc:dem:demres:v:27:y:2012:i:15
    DOI: 10.4054/DemRes.2012.27.15
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    References listed on IDEAS

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    1. Samuel Preston, 1976. "Family sizes of children and family sizes of women," Demography, Springer;Population Association of America (PAA), vol. 13(1), pages 105-114, February.
    2. Samuel Preston & Christine Himes & Mitchell Eggers, 1989. "Demographic Conditions Responsible for Population Aging," Demography, Springer;Population Association of America (PAA), vol. 26(4), pages 691-704, November.
    3. James W. Vaupel & Annette Baudisch & Martin Dölling & Deborah A. Roach & Jutta Gampe, 2004. "The case for negative senescence," MPIDR Working Papers WP-2004-002, Max Planck Institute for Demographic Research, Rostock, Germany.
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    Cited by:

    1. Markus Sauerberg & Marc Luy, 2024. "Standardized mean age at death (MADstd): Exploring its potentials as a measure of human longevity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 50(30), pages 871-898.
    2. Carl Schmertmann, 2020. "Revivorship and life lost to mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(17), pages 497-512.
    3. Bonetti, Marco & Basellini, Ugofilippo & NIGRI, ANDREA, 2023. "The Average Uneven Mortality index: Building on the "e-dagger" measure of lifespan inequality," SocArXiv xb6vq, Center for Open Science.

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    More about this item

    Keywords

    population average; covariance; weighting function;
    All these keywords.

    JEL classification:

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

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