IDEAS home Printed from https://ideas.repec.org/a/dem/demres/v51y2024i24.html
   My bibliography  Save this article

On the relationship between life expectancy, modal age at death, and the threshold age of the life table entropy

Author

Listed:
  • Chiara Micheletti

    (Universitat Autònoma de Barcelona)

  • Francisco Villavicencio

    (Universitat de Barcelona)

Abstract

Background: Indicators of longevity like the life expectancy at birth or the modal age at death are always positively affected by improvements in mortality. Instead, for lifespan variation it has been shown that there exists a threshold age above and below which averting deaths respectively increases or decreases such variation. Objective: Within a Gompertz force of mortality setting, we aim to provide approximations of the life expectancy at birth and the threshold age of the life table entropy in terms of the modal age at death, highlighting the interrelationships holding among the three. Results: In the Gompertz framework, a tight relationship exists between the life expectancy at birth, the threshold age of the life table entropy, and the modal age at death, with the former two moving together and in parallel to the latter. We apply this theoretical result to life table data from the Human Mortality Database to show how the different relationships evolve over time. We observe a remarkable association between the modal and the threshold ages, even in populations with high mortality levels. Contribution: We provide approximations of the life expectancy at birth and the threshold age of the life table entropy in terms of the Gompertz modal age at death. This is a mathematical demography paper that builds upon previous research by James W. Vaupel and illustrates the beauty – and oftentimes simplicity – of the mathematical relationships between demographic concepts.

Suggested Citation

  • Chiara Micheletti & Francisco Villavicencio, 2024. "On the relationship between life expectancy, modal age at death, and the threshold age of the life table entropy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 51(24), pages 763-788.
    • Handle: RePEc:dem:demres:v:51:y:2024:i:24
    DOI: 10.4054/DemRes.2024.51.24
    as

    Download full text from publisher

    File URL: https://www.demographic-research.org/volumes/vol51/24/51-24.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.4054/DemRes.2024.51.24?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Adrien Remund & Carlo G. Camarda & Tim Riffe, 2018. "A Cause-of-Death Decomposition of Young Adult Excess Mortality," Demography, Springer;Population Association of America (PAA), vol. 55(3), pages 957-978, June.
    2. Isaac Sasson, 2016. "Trends in Life Expectancy and Lifespan Variation by Educational Attainment: United States, 1990–2010," Demography, Springer;Population Association of America (PAA), vol. 53(2), pages 269-293, April.
    3. Nathan Keyfitz, 1977. "What difference would it make if cancer were eradicated? An examination of the taeuber paradox," Demography, Springer;Population Association of America (PAA), vol. 14(4), pages 411-418, November.
    4. Noreen Goldman & Graham Lord, 1986. "A new look at entropy and the life table," Demography, Springer;Population Association of America (PAA), vol. 23(2), pages 275-282, May.
    5. 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.
    6. Trifon Missov & Adam Lenart & Laszlo Nemeth & Vladimir Canudas-Romo & James W. Vaupel, 2015. "The Gompertz force of mortality in terms of the modal age at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(36), pages 1031-1048.
    7. Iain D. Currie, 2016. "On fitting generalized linear and non-linear models of mortality," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(4), pages 356-383, April.
    8. Zhen Zhang & James W. Vaupel, 2009. "The age separating early deaths from late deaths," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 20(29), pages 721-730.
    9. Owen R. Jones & Alexander Scheuerlein & Roberto Salguero-Gómez & Carlo Giovanni Camarda & Ralf Schaible & Brenda B. Casper & Johan P. Dahlgren & Johan Ehrlén & María B. García & Eric S. Menges & Pedro, 2014. "Diversity of ageing across the tree of life," Nature, Nature, vol. 505(7482), pages 169-173, January.
    10. Serena Vigezzi & Jose Manuel Aburto & Iñaki Permanyer & Virginia Zarulli, 2022. "Divergent trends in lifespan variation during mortality crises," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 46(11), pages 291-336.
    11. Zhen Zhang & James W. Vaupel, 2009. "The age separating early deaths from late deaths," MPIDR Working Papers WP-2009-004, Max Planck Institute for Demographic Research, Rostock, Germany.
    12. Shiro Horiuchi & Nadine Ouellette & Siu Lan Karen Cheung & Jean-Marie Robine, 2013. "Modal age at death: lifespan indicator in the era of longevity extension," Vienna Yearbook of Population Research, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna, vol. 11(1), pages 37-69.
    13. Vladimir Canudas-Romo, 2008. "The modal age at death and the shifting mortality hypothesis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 19(30), pages 1179-1204.
    14. Jose Manuel Aburto & Jesús-Adrián Alvarez & Francisco Villavicencio & James W. Vaupel, 2019. "The threshold age of the lifetable entropy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(4), pages 83-102.
    15. Jacob Martin & Jose Manuel Aburto & Iñaki Permanyer, 2023. "Dynamics of the coefficient of variation of the age at death distribution," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 49(38), pages 1063-1086.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wen Su & Vladimir Canudas-Romo, 2024. "Cross-sectional Average Length of Life Entropy ( $${\mathcal{H}}_{\text{CAL}}$$ H CAL ): International Comparisons and Decompositions," European Journal of Population, Springer;European Association for Population Studies, vol. 40(1), pages 1-23, December.
    2. Aburto, José Manuel & Basellini, Ugofilippo & Baudisch, Annette & Villavicencio, Francisco, 2022. "Drewnowski’s index to measure lifespan variation: Revisiting the Gini coefficient of the life table," Theoretical Population Biology, Elsevier, vol. 148(C), pages 1-10.
    3. Jacob Martin & Jose Manuel Aburto & Iñaki Permanyer, 2023. "Dynamics of the coefficient of variation of the age at death distribution," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 49(38), pages 1063-1086.
    4. Wen Su & Alyson van Raalte & Jose Manuel Aburto & Vladimir Canudas-Romo, 2024. "Subnational contribution to life expectancy and life span variation changes: Evidence from the United States," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 50(22), pages 583-624.
    5. Jos'e Manuel Aburto & Ugofilippo Basellini & Annette Baudisch & Francisco Villavicencio, 2021. "Drewnowski's index to measure lifespan variation: Revisiting the Gini coefficient of the life table," Papers 2111.11256, arXiv.org.
    6. Serena Vigezzi & Jose Manuel Aburto & Iñaki Permanyer & Virginia Zarulli, 2022. "Divergent trends in lifespan variation during mortality crises," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 46(11), pages 291-336.
    7. Henrik Brønnum-Hansen & Juan Carlos Albizu-Campos Espiñeira & Camila Perera & Ingelise Andersen, 2023. "Trends in mortality patterns in two countries with different welfare models: comparisons between Cuba and Denmark 1955–2020," Journal of Population Research, Springer, vol. 40(2), pages 1-28, June.
    8. Oscar E Fernandez & Hiram Beltrán-Sánchez, 2022. "Life span inequality as a function of the moments of the deaths distribution: Connections and insights," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-17, January.
    9. Duncan Gillespie & Meredith Trotter & Shripad Tuljapurkar, 2014. "Divergence in Age Patterns of Mortality Change Drives International Divergence in Lifespan Inequality," Demography, Springer;Population Association of America (PAA), vol. 51(3), pages 1003-1017, June.
    10. Alyson van Raalte & Pekka Martikainen & Mikko Myrskylä, 2014. "Lifespan Variation by Occupational Class: Compression or Stagnation Over Time?," Demography, Springer;Population Association of America (PAA), vol. 51(1), pages 73-95, February.
    11. Tomasz Wrycza, 2014. "Entropy of the Gompertz-Makeham mortality model," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(49), pages 1397-1404.
    12. Jose Manuel Aburto & Jesús-Adrián Alvarez & Francisco Villavicencio & James W. Vaupel, 2019. "The threshold age of the lifetable entropy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(4), pages 83-102.
    13. Beltrán-Sánchez, Hiram & Soneji, Samir, 2011. "A unifying framework for assessing changes in life expectancy associated with changes in mortality: The case of violent deaths," Theoretical Population Biology, Elsevier, vol. 80(1), pages 38-48.
    14. Francisco Goerlich, 2020. "Distributionally adjusted life expectancy as a life table function," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 43(14), pages 365-400.
    15. Fernandez, Oscar E. & Beltrán-Sánchez, Hiram, 2015. "The entropy of the life table: A reappraisal," Theoretical Population Biology, Elsevier, vol. 104(C), pages 26-45.
    16. Tomasz Wrycza, 2014. "Variance in age at death equals average squared remaining life expectancy at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(50), pages 1405-1412.
    17. Alyson A. van Raalte & Pekka Martikainen & Mikko Myrskylä, 2012. "Lifespan variation by occupational class: compression or stagnation over time?," MPIDR Working Papers WP-2012-010, Max Planck Institute for Demographic Research, Rostock, Germany.
    18. José M. Aburto & Alyson A. van Raalte, 2017. "Lifespan dispersion in times of life expectancy fluctuation: the case of Central and Eastern Europe," MPIDR Working Papers WP-2017-018, Max Planck Institute for Demographic Research, Rostock, Germany.
    19. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    20. Lucia Zanotto & Vladimir Canudas-Romo & Stefano Mazzuco, 2021. "A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 1-27, March.

    More about this item

    Keywords

    life expectancy; lifespan variation; longevity; mode; mortality; Gompertz law;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:dem:demres:v:51:y:2024:i:24. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Editorial Office (email available below). General contact details of provider: https://www.demogr.mpg.de/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.