IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v108y2020icp1-7.html
   My bibliography  Save this article

Threshold ages for the relation between lifetime entropy and mortality risk

Author

Listed:
  • Meyer, Patrick
  • Ponthiere, Gregory

Abstract

We study the effect of a change in age-specific probability of death on risk about the duration of life measured by Shannon’s entropy defined to the base 2. We first show that a rise in the probability of death at age n increases lifetime entropy at age k≤n if and only if the quantity of information revealed by the event of a death at age n exceeds lifetime entropy at age n+1 divided by the probability to survive from age k to age n+1. There exist, under general conditions, two threshold ages: first, a low threshold age below which a rise in mortality risk decreases lifetime entropy, and above which it raises lifetime entropy; second, a high threshold age above which a rise in mortality risk reduces lifetime entropy. Using French life tables, we show that the gap between those two threshold ages has been increasing over the last two centuries.

Suggested Citation

  • Meyer, Patrick & Ponthiere, Gregory, 2020. "Threshold ages for the relation between lifetime entropy and mortality risk," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 1-7.
    • Handle: RePEc:eee:matsoc:v:108:y:2020:i:c:p:1-7
    DOI: 10.1016/j.mathsocsci.2020.07.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489620300640
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2020.07.004?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
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Väinö Kannisto, 2000. "Measuring the compression of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(6).
    2. Patrick Meyer & Gregory Ponthiere, 2020. "Human lifetime entropy in a historical perspective (1750–2014)," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 14(1), pages 129-167, January.
    3. Antoine Bommier, 2006. "Uncertain Lifetime And Intertemporal Choice: Risk Aversion As A Rationale For Time Discounting," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(4), pages 1223-1246, November.
    4. John Wilmoth & Shiro Horiuchi, 1999. "Rectangularization revisited: Variability of age at death within human populations," Demography, Springer;Population Association of America (PAA), vol. 36(4), pages 475-495, November.
    5. Smits, Jeroen & Monden, Christiaan, 2009. "Length of life inequality around the globe," Social Science & Medicine, Elsevier, vol. 68(6), pages 1114-1123, March.
    6. 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.
    7. Ryan D. Edwards & Shripad Tuljapurkar, 2005. "Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries," Population and Development Review, The Population Council, Inc., vol. 31(4), pages 645-674, December.
    8. Shripad Tuljapurkar & Ryan Edwards, 2011. "Variance in death and its implications for modeling and forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(21), pages 497-526.
    9. 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.
    10. 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.
    11. 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.
    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. Aburto, José Manuel & Kristensen, Frederikke Frehr & Sharp, Paul, 2021. "Black-white disparities during an epidemic: Life expectancy and lifespan disparity in the US, 1980–2000," Economics & Human Biology, Elsevier, vol. 40(C).
    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. 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.
    4. 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.
    5. Joseph T. Lariscy & Claudia Nau & Glenn Firebaugh & Robert A. Hummer, 2016. "Hispanic-White Differences in Lifespan Variability in the United States," Demography, Springer;Population Association of America (PAA), vol. 53(1), pages 215-239, February.
    6. 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.
    7. Michal Engelman & Hal Caswell & Emily Agree, 2014. "Why do lifespan variability trends for the young and old diverge? A perturbation analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(48), pages 1367-1396.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Patrick Meyer & Gregory Ponthiere, 2020. "Human lifetime entropy in a historical perspective (1750–2014)," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 14(1), pages 129-167, January.
    13. 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.
    14. 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.
    15. Dmitri A. Jdanov & Vladimir M. Shkolnikov & Alyson A. van Raalte & Evgeny M. Andreev, 2017. "Decomposing Current Mortality Differences Into Initial Differences and Differences in Trends: The Contour Decomposition Method," Demography, Springer;Population Association of America (PAA), vol. 54(4), pages 1579-1602, August.
    16. José Manuel Aburto & Alyson van Raalte, 2018. "Lifespan Dispersion in Times of Life Expectancy Fluctuation: The Case of Central and Eastern Europe," Demography, Springer;Population Association of America (PAA), vol. 55(6), pages 2071-2096, December.
    17. 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.
    18. Glenn Firebaugh & Francesco Acciai & Aggie Noah & Christopher Prather & Claudia Nau, 2014. "Why Lifespans Are More Variable Among Blacks Than Among Whites in the United States," Demography, Springer;Population Association of America (PAA), vol. 51(6), pages 2025-2045, December.
    19. Alyson van Raalte & Mikko Myrskylä & Pekka Martikainen, 2015. "The role of smoking on mortality compression," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(20), pages 589-620.
    20. 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.

    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:eee:matsoc:v:108:y:2020:i:c:p:1-7. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.