IDEAS home Printed from https://ideas.repec.org/p/hal/psewpa/halshs-01409679.html
   My bibliography  Save this paper

Human Lifetime Entropy in a Historical Perspective (1750-2014)

Author

Listed:
  • Patrick Meyer

    () (Lab-STICC_TB_CID_DECIDE - Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance - ENIB - École Nationale d'Ingénieurs de Brest - UBS - Université de Bretagne Sud - UBO - Université de Brest - Télécom Bretagne - IBNM - Institut Brestois du Numérique et des Mathématiques - UBO - Université de Brest - UEB - Université européenne de Bretagne - European University of Brittany - ENSTA Bretagne - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique, LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l'Information - Institut Mines-Télécom [Paris] - Télécom Bretagne - UEB - Université européenne de Bretagne - European University of Brittany)

  • Grégory Ponthière

    (ERUDITE - Equipe de Recherche sur l’Utilisation des Données Individuelles en lien avec la Théorie Economique - UPEM - Université Paris-Est Marne-la-Vallée - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12, PSE - Paris School of Economics, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

Abstract

Although it is widely acknowledged that life is risky, it is difficult to provide an intuitive indicator of the riskiness of life, whose metric would have a concrete counterpart for the layman. This paper uses the Shannon entropy index to the base 2 to quantify, in terms of bits (i.e. the amount of information revealed by tossing a fair coin), the risk relative to the age at death in 37 countries from the Human Mortality Database. We identify 5 major stylized facts: (1) over the last two centuries, (period) life entropy at birth exhibits an inverted U shape pattern with a maximum in the first half of the 20th century (at about 6 bits); (2) over the last 150 years, Western countries have converged in terms of (period) life entropy at birth towards levels of 5.6 bits for men and 5.5 bits for women; (3) curves of (period) life entropy at birth for men and women crossed during the 20th century; (4) the entropy age profi le shifted from a non-monotonic profi le (in the 18th and 19th centuries) to a strictly decreasing pro file (in the 20th and 21th centuries); (5) men exhibit a higher life entropy than women below ages 50-55, and a lower one after ages 50-55.

Suggested Citation

  • Patrick Meyer & Grégory Ponthière, 2016. "Human Lifetime Entropy in a Historical Perspective (1750-2014)," PSE Working Papers halshs-01409679, HAL.
  • Handle: RePEc:hal:psewpa:halshs-01409679
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01409679
    as

    Download full text from publisher

    File URL: https://halshs.archives-ouvertes.fr/halshs-01409679/document
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mirowsky, John, 1999. "Subjective life expectancy in the US: correspondence to actuarial estimates by age, sex and race," Social Science & Medicine, Elsevier, vol. 49(7), pages 967-979, October.
    2. Brouwer, Werner B.F. & van Exel, N. Job A., 2005. "Expectations regarding length and health related quality of life: Some empirical findings," Social Science & Medicine, Elsevier, vol. 61(5), pages 1083-1094, September.
    3. 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.
    4. Kopczuk Wojciech & Slemrod Joel, 2005. "Denial of Death and Economic Behavior," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 5(1), pages 1-26, August.
    5. Väinö Kannisto, 2000. "Measuring the compression of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(6), September.
    6. Daniel S. Hamermesh, 1985. "Expectations, Life Expectancy, and Economic Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 100(2), pages 389-408.
    7. Brown, Jeffrey R. & Finkelstein, Amy, 2007. "Why is the market for long-term care insurance so small?," Journal of Public Economics, Elsevier, vol. 91(10), pages 1967-1991, November.
    8. 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.
    9. 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, March.
    10. Jeffrey R. Brown & Amy Finkelstein, 2009. "The Private Market for Long‐Term Care Insurance in the United States: A Review of the Evidence," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(1), pages 5-29, March.
    11. repec:aph:ajpbhl:1983:73:8:911-914_1 is not listed on IDEAS
    12. Jeffrey Brown & Amy Finkelstein, 2011. "Insuring Long Term Care In the US," NBER Working Papers 17451, National Bureau of Economic Research, Inc.
    13. 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.
    14. Smits, Jeroen & Monden, Christiaan, 2009. "Length of life inequality around the globe," Social Science & Medicine, Elsevier, vol. 68(6), pages 1114-1123, March.
    15. Siu Cheung & Jean-Marie Robine & Edward Tu & Graziella Caselli, 2005. "Three dimensions of the survival curve: horizontalization, verticalization, and longevity extension," Demography, Springer;Population Association of America (PAA), vol. 42(2), pages 243-258, May.
    16. Ryan Edwards, 2013. "The cost of uncertain life span," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1485-1522, October.
    17. Jeffrey R. Brown & Amy Finkelstein, 2011. "Insuring Long-Term Care in the United States," Journal of Economic Perspectives, American Economic Association, vol. 25(4), pages 119-142, Fall.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Patrick Meyer & Grégory Ponthiere, 2019. "Threshold Ages for the Relation between Lifetime Entropy and Mortality Risk," Erudite Working Paper 2019-18, Erudite.

    More about this item

    Keywords

    entropy; measurement; mortality risk; longevity; age at death;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hal:psewpa:halshs-01409679. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.