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

Listed author(s):
  • 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 - UEB - Université européenne de Bretagne - 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 - UEB - Université européenne de Bretagne - Télécom Bretagne - Institut Mines-Télécom [Paris])

  • 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-Jourdan Sciences Economiques - 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, PSE - Paris School of Economics)

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.

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Paper provided by HAL in its series PSE Working Papers with number halshs-01409679.

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Date of creation: Dec 2016
Handle: RePEc:hal:psewpa:halshs-01409679
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01409679
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  1. 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.
  2. Väinö Kannisto, 2000. "Measuring the compression of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(6), September.
  3. 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.
  4. Jeffrey Brown & Amy Finkelstein, 2011. "Insuring Long Term Care In the US," NBER Working Papers 17451, National Bureau of Economic Research, Inc.
  5. 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.
  6. 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.
  7. 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.
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