Human lifetime entropy in a historical perspective (1750–2014)

Patrick Meyer () and Gregory Ponthiere
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Patrick Meyer: Lab-STICC_TB_CID_DECIDE - Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance - UEB - Université européenne de Bretagne - European University of Brittany - 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 - ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique, IMT Atlantique - LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l'Information - IMT Atlantique - IMT Atlantique - IMT - Institut Mines-Télécom [Paris], Lab-STICC_IMTA_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 - ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique - UBL - Université Bretagne Loire - IMT Atlantique - IMT Atlantique - IMT - Institut Mines-Télécom [Paris]

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Abstract: This paper uses Shannon's entropy index to the base 2 to quantify the risk relative to the age at death in terms of bits (i.e. the amount of information revealed by tossing a fair coin). We first provide a simple decomposition of Shannon's lifetime entropy index that allows us to analyse the determinants of lifetime entropy (in particular its relation with Wiener's entropy of the event "death at a particular age conditional on survival to that age") and to study how the risk about the duration of life is resolved as the individual becomes older. Then, using data on 37 countries from the Human Mortality Database, we show that, over the last two centuries, (period) lifetime entropy at birth has exhibited, in all countries, an inverted-U shape pattern with a maximum in the first half of the twentieth century (at 6 bits), and reaches, in the early twenty-first century, 5.6 bits for men and 5.5 bits for women. It is also shown that the entropy age profile shifted from a non-monotonic profile (in the eighteenth and nineteenth centuries) to a strictly decreasing profile (in the twentieth and twenty-first centuries).

Date: 2020-01
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Published in Cliometrica, 2020, 14 (1), pp.129-167. ⟨10.1007/s11698-019-00185-y⟩

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Related works:
Journal Article: Human lifetime entropy in a historical perspective (1750–2014) (2020)
Journal Article: Human lifetime entropy in a historical perspective (1750–2014) (2020)
Working Paper: Human lifetime entropy in a historical perspective (1750–2014) (2020)
Working Paper: Human Lifetime Entropy in a Historical Perspective (1750-2014) (2019)
Working Paper: Human Lifetime Entropy in a Historical Perspective (1750-2014) (2016)
Working Paper: Human Lifetime Entropy in a Historical Perspective (1750-2014) (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-02489701

DOI: 10.1007/s11698-019-00185-y

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