Human lifetime entropy in a historical perspective (1750–2014)
Patrick Meyer
(1, 2, 3)
,
Grégory Ponthière
(4, 5, 6)
1
Lab-STICC_TB_CID_DECIDE
2 IMT Atlantique - LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l'Information
3 Lab-STICC_IMTA_CID_DECIDE
4 PSE - Paris School of Economics
5 ERUDITE - Equipe de Recherche sur l’Utilisation des Données Individuelles en lien avec la Théorie Economique
6 PJSE - Paris Jourdan Sciences Economiques
2 IMT Atlantique - LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l'Information
3 Lab-STICC_IMTA_CID_DECIDE
4 PSE - Paris School of Economics
5 ERUDITE - Equipe de Recherche sur l’Utilisation des Données Individuelles en lien avec la Théorie Economique
6 PJSE - Paris Jourdan Sciences Economiques
Patrick Meyer
- Fonction : Auteur
- PersonId : 14546
- IdHAL : patrick-meyer
- ORCID : 0000-0001-6479-213X
- IdRef : 19306846X
Grégory Ponthière
- Fonction : Auteur
- PersonId : 1129355
- ORCID : 0000-0002-7328-4441
- IdRef : 189782714
Résumé
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).
Domaines
Economies et financesFormat du dépôt | Notice |
---|---|
Type de dépôt | Article dans une revue |
Titre |
en
Human lifetime entropy in a historical perspective (1750–2014)
|
Résumé |
en
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).
|
Auteur(s) |
Patrick Meyer
1, 2, 3
, Grégory Ponthière
4, 5, 6
1
Lab-STICC_TB_CID_DECIDE
( 390402 )
- France
2
IMT Atlantique - LUSSI -
Département Logique des Usages, Sciences sociales et Sciences de l'Information
( 490128 )
- IMT Atlantique - Campus de Brest :-Technopôle Brest-Iroise CS 8381829238 BREST Cedex 3
- France
3
Lab-STICC_IMTA_CID_DECIDE
( 486354 )
- Technopole Brest Iroise CS 83818 29238 BREST CEDEX 3
- France
4
PSE -
Paris School of Economics
( 301309 )
- 48 boulevard Jourdan 75014 Paris
- France
5
ERUDITE -
Equipe de Recherche sur l’Utilisation des Données Individuelles en lien avec la Théorie Economique
( 74242 )
- UPEM, 5 boulevard Descartes, 77454 Marne-la-Vallée CEDEX 2
UPEC - Faculté de sciences économiques et de gestion
Mail des mèches Rue Poète et Sellier 94010 Créteil Cedex
- France
6
PJSE -
Paris Jourdan Sciences Economiques
( 578027 )
- 48 boulevard Jourdan 75014 Paris
- France
|
Langue du document |
Anglais
|
Nom de la revue |
|
Vulgarisation |
Non
|
Comité de lecture |
Oui
|
Audience |
Internationale
|
Date de publication |
2020-01
|
Volume |
14
|
Numéro |
1
|
Page/Identifiant |
129-167
|
Domaine(s) |
|
DOI | 10.1007/s11698-019-00185-y |
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