M. Sánchez-Romero, D. Ediev, G. Feichtinger, A. Fürnkranz-Prskawetz:

"How many old people have ever lived?";

Demographic Research,36(2017), 54; S. 1667 - 1702.

BACKGROUND

Uninformed generalizations about how many elderly people have ever lived, based on a

poor understanding of demography, are found in a surprising number of important publications.

OBJECTIVE

We extend the methodology applied to the controversial question "how many people have

ever been born?" initiated by Fucks, Winkler, and Keyfitz, to the proportion of people

who have ever reached a certain age y and are alive today (denoted as π(y, T)).

METHODS

We first analyze the fraction π(y, T) by using demographic data based on UN estimates.

Second, we show the main mathematical properties of π(y, T) by age and over time.

Third, we complete our analysis by using alternative population models.

RESULTS

We estimate that the proportion who have ever been over 65 that are alive today (as of

2010) ranges between 5.5 and 9.5%. We extend the formal demographic literature by

considering the fraction of interest in two frequently referred models: the stable and

hyperbolic growth populations.

1 Wittgenstein Centre for Demography and Global Human Capital (IIASA,VID/OAW, WU). ¨

E-Mail: miguel.sanchez@oeaw.ac.at.

2 North Caucasian State Humanitarian Technological Academy (IAMIT), Lomonosov Moscow State University

(HSMSS/Demography Department), Wittgenstein Centre for Demography and Global Human Capital

(IIASA,VID/OAW, WU). E-Mail: ediev@iiasa.ac.at. ¨

3 Vienna University of Technology (TU Wien), Wittgenstein Centre for Demography and Global Human Capital

(IIASA,VID/OAW, WU). E-Mail: gustav.feichtinger@tuwien.ac.at. ¨

4 Vienna University of Technology (TU Wien), Wittgenstein Centre for Demography and Global Human Capital

(IIASA,VID/OAW, WU). E-Mail: afp@econ.tuwien.ac.at. ¨

http://www.demographic-research.org 1667

Sanchez-Romero et al. ´ : How many old people have ever lived?

CONCLUSIONS

We show that statements claiming half of all people who have ever reached the age of

65 are alive today ranges would never be attainable, neither theoretically nor empirically,

according to existing data.

CONTRIBUTION

We have produced for the first time a harmonized reconstruction of the human population

by age throughout history. For a given contemporaneous time T, we demonstrate analytically

and numerically that π(y, T) is nonmonotonic in age y. For a given age y, we show

that π(y, T) may also be nonmonotonic with respect to T.

people ever lived/elder/population ageing/formal demography

http://dx.doi.org/10.4054/DemRes.2017.36.54

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.