How Long Do We Live?: Demographic Models and Reflections on Tempo Effects

280 Pages·2008·2.22 MB·English

by  Elisabetta Barbi (auth.), Professor Elisabetta Barbi, Professor James W. Vaupel, Professor John Bongaarts (eds.)

Demographic Research Monographs
A Series of the Max Planck Institute
for Demographic Research, Rostock, Germany
Editor-in-chief: James W. Vaupel
Demographic Research Monographs
E. Barbi, S. Bertino, E. Sonnino (Eds.)
Inverse Projection Techniques
2004. XI, 137 pages. 978-3-540-20931-7
G. Doblhammer
The Late Life Legacy of Very Early Life
2004. X, 204 pages. 978-3-540-22105-0
R. Rau
Seasonality in Human Mortality
2007. XV, 214 pages. 978-3-540-44900-3
A. Baudisch
Inevitable Aging?
2008. XXI, 170 pages. 978-3-540-76655-1
Elisabetta Barbi · John Bongaarts
James W. Vaupel
Editors
How Long
DoWe Live?
Demographic Models and
Reflections on Tempo Effects
123
Professor Elisabetta Barbi Professor James W. Vaupel
University of Messina Max Planck Institute
Department of Economics, for Demographic Research
Statistics, Mathematics Konrad-Zuse-Straße 1
and Sociology “W. Pareto” 18057 Rostock
Via Tommaso Cannizzaro 278 Germany
98100 Messina
Foreword
How should life expectancy be calculated? More generally, how should life ta-
bles be estimated? Since John Graunt’s pioneering contribution, read before
the Royal Society of London at 6 p.m. on the 27th of February 1661, demogra-
phers have developed better and better methods. Some concerns were raised,
including concerns about how to deal with heterogeneous populations pub-
lished in an article in Demography in 1979 that I wrote with Kenneth Manton
and Eric Stallard. Yet, a few years ago nearly all demographers believed that
as long as the underlying population and death counts were accurate, then
lifetables could be reliably estimated.
John Bongaarts and Griff Feeney launched a revolutionary assault on this
dogma. Two key contributions by them are reprinted in Part I of this mono-
graph. Some very good demographers agreed, as least in part, with Bon-
gaarts’ and Feeney’s radical argument that when death rates are changing,
then tempo effects distort conventional calculations of life expectancy. Other
very good demographers disagreed. So John Bongaarts and I brought some
leading demographers together in a research meeting, co-sponsored by the
Max Planck Institute for Demographic Research and the Population Coun-
cil and held in New York City on November 18 and 19, 2004. Many of the
papers discussed at the workshop, generally after considerable revision, were
published in Demographic Research in 2005 and 2006. Nine of these articles,
in some cases somewhat revised, are published in this monograph: they are
the first seven chapters in Part II and the two chapters in Part III. Some pro-
vide support for the importance of tempo effects; others raise doubts, either
about the general concept or about methods proposed to remove the alleged
distortions.
Five additional contributions are published in this monograph. The In-
troduction, by Elisabetta Barbi, provides an overview of the monograph-and
thinking about tempo effects on mortality. The final chapter in Part II, by
Marc Luy, is a considerably expanded version of a shorter article published in
Demographic Research; it applies tempo methods to study the convergence of
death rates in East vs. West Germany following unification in 1989. The two
VI Foreword
chapters in Part IV are both new. In the first, John Bongaarts and Griff Feeney
share their afterthoughts. In the second, I present four simple examples that
demonstrate how and why mortality change can roil lifetable calculations. Fi-
nally, an Appendix by Jutta Gampe and Anatoli Yashin provides two proofs
of a formula developed by Griff Feeney; this material was previously published
in Demographic Research.
The chapters in this monograph are competently written, but nearly all
of them are difficult to read. The material is complicated, controversial, and
difficult to explain. I finally began to understand tempo effects, and the more
general concept of turbulence in demographic rates, when I worked through
some stylized examples. Some readers of this monograph might, therefore,
want to start with my concluding chapter. Others may find it more satisfying
to experience the developments of ideas by reading the book through from
the beginning.
The series of Demographic Research Monographs is under the editorial su-
pervision of the Max Planck Institute for Demographic Research. I am Editor-
in-Chief. I am advised by an Editorial Board that currently consists of Prof.
Elisabetta Barbi (Messina University, Italy), Prof. Gabriele Doblhammer (Ro-
stock University, Germany), Dr. Jutta Gampe (Max Planck Institute), Prof.
Joshua Goldstein (Max Planck Institute), and Prof. Bernard Jeune (Univer-
sity of Southern Denmark). Additional members of the Editorial Board will
be appointed as needed to review manuscripts submitted for possible publi-
cation. The current manuscript was reviewed and accepted by James Vaupel,
Elisabetta Barbi and Joshua Goldstein.The Editors thank Tobias Strauss for
helping prepare the manuscript for publication.
The Demographic Research Monographs series can be considered the
successor to the series called Odense Monographs on Population Aging,
edited by Bernard Jeune and James Vaupel. The volumes in this now-
terminated series were first published as hardcover books by an academic
publisher, Odense University Press, and subsequently made available online
at www.demogr.mpg.de/books/odense. The nine Odense Monographs on Pop-
ulation Aging include two collections of research articles that focus on specific
subjects on the frontier of demographic research, three volumes by senior re-
searchers that present path-breaking findings, a review of research on a topic
of emerging interest, a presentation of a new method for analysis of demo-
graphic data, an outstanding doctoral dissertation, and a unique collection of
important demographic data on non-human species.
The series of Demographic Research Monographs will continue this mix,
with books that are often under 200 pages in length, that have a clear focus,
and that significantly advance demographic knowledge. Research related to
population aging will continue to be a focus on the series, but it will not
the only one. The series will embrace all of demography, broadly defined.
As indicated by the first volume in the series, an important subject will be
historical demography. We also plan to publish research on fertility and family
dynamics. Mathematical demography is the core of the population sciences
Foreword VII
and we will strive to foster monographs, such as this one, that use mathematics
and statistics to further develop the theories and methods of demography.
Biodemography is a small but rapidly growing and particularly innovative
branch of demography: we will seize opportunities to publish monographs at
the intersection of biology and demography, pertaining both to humans and
other species, and including demographic research with ties to such fields as
epidemiology, genetics, evolutionary biology, life-history biology, experimental
demography, and paleodemography. The previous monograph in the series,
Inevitable Aging? by Annette Baudisch, combines mathematical demography
and biodemography.
Each volume in the Demographic Research Monograph series will have a
substantial link to the Max Planck Institute for Demographic Research. As
well as being published as hardcover books by Springer-Verlag, the volumes
of the Max Planck series of Demographic Research Monographs will subse-
quently be available at www.demogr.mpg.de/books/drm. The online version
may include color graphs, supplemental analyses, databases and other ancil-
lary or enhanced material. Parallel publication online and in print is a signif-
icant innovation that will make the monograph series particularly useful to
scholars and students around the world.
James W. Vaupel
Editor-in-Chief
Contents
How long do we live? Demographic models and reflections on
tempo effects: An introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Elisabetta Barbi
1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Overview of the monograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
I. Theoretical basis for the mortality tempo effect
Estimating mean lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
John Bongaarts, Griffith Feeney
1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
The quantum and tempo of life-cycle events . . . . . . . . . . . . . . . . . . . 29
John Bongaarts, Griffith Feeney
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2 Background: age-specific event rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Period quantum and tempo measures of the 2nd kind . . . . . . . . . . . . . 32
4 Period quantum and tempo measures of the 1st kind . . . . . . . . . . . . . . 46
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
X Contents
II. Critiques, extensions and applications of the mortality tempo
effect
Demographic translation and tempo effects: An accelerated
failure time perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Germa´n Rodr´ıguez
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2 Fertility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3 Mortality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Lifesaving, lifetimes and lifetables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
James W. Vaupel
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2 How saving a life alters life expectancy . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3 Individual lifetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4 The triangle of turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5 How large is the distortion? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6 Considerations about true life expectancy. . . . . . . . . . . . . . . . . . . . . . . . 101
7 A model of stretched lifetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8 Quantum and tempo vs. proportions and increments . . . . . . . . . . . . . . 103
9 Directions for research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Tempo and its tribulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Kenneth W. Wachter
1 Tempo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2 Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3 Representation of M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4 The moving average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5 Period counts of deaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6 Current latent conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7 Total fertility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Tempo effects in mortality: An appraisal . . . . . . . . . . . . . . . . . . . . . . . 129
Michel Guillot
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
2 The existence of tempo effects in mortality . . . . . . . . . . . . . . . . . . . . . . 131
3 Bongaarts and Feeney’s tempo-adjusted life expectancy . . . . . . . . . . . 134
4 Evaluating Bongaarts and Feeney’s “proportionality” assumption . . . 135
5 Bongaarts and Feeney’s definition of changes in period mortality
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6 Assessing indicators of period mortality conditions: e0 vs. CAL . . . . 144
Contents XI
7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Increments to life and mortality tempo . . . . . . . . . . . . . . . . . . . . . . . . 153
Griffith Feeney
1 Time-discrete increments to life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
2 Empirical results: Swedish females, 1751-2002 . . . . . . . . . . . . . . . . . . . 154
3 Time-continuous cohort-indexed increments to life . . . . . . . . . . . . . . . 155
4 Time-continuous period-indexed increments to life . . . . . . . . . . . . . . . . 158
5 Relation between cohort and period increments to life . . . . . . . . . . . . . 159
6 Robustness of the Bongaarts-Feeney tempo adjustment formula . . . . 162
7 Increments to life and mortality tempo: mixed models . . . . . . . . . . . . . 163
8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Mortality tempo versus removal of causes of mortality:
Opposite views leading to different estimations of life
expectancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Herv´e Le Bras
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
2 Decreasing mortality as a sign of delay in deaths . . . . . . . . . . . . . . . . . 168
3 Decreasing mortality as a change in the causes of death . . . . . . . . . . . 170
4 Removing one cause of death: deeper insights . . . . . . . . . . . . . . . . . . . . 171
5 A numerical example of the two methods . . . . . . . . . . . . . . . . . . . . . . . . 172
6 Which life table is the reference table? . . . . . . . . . . . . . . . . . . . . . . . . . . 174
7 Unifying the two views: the repartition function of the delays by
age and duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8 Which is the best model? A discussion of the two methods . . . . . . . . 178
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Tempo effect on age-specific death rates . . . . . . . . . . . . . . . . . . . . . . . 191
Shiro Horiuchi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
2 Intuitive visual explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
3 Mathematical presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Mortality tempo-adjustment: Theoretical considerations and
an empirical application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Marc Luy
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203