Applied Mathematical Demography

460 Pages·1985·8.29 MB·English

by  Nathan Keyfitz (auth.)

Springer Texts in Statistics
Advisors:
Stephen Fienberg Ingram Olkin
Nathan Keyfitz
Applied Mathematical
DeInography
Second Edition
With 41 Illustrations
Springer Science+Business Media, LLC
Nathan Keyfitz
IIASA
A-2361 Laxenburg
Austria
Series Advisors
Stephen Fienberg Ingram Olkin
Department of Statistics Department of Statistics
Carnegie-Melon University Stanford University
Pittsburgh, PA 15213 Stanford, CA 94305
U.S.A. U.S.A.
AMS Subject Classifications: 92A15, 62P99
Library of Congress Cataloging in Publication Data
Keyfitz, Nathan
Applied mathematical demography.
(Springer texts in statistics)
Bibliography: p.
Includes index.
1. Demography - Mathematical models. 1. Title.
II. Series.
HB849.51.K49 1985 304.6'01'51 85-16430
© 1985 by Springer Science+Business Media New York
Originally published by Springer-Verlag Berlin Heidelberg New York Tokyo in 1985
Softcover reprint ofthe hardcover 2nd edition 1985
AII rights reserved. No part of this book may be translated or reproduced in any
form without written permission from Springer Science+Business Media, LLC.
Typeset by J. W. Arrowsmith Ud., Bristol, England.
987 6 543 2
ISBN 978-1-4757-1881-2 ISBN 978-1-4757-1879-9 (eBook)
DOI 10.1007/978-1-4757-1879-9
To the students at Chicago, Berkeley, and Harvard
who are responsible for any merit this book may have
PREFACE TO THE SPRINGER EDITION
What follows is a new edition of the second in a series of three books
providing an account of the mathematical development of demography.
The first, Introduction to the Mathematics of Population (Addison-Wesley,
1968), gave the mathematical background. The second, the original of the
present volume, was concerned with demography itself. The third in the
sequence, Mathematics Through Problems (with John Beekman; Springer
Verlag, 1982), supplemented the first two with an ordered sequence of
problems and answers.
Readers interested in the mathematics may consult the earlier book,
republished with revisions by Addison-Wesley in 1977 and still in print.
There is no overlap in subject matter between Applied Mathematical
Demography and the Introduction to the Mathematics of Population. Three
new chapters have been added, dealing with matters that have come recently
into the demographic limelight: multi-state calculations, family demogra
phy, and heterogeneity.
vii
PREFACE
This book is concerned with commonsense questions about, for instance,
the effect of a lowered death rate on the proportion of old people or the
effect of abortions on the birth rate. The answers that it reaches are not
always commonsense, and we will meet instances in which intuition has to
be adjusted to accord with what the mathematics shows to be the case.
Even when the intuitive answer gives the right direction of an effect,
technical analysis is still needed to estimate its amount. We may see
intuitively that the drop from an increasing to a stationary population will
slow the promotion for the average person in a factory or office, but
nothing short of an integral equation can show that each drop of I percent
in the rate of increase will delay promotion to middle-level positions by 2.3
years.
The aim has been to find answers that will be serviceable to those
working on population and related matters, whether or not they care to go
deeply into the mathematics behind the answers. My earlier book, In
troduction to the Mathematics of Population, had the opposite purpose of
developing the theory, and mentioned applications mostly to illuminate the
theory. Because of their different objectives there is virtually no overlap
between the two books.
Population theory has developed at a sufficiently fast rate and in enough
directions that no book of reasonable size can include all of its applica
tions. A full development of theory ought to recognize not only age
specific rates of birth and death but also two sexes and two or more
species. Age-specific rates can vary through time, and the theory can be
stochastic in allowing to each individual member of the population his own
separate risk, or deterministic in supposing that whatever probability
applies to each individual is also the fraction of the population that
succumbs to the risk. Thus population theory can be classified into the 16
categories shown in the accompanying table. By far the largest part of
viii
Preface ix
what is taken up in this book falls into the upper left category: it deals with
one sex, usually female, and one species, man; it takes the age-specific
rates of birth and death as fixed through time; it is deterministic rather
than stochastic. This upper left-hand cell is conceptually the simplest of the
16, and it is mathematically the most tractable. But are these decisive
arguments for its emphasis, given that real populations include two sexes;
human populations interact with other species; birth and death rates
change through time; and all life is stochastic?
Classification of population theory
Fixed rate Changing rate
Deterministic Stochastic Deterministic Stochastic
One sex
One species *
Two or more species
Two sexes
One species
Two or more species
The art of theory construction is to start with simple assumptions and then
to introduce greater realism, which means more complexity, as required.
On the path from simplicity to realism one must stop at a compromise
point. My taste may not always be that of my readers; they may often say
that a particular model I use is too simple, that they need to take into
account factors that I neglect. This line of criticism is welcome, even
though it leads to further and more difficult mathematics.
During 10 or more years of work on this book I have incurred more
obligations than I can acknowledge or even remember. Students pointed
out errors and obscurities; they helped in some cases by conspicuously
failing to understand what I was saying and compelling me to think the
matter through afresh. Colleagues looked at drafts and were generous with
comments. Editors and referees of journals were helpful, especially Paul
Demeny. No one is responsible for errors that remain but me.
Among these colleagues, students and correspondents who have been a
source of ideas and a means of correcting errors, I recall especially William
Alonso, Barbara Anderson, Brian Arthur, John C. Barrett, Ansley J. Coale,
William Cochrane, Joel E. Cohen, Prithwis Das Gupta, Paul Demeny,
Lloyd Demetrius, James Dobbins, Barry Edmonston, Jamie Eng, Thomas
Espenshade, Nora Federici, Griffith Feeney, Gustav Feichtinger, Jair
Fereira-Santos, James Frauenthal, A. G. Fredrickson, Robert Gardiner,
Campbell Gibson, Noreen Goldman, Antonio Golini, David Goodman,
x Preface
Leo A. Goodman, Louis Henry, Jan Hoem, Barbara Keyfitz, S. Krish
namoorthy, Paul Kwong, Juan Carlos Lerda, John Lew, Gary Littman,
Robert Lundy, James G. March, Robert Mare, George Masnick, John
McDonald, David McFarland, Geoffrey McNicoll, Paul Meier, Jane
Menken, Walter Meyer, George C. Myers, Frank Oechsli, Beresford
Parlett, James Pick, Robert G. Potter, Jr., Samuel H. Preston, Thomas
Pullum, Robert Retherford, Roger Revelle, Andrei Rogers, Norman
Ryder, Paul Samuelson, Robert Sembi ring, David P. Smith, Leroy O.
Stone, Richard Stone, Michael Stoto, Michael Teitelbaum, Harold A.
Thomas, Robert Traxler, James Trussell, Etienne Van de Walle, Kenneth
Wachter, Frans Willekens and Harrison White, everyone of whom has
had some effect on the book. To be singled out especially for their help in
the final stages are Noreen Goldman, David P. Smith, Gary Littman, S.
Krishnamoorthy, and Michael Stoto, who read much of the manuscript
and all of the page proof.
The most important acknowledgment is to my wife, who edited and
typed the manuscript, some parts of it many times.
NATHAN KEYFITZ
Cambridge. Massachusetts
February 1977
NOTE. Conventions in the printing of this book include parentheses around references to
equations when these are used independently of any descriptive term-"We see from (1.1.1)
that ... "-and omission of parentheses when the number is in apposition to such words as
"equation." and "expression"-"Expression 1.1.1 is ... :.
ACKNOWLEDGMENTS
An early version of Section 1.3 appeared as "How many people have lived
on the earth?" Demography 3: 581-582 (1966).
Section 1.9 was published as "A general condition for stability in
demographic processes," Canadian Studies in Population 1: 29-35 (1974).
The life table method of Chapter 2 first appeared as "An improved life
table method," Biometrics 31: 889-899 (1975) (with James Frauenthal).
Much of Chapter 3 was included in "Mortality comparisons: The
male-female ratio," Genus 31: 1-34 (1975) (with Antonio Golini).
Section 4.8 is a condensed version of "Individual mobility in a stationary
population," Population Studies 27: 335-352 (1973).
Some of Section 6.5 appeared in "Migration as a means of population
control," Population Studies 25: 63-72 (1971).
Section 6.6 is an abridged version of "On the momentum of population
growth," Demography 8: 71-80 (1971).
Parts of Section 7.3 were published as "Age distribution and the stable
equivalent," Demography 6: 261-269 (1969).
Some parts of Chapter 8, as we\1 as Section 9.3, were included in "On
future population," Journal of the American Statistical Association 67:
347-363 (1972).
Section 9.5 is an abridged version of "Backward population projection
by a generalized inverse," Theoretical Population Biology 6: 135-142 (1974)
(with T. N. E. Grevi\1e).
The substance of Sections 9.10 and 9.11 was included in "Population
waves," in Population Dynamics (edited by T. N. E. Grevi\1e), Academic
Press, 1972, pp. 1-38.
Parts of Chapter 10 are from "Family formation and the frequency of
various kinship relationships." Theoretical Population Biology 5: 1-27
(1974) (with Leo A. Goodman and Thomas W. Pu\1um). and "Addendum:
Family formation and the frequency of various kinship relationships,"
xi
xii Acknowledgments
Theoretical Population Biology 8: 376-381 (1975) (with Leo A. Goodman
and Thomas W. Pullum).
An early statement of Section 11.1 appeared as "How birth control
affects births," Social Biology 18: 109-121 (1971).
Chapter 12 is reprinted with some modifications from "How do we
know the facts of demography?" Population and Development Review 1:
267-288 (1975).