DEMOGRAPHYyears? Formal demography answers this question
for aggregates seen as populations. This formal
part of demography is fairly independent of the
traditional social sciences and has a lengthy history
in mathematics and statistics (Smith and Keyfitz
1977; Stone 1997; Desrosières 1998). It depends
on a definition of age and on the relationship of
age to fertility and mortality. Those relationships
certainly are socially conditioned, but their major
outlines are constrained by biology.
Beyond pursuing formal demography, the task
of most social scientist-demographers is detailing
the relationships between demographic change
and other aspects of social change. Working with
concepts, methods, and questions arising from the
traditions of each of the social science disciplines
as well as those of demography per se, schol-
ars have investigated the relationship between
demographic changes and such social changes
as those in the nature of families (Davis 1985;
Sweet and Bumpass 1987; Bumpass 1990; Waite
1995), levels of economic growth (Johnson and
Lee 1987; Nerlove and Raut 1997), the develop-
ment of colonialism (McNeill 1990), changes in
kinship structures (Dyke and Morrill 1980), na-
tionalism and interethnic strife (Tietelbaum and
Winter 1998), and the development of the nation-
state (Watkins 1991).
FORMAL DEMOGRAPHYAt the heart of demography is a body of strong and
useful mathematical theory about how popula-
tions renew themselves (Keyfitz 1968, 1985; Coale
1972; Bourgeois-Pichat 1994). The theory envi-
sions a succession of female birth cohorts living
out their lives subject to a schedule of age-specific
mortality chances and age-specific chances of hav-
ing a female baby. In the simplest form of the
model the age-specific rates are presumed con-
stant from year to year.
Each new annual birth cohort is created be-
cause the age-specific fertility rates affect women
in earlier birth cohorts who have come to a specific
age in the year in question. Thus, the mothers of a
new cohort of babies are spread among previous
cohorts. The size of the new cohort is a weighted
average of the age-specific fertility rates. The sizes
of preceding cohorts, survived to the year in ques-
tion, are the weights.
As a cohort of women age through their fertile
period, they die and have children in successive
years according to the age-specific rates appropri-
ate to those years. Thus, the children of a single
birth cohort of women are spread over a sequence
of succeeding birth cohorts.The number of girls ever born to a birth
cohort, taken as a ratio to the initial size of the
cohort, is implicit in the age-specific fertility and
mortality rates. This ratio, called the net reproduc-
tion rate, describes the growth rate over a genera-
tion that is implicit in the age-specific rates. The
length of this generation is also implicit in the age-
specific rates as the average age of mothers at the
birth of the second-generation daughters. With a
rate of increase over a generation and a length of
the generation, it is clear that an annual rate of
increase is intrinsic to the age-specific rates.The distribution of the children of a birth
cohort over a series of succeeding cohorts has an
important effect. If an unusually small or large
birth cohort is created, the effects of its largeness
or smallness will be distributed among a number
of succeeding cohorts. In each of those succeeding
cohorts, the effect of the unusual cohort is aver-
aged with that of other birth cohorts to create the
new cohort’s size. Those new cohorts’ ‘‘inherited’’
smallness or largeness, now diminished by averag-
ing, will also be spread over succeeding cohorts. In
a few generations the smallness or largeness will
have averaged out and no reflection of the initial
disturbance will be apparent.Thus, without regard to peculiarities in the
initial age distribution, the eventual age distribu-
tion of a population experiencing fixed age-specif-
ic fertility and mortality will become proportion-
ately constant. As this happens, the population will
take on a fixed aggregate birth and death rate and,
consequently, a fixed rate of increase. The popula-
tion so created is called a stable population and its
rates, called intrinsic rates, are those implicit in the
net reproduction rate and the length of a genera-
tion. Such rates, as well as the net reproduction
rates, are frequently calculated for the age-specific
fertility and mortality rates occurring for a single
year as a kind of descriptive, ‘‘what if’’ summary.This theory is elaborated in a number of ways.
In one variant, age-specific rates are not constant
but change in a fixed way (Lopez 1961). In another