Encyclopedia of Sociology

DEMOGRAPHIC METHODS

inadequate to be significantly misleading. For ex-
ample, in some countries we have learned that as
few as half of all actual deaths are recorded. If we
mistakenly assume the value of the actual number
to be the registered number, then we will substan-
tially overestimate life expectancy in these popula-
tions. In essence, we will incorrectly infer that
people are dying at a slower rate than is truly
the case.

The Stable Population Model. Much demo-
graphic estimation has relied on the notion of
stability. A stable population is defined as one that is
established by a long history of unchanging fertili-
ty and mortality patterns. This criterion gives rise
to a fixed proportionate age distribution, constant
birth and death rates, and a constant rate of popu-
lation growth (see, e.g., Coale 1972). The basic
stable population equation is:

c(a) = be-rap(a) (^14 )

where c(a) is the proportion of the population
exact age a, b is the crude birth rate, r is the rate of
population growth, and p(a) is the proportion of
the population surviving to exact age a. Various
mathematical relationships have been shown to
obtain among the demographic variables in a sta-
ble population. This becomes clear when we multi-
ply both sides of the equation by the total popula-
tion size. Thus, we have:

N(a) = Be-rap(a) ( 15 )

where N(a) is the number of individuals in the
population exact age a and B is the current annual
number of births. We can see that the number of
people aged a this year is simply the product of the
number of births entering the population a years
ago—namely, the current number of births times
a growth rate factor, which discounts the births
according to the constant population growth rate,
r (which also applies to the growth of the number
of births over time)—and the proportion of a birth
cohort that survives to be aged a today. Note that
the constancy over time of the mortality schedule,
p(a), and the growth rate, r, are crucial to the
validity of this interpretation.

When we assume a population is stable, we are
imposing structure upon the demographic rela-
tionships existing therein. In a country where data

are inadequate, indirect methods allow us—by

drawing upon the known structure implied by

stability—to piece together sometimes inaccurate

information and ultimately derive sensible esti-

mates of the population parameters. The essential

strategy in indirect demographic estimation is to

infer a value or set of values for a variable whose

elements are either unobserved or inaccurate from

the relationship among the remaining variables in

the above equation (or an equation deriving from

the one above). We find that these techniques are

robust with respect to moderate departures from

stability, as in the case of quasi-stable populations,

in which only fertility has been constant and mor-

tality has been gradually changing.

The Nonstable Population Model. Through-

out much of the time span during which indirect

estimation has evolved, there have been many

countries where populations approximated sta-

bility. In recent decades, however, many countries

have experienced rapidly declining mortality or

declining or fluctuating fertility and, thus, have

undergone a radical departure from stability. Con-

sequently, previously successful indirect methods,

grounded in stable population theory, are, with

greater frequency, ill-suited to the task for which

they were devised. As is often the case, necessity is

the mother of invention and so demographers

have sought to adapt their methodology to the

changing world.

In the early 1980s, a methodology was devel-

oped that can be applied to populations that are

far from stable (see, e.g., Bennett and Horiuchi

1981; and Preston and Coale 1982). Indeed, it is

no longer necessary to invoke the assumption of

stability, if we rely upon the following equation:

c(a) = b. exp [^ - ∫^ r (x) dx]. p (a)

a

0

( 16 )

where r(x) is the growth rate of the population at

exact age x. This equation holds true for any closed

population, and, indeed, can be modified to ac-

commodate populations open to migration.

The implied relationships among the age dis-

tribution of living persons and deaths, and rates of

growth of different age groups, provide the basis

for a wide range of indirect demographic methods

that allow us to infer accurate estimates of basic