DEMOGRAPHIC METHODSdemographic parameters that ultimately can be
used to better inform policy on a variety of issues.
Two examples are as follows.
First, suppose we have the age distribution for
a country at each of two points in time, in addition
to the age distribution of deaths occurring during
the intervening years. We may then estimate the
completeness of death registration in that popula-
tion using the following equation (Bennett and
Horiuchi 1981):
N(a) = ∫^ D (x) exp [ ∫ r (u) du] dx
∞ x
aa~ ( 17 )where (a) is the estimated number of people at
exact age a, D(x) is the number of deaths at exact
age x and r(u) is the rate of the growth of the
number of persons at exact age u between the two
time points. By taking the ratio of the estimated
number of persons with the enumerated popula-
tion, we have an estimate of the completeness of
death registration in the population relative to the
completeness of the enumerated population. This
relative completeness (in contrast to an ‘‘absolute’’
estimate of completeness) is all that is needed to
determine the true, unobserved age-specific death
rates, which in turn allows one to construct an
unbiased life table.
A second example of the utility of the nonstable
population framework is shown by the use of the
following equation:
N (x)
N (a)
= x-apa exp [^ ∫^ r (u) du]x
a( 18 )where N(x) and N(a) are the number of people
exact ages x and a, respectively, and x−apa is the
probability of surviving from age a to age x accord-
ing to period mortality rates. By using variants of
this equation, we can generate reliable population
age distributions (e.g., in situations in which cen-
suses are of poor quality) from a trustworthy life
table (Bennett and Garson 1983).
MORTALITY MODELINGThe field of demography has a long tradition of
developing models that are based upon empirical
regularities. Typically in demographic modeling,
as in all kinds of modeling, we try to adhere to the
principle of parsimony—that is, we want to be as
efficient as possible with regard to the detail, and
therefore the number of parameters, in a model.
Mortality schedules from around the world
reveal that death rates follow a common pattern of
relatively high rates of infant mortality, rates that
decline through early childhood until they bottom
out in the age range of five to fifteen or so, then
rates that increase slowly through the young and
middle adult years, and finally rising more rapidly
during the older adult ages beyond the forties or
fifties. Various mortality models exploit this regu-
lar pattern in the data. Countries differ with re-
spect to the overall level of mortality, as reflected
in the expectation of life at birth, and the precise
relationship that exists among the different age
components of the mortality curve.Coale and Demeny (1983) examined 192 mor-
tality schedules from different times and regions
of the world and found that they could be catego-
rized into four ‘‘families’’ of life tables. Although
overall mortality levels might differ, within each
family the relationships among the various age
components of mortality were shown to be similar.
For each family, Coale and Demeny constructed a
‘‘model life table’’ for females that was associated
with each of twenty-five expectations of life at birth
from twenty through eighty. A comparable set of
tables was developed for males. In essence, a re-
searcher can match bits of information that are
known to be accurate in a population with the
corresponding values in the model life tables, and
ultimately derive a detailed life table for the popu-
lation under study. In less developed countries,
model life tables are often used to estimate basic
mortality parameters, such as e 0 or the crude death
rate, from other mortality indicators that may be
more easily observable.Other mortality models have been developed,
the most notable being that by Brass (1971). Brass
noted that one mortality schedule could be related
to another by means of a linear transformation of
the logits of their respective survivorship proba-
bilities (i.e., the vector of lx values, given a radix of
one). Thus, one may generate a life table by apply-
ing the logit system to a ‘‘standard’’ or ‘‘reference’’
life table, given an appropriate pair of parameters
that reflect (l) the overall level of mortality in the
population under study, and (2) the relationship
between child and adult mortality.