DEMOGRAPHIC METHODSMARRIAGE, FERTILITY, AND
MIGRATION MODELSCoale (1971) observed that age distributions of
first marriages are structurally similar in different
populations. These distributions tend to be smooth,
unimodal, and skewed to the right, and to have a
density close to zero below age fifteen and above
age fifty. He also noted that the differences in age-
at-marriage distributions across female popula-
tions are largely accounted for by differences in
their means, standard deviations, and cumulative
values at the older ages, for example, at age fifty.
As a basis for the application of these observations,
Coale constructed a standard schedule of age at
first marriage using data from Sweden, covering
the period 1865 through 1869. The model that is
applied to marriage data is represented by the
following equation:
( 20 )g (a) = 1.2813 exp{–1.145 ( +
E
σa–μ
σ0.805) – exp[ –1.896 ( a–σμ+0.805)]}
where g(a) is the proportion marrying at age a in
the observed population and μ, σ, and E are,
respectively, the mean and the standard deviation
of age at first marriage (for those who ever marry),
and the proportion ever marrying.
The model can be extended to allow for
covariate effects by stipulating a functional rela-
tionship between the parameters of the model
distribution and a set of covariates. This may be
specified as follows:
μi = Xi′ α ′σi = Yi′ β (^) ′
Εi = Zi′ Y (^) ′
( 20 )
where Xi, Yi, and Zi are the vector values of charac-
teristics of an individual that determine, respec-
tively, μi, σi, and Ei, and α, ß, and Y are the
associated parameter vectors to be estimated.
Because the model is parametric, it can be
applied to data referring to cohorts who have yet
to complete their marriage experience. In this
fashion, the model can be used for purposes of
projection (see, e.g., Bloom and Bennett 1990).
The model has also been found to replicate well
the first birth experience of cohorts (see, e.g.,
Bloom 1982).
Coale and Trussell (1974), recognizing the
empirical regularities that exist among age profiles
of fertility across time and space and extending the
work of Louis Henry, developed a set of model
fertility schedules. Their model is based in part on
a reference distribution of age-specific marital
fertility rates that describes the pattern of fertility
in a natural fertility population—that is, one that
exhibits no sign of controlling the extent of child-
bearing activity. When fitted to an observed age
pattern of fertility, the model’s two parameters
describe the overall level of fertility in the popula-
tion and the degree to which their fertility within
marriage is controlled by some means of contra-
ception. Perhaps the greatest use of this model has
been devoted to comparative analyses, which is
facilitated by the two-parameter summary of any
age pattern of fertility in question.
Although the application of indirect demo-
graphic estimation methods to migration analysis
is not as mature as that to other demographic
processes, strategies similar to those invoked by
fertility and mortality researchers have been ap-
plied to the development of model migration sched-
ules. Rogers and Castro (1981) found that similar
age patterns of migration obtained among many
different populations. They have summarized these
regularities in a basic eleven-parameter model,
and, using Brass and Coale logic, explore ways in
which their model can be applied satisfactorily to
data of imperfect quality.
The methods described above comprise only a
small component of the methodological tools avail-
able to demographers and to social scientists, in
general. Some of these methods are more readily
applicable than others to fields outside of demog-
raphy. It is clear, for example, how we may take
advantage of the concept of standardization in a
variety of disciplines. So, too, may we apply life
table analysis and nonstable population analysis to
problems outside the demographic domain. Any
analogue to birth and death processes can be
investigated productively using these central meth-
ods. Even the fundamental concept underlying the
above mortality, fertility, marriage, and migration
models—that is, exploiting the power to be found
in empirical regularities—can be applied fruitfully
to other research endeavors.