CAUSAL INFERENCE MODELSthere is no p 21 in the model, so that r 12 cannot be
decomposed. Its value of 0.516 has been inserted
into the diagram, however. The implication of a
failure to commit oneself on the direction of cau-
sation between these two variables is that decom-
positions of subsequent rij will involve expressions
that are sometimes combinations of the relevant
p’s and the unexplained association between fa-
ther’s education and occupation. This, in turn,
means that the indirect effects of one of these
variables ‘‘through’’ the other cannot be assessed.
One can determine the direct effects of, say, fa-
ther’s occupation on respondent’s education, or
its indirect effects on occupation in 1962 through
first job, but not ‘‘through’’ father’s education. If
one had, instead, committed oneself to the direc-
tional flow from father’s education to father’s
occupation, a not unreasonable assumption, then
all indirect effects and spurious connections could
be evaluated. Sometimes it is indeed necessary to
make use of double-headed arrows when the direc-
tion of causation among the most causally prior
variables cannot be specified, but one then gives
up the ability to trace out those indirect effects or
spurious associations that involve these unexplained
correlations.
The second feature of the Blau-Duncan dia-
gram worth noting involves the small, unattached
arrows coming into each of the ‘‘dependent’’ vari-
ables in the model. These of course represent the
disturbance terms, which in a correctly specified
model are taken to be uncorrelated. But the magni-
tudes of these effects of outside variables are also
provided in the diagram to indicate just how much
variance remains unexplained by the model. Each
of the numerical values of path coefficients com-
ing in from these outside variables, when squared,
turns out to be the equivalent of 1 − R^2 , or the
variances that remain unexplained by all of the
included explanatory variables. Thus there is con-
siderable unexplained variance in respondent’s
education (0.738), first job (0.669), and occupa-
tion in 1962 (0.567), indicating, of course, plenty
of room for other factors to operate. The chal-
lenge then becomes that of locating additional
variables to improve the explanatory value of the
model. This has, indeed, been an important stimu-
lus to the development of the status attainment
literature that the Blau-Duncan study subsequent-
ly spawned.
The placement of numerical values in such
path diagrams enables the reader to assess, rather
easily, the relative magnitudes of the several direct
effects. Thus, father’s education is inferred to have
a moderately strong direct effect on respondent’s
education, but none on the respondent’s occupa-
tional status. Father’s occupation is estimated to
have somewhat weaker direct effects on both re-
spondent’s education and first job but a much
weaker direct effect on his later occupation. The
direct effects of respondent’s education on first
job are estimated to be only somewhat stronger
than those on the subsequent occupation, with
first job controlled. In evaluating these numerical
values, however, one must keep in mind that all
variables have been expressed in standard devia-
tion units rather than some ‘‘natural’’ unit such as
years of schooling. This in turn means that if
variances for, say, men and women or blacks and
whites are not the same, then comparisons across
samples should be made in terms of unstandardized,
rather than standardized, coefficients.SIMULTANEOUS EQUATION MODELSRecursive modeling requires one to make rather
strong assumptions about temporal sequences.
This does not, in itself, rule out the possibility of
reciprocal causation provided that lag periods can
be specified. For example, the actions of party A
may affect the later behaviors of party B, which in
turn affect still later reactions of the first party.
Ideally, if one could watch a dynamic interaction
process such as that among family members, and
accurately record the temporal sequences, one
could specify a recursive model in which the be-
haviors of the same individual could be represent-
ed by distinct variables that have been temporally
ordered. Indeed Strotz and Wold (1960) have
cogently argued that many simultaneous equation
models appearing in the econometric literature
have been misspecified precisely because they do
not capture such dynamic features, which in causal
models should ideally involve specified lag peri-
ods. For example, prices and quantities of goods
do not simply ‘‘seek equilibrium.’’ Instead, there
are at least three kinds of autonomous actors—
producers, customers, and retailers or wholesal-
ers—who react to one another’s behaviors with
varying lag periods.