DIFFERENTIAL FERTILITY, IQ, AND EQUILIBRIUM: EXPLAINED SIMPLY
Julian L. Simon
Samuel Preston and Cameron Campbell (1993) show that differ-
ential fertility cannot drive down IQ indefinitely, but instead
some equilibrium level is reached. This conclusion is important
and provocative. But others may share my difficulty absorbing
their results because the underlying process is complex. The
following intuitive verbal explanation may therefore be useful,
together with a simple equilibrium table presented by I. J. Good.
The central result in the Preston and Campbell model follows
from two realistic assumptions: 1) There is some variability in
the IQ of children relative to that of parents; this variability
is the key element in Francis Galton's discussion of intelli-
gence. The extent of the dependence of a child's IQ on that of
the parents may be large or it may be zero for the purposes of
the P-C model. 2) There is some floor underneath IQ. This floor
could be at (say) IQ 70, below which people do not reproduce, or
it could be zero.
Imagine that everyone in some generation 1 starts in the
lowest IQ category, so that a further fall in IQ is impossible.
When couples have children there will be some variability in the
IQ of offspring. This implies that some children in generation 2
must have IQs higher than their parents have. Generation 2 must
therefore have a higher average than generation 1.
Some children in generation 3 have IQs higher than do their
parents in generation 2, but others have IQs lower than do their
parents, so it is unknown whether the average IQ of generation 3
is higher than that of generation 2. But the average of genera-
tion 3 must be higher than that of generation 1.
The above argument implies that average IQ cannot be driven
down to the lowest possible individual IQ, no matter what matter
what the fertility structure.
Nothing said so far proves that there must be some stable
equilibrium above the floor IQ; there could be continuing varia-
tion in the average. But if one accepts that there is some
ceiling on the process - either by analogy to the floor assumed
above, or because one believes (as do the writers who Preston and
Campbell address themselves to) that there exists an inverse
relationship between fertility and income, as well as an inverse
relationship between income and IQ, a combination that would
exert pressure downwards on average IQ - then one at least
believes that the variation in the average is bounded, and that
there exists some sort of cyclic or chaotic equilibrium. And
unless one has reason to believe that the process is indeed a
chaotic one - which would require two opposed forces balanced in
particular feedback form - and if one assumes that the parameters
remain fixed, it seems reasonable that the process should move
toward the stable equilibrium that Preston and Campbell derive.
Good (1968) illustrates the equilibrating process. Under
the heading of "Fallacies, Statistical" in The Encyclopedia of
the Social Sciences, Good included the proposition that "if
intelligent people tend to have fewer children than less
intelligent people and that the level of intelligence is
hereditary... the average level of intelligence will necessarily
decline". His proof that this is a fallacy runs as follows:
Imagine a population in which 10 per cent of men are
intelligent and 90 per cent are unintelligent and that,
on the average, 100 intelligent fathers have 46 kids,
of whom 28 are intelligent and 18 unintelligent, where-
as 100 unintelligent fathers have 106 sons, of whom 98
are unintelligent and 8 are intelligent. It will be
seen from Table 1 that the proportion of intelligent
males would remain steady in expectation (1968, p.
297).
Table 1 - Hypothetical proportions of intelligent and
unintelligent sons
SONS
Intelligent Unintelligent
100 intelligent 28 18
FATHERS
900 unintelligent 72 882
Total 100 900
It is hoped that taken together, the simulation by Preston
and Campbell, Good's simple equilibrium model, and the verbal
explanation given above will give the lie to what Good properly
calls a fallachy.
REFERENCE
Good, I. J. "Fallacies, Statistical" International
Encyclopedia of the Social Sciences, Vol 5 (New York: Macmillan
and Free Press, 1968), pp. 292-301,
Preston, Samuel H., and Cameron Campbell, "Differential
Fertility and the Distribution of Traits: The Case of IQ",
American Journal of Sociology, March, 1993.
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