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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