Subject:Re: Family Income Distribution Changes past 2 decades - not pretty 
       Date: Fri, 02 Jan 1998 22:53:48 GMT 
       From: OldNasty@mindspring.com (Grinch)
    
 Newsgroups: alt.politics, alt.politics.economics, sci.econ, 
worldnet.topics.family
 

Before becoming alarmed about trends in income distribution, it is a
worthwhile exercise to ask: "What would be the nature of income
distribution in an 'ideal' society?"
    Without doing this, you can't really make any qualitative judgment
about income distribution in real society.  Maybe the ideal income
distribution is closer to the real one than you think.  Without
examining the question, how do you know?

We can try a thought experiment by describing an "ideal" society and
seeing the kind of income distribution it implies when measured in
"quintiles" --  the most common method of measurement used by the
Census and others, so often cited in the press and Usenet posts.

Let's start with a society where all members are really *exactly*
equal -- a society of termites, perhaps. (After the queen has been
deposed, of course. Call this "the allegory of the termites" if you
wish.)
      Say that one generation of termites is hatched each year,
promptly sets off to work for 36 years (long-lived bugs these are)
then promptly dies. The population is absolutely stable, with the
numbers of new termites hatching and 36-year-old ones dying being
exactly the same each year. Each termite does exactly the same work,
and each receives income matching the productive value of its work.
      Obviously, income is the same for all -- so a Census-like
"quintile" analysis shows perfect equality for all five income
quintiles of termite society.

      But this isn't really a satisfactory model for humans, because
the society is stagnant. There is no growth or progress. Without
progress, we could all be experiencing economic equality while still
living in caves, picking berries, and hunting with sharpened sticks
throughout hard, short lives.

      So let's make one small change: Let the termites become capable
of *learning* over their lives, so each increases its productivity by,
say, 2% every year after it is born (first-year productivity remaining
unchanged because they haven't learned anything yet).
      A 35-year transition period ensues, as the first generation of
hatchlings to learn reaches its maximum old age and the limits of
termite knowledge.  Thereafter, termite society becomes unchanging
again.
      After this point, the oldest termites will be twice as
productive as the youngest and thus will have twice the income
(1.02^35 = 2), and each termite's lifetime income will have increased
about 50%.  So the society as a whole will be 50% wealthier as well.
      Also, each termite to be hatched forever after will have
*exactly the same* lifetime income as every other -- you can't get
more equal than that.
      However, when you apply Census-like "quintile" analysis you find
that significant income inequality has appeared in termite society.
The top quintile has 77% more income than the bottom quintile.  If you
equate an increase in quintile income inequality with injustice, you
will conclude that our termite society has become unjust.
     Surely most people would believe that increasing everyone's
lifetime income by 50% while maintaining perfect income equality is a
*good* thing -- but our quintile analysis says the opposite.

     Be that as it may, our termite society still is not a
satisfactory model for humans, because after one termite lifetime of
progress it has returned to stagnation.  We may have gotten out of our
caves, but not very far out, and we are progressing no further.

       So let's make one more small change: Let termite society become
capable of *accumulating* learning, so the amount that each termite
learns each year itself increases by 2%, and let this process continue
indefinitely.
       This creates a society where each generation of children will
have a better life than their parents. True equality is sacrificed to
the extent that the children will have more -- but I think most people
would consider this to be good rather than bad.  Moreover, *perfect*
income equality can be maintained among the members of each
generation.  And equity among different generations can be maintained
by having each's gain relative to its predecessor be exactly the same.
      I think a fair number of people would accept this as an "ideal"
model for income distribution.

      Putting it into practice with our termites, we find that as the
termites build on their predecessors' accumulated knowledge, the size
of the "step" increase in productivity between each termite generation
grows 2% annually, and this process continues indefinitely into the
future.
     (Originally, one-year-old termites are 1.02 times as productive
as hatchlings. In the first year of accumulating knowledge,
one-year-olds are 1.0204 times as productive as hatchlings.  In the
second year they are 1.0208 times as productive, and so on. The same
effect is seen at older ages, so productivity gains compound up as
termites grow older, and out over the years as termite society becomes
more productive as a whole.)
      The result is that the productivity of the oldest termites
starts increasing again -- and so does their income. After another 35
years or so, the oldest termites have *three times* the income of the
youngest, and lifetime income *double* that of their original ignorant
ancestors.
      Still, every member of every generation has *exactly the same*
lifetime income.  But now, each termite generation will have more
income than the generation that preceded it, as their society's income
increases perpetually.

     It seems we have attained our income distribution "ideal" --
perfect income equality among peers ... perpetual growth, so each
generation will be wealthier than its predecessor  ... and equity
between generations, as each will be richer than its predecessor by
exactly the same percentage amount.

     But when we apply "quintile" income distribution analysis we
find, alas, our society has grown *far* more unequal and unjust.  The
income of the top quintile has now grown to 2½  times that of the
bottom quintile.
     Even worse, the top quintile is pulling away from the bottom
quintile at an *accelerating* rate. The richer society becomes,  the
more dramatic the growth of income inequality by quintile becomes.  If
income growth continues indefinitely,  inequality between income
quintiles will grow indefinitely, ever and ever faster  -- even though
the income distribution is "ideal", and the society is marching
towards unbounded wealth fairly shared by all.

      What this little scenario demonstrates is that the proper way to
use income as a measure of welfare inequality is by comparing the
*lifetime incomes* of individuals in different situations -- and not
by lining up people in order of how much income they have at any one
point in time and comparing the difference between those at the front
of the line and those at the rear.

      In an economy that is experiencing growth in productivity and
income, "quintile" income comparisons produce inherently distorted
results by not adjusting for age and future earnings.
      Those who are really the *richest* (the youngest, who have the
greatest lifetime incomes) are treated as if they are the *poorest*
(because they have less current income than older persons, who have
less lifetime income). This distortion grows every year, even with an
"ideal" income distribution.

      This is not a mere theoretical observation.  It has a real
impact on national income statistics.  A recent paper published by the
Federal Reserve shows that even if income inequality is *completely
eliminated*  among persons of equal age and education (men and women,
whites and minorities, etc.), inequality among income quintiles will
continue to *grow* during coming years due solely to demographic
changes and the rising productivity that results from increased
education.  (I'll post the URL to this when I get back to my office.)
       Static quintile comparisons don't reveal the dynamic forces
that are driving the quintiles apart, and so lead uninformed observers
to assume that the widening gap between quintiles must be a sign of
something bad rather than something good.  I'd propose this as a prime
example of Mr. Conover's "snapshot fallacy".
      
      Quintile income figures are used much more commonly than
"lifetime" figures simply because they are much easier to get -- go to
the Census web page and there they are.  Also, they *seem* to tell an
obvious story that anyone can understand without much thought.
      Lifetime figures are harder to compute because no one knows the
future, so you have to make some projections and assumptions.   That
makes them seem speculative to some.
      But that's no excuse for being blind to the inherent bias in
static quintile income analysis, or for jumping to sweeping
conclusions on the basis of it without fully comprehending what one is
talking about.

       (Further simple adjustments to our termite society to make it
more "realistic" would also make it more unequal.  Say that the
population is growing so there are more young termites than old, or
that old termites have extended retirements during which they consume
ample savings not included in their incomes. Factors like these
broaden the measured gap between income quintiles while having *no*
effect on any termite's lifetime income or on the real distribution of
income among them -- another statistical illusion that makes things
appear worse than they are.)
 
       Of course, we live in a far from "ideal" society, and there are
whole range of other factors that act to widen or close the observed
quintile income gap, for good and ill.  I'll mention some of these in
another post.  (Mr. Hodges is really good at drawing over-long
responses from me.)
       
       But the next time you feel alarmed by a report that the gap
between income quintiles is widening, remember: If you lived in a
society that shared its income with perfect equality among peers, and
with perfect fairness among generations, and which was progressing at
a steady rate to Utopia, it would report a gap among income quintiles
that was widening every year at an ever accelerating rate.
       

Happy New Year to all!