Pay Scales in Black and White
This column is about racial
discrimination. But more importantly, it's about how a little arithmetic can go
a long way toward settling a controversy.
The controversy I have in
mind is, Why do blacks earn less than whites do? The easiest hypothesis is that
the employers discriminate. Some commentators have attempted to dismiss that
hypothesis on the grounds that discrimination is costly (because it entails a
willingness to pay premium wages for white workers) and therefore unattractive
to employers with an eye on the bottom line.
But that
kind of dismissal is too glib, because it is not based on any estimate of how
much it costs to discriminate. Without that estimate, we can't even
begin to think about whether the cost is high enough to make much
difference.
Iwant to provide the missing estimate, starting with a few
assumptions that are reasonably commensurate with reality. First, I'll suppose
that blacks constitute 10 percent of the work force. Second, I'll suppose that
blacks, because of discrimination, earn 60 percent of what whites earn. Third,
I'll make an assumption (again guided by real-world observations) about what
happens to corporate revenue: I'll assume that for every dollar paid to the
workers, a half dollar gets paid to the bondholders and the stockholders
collectively--let's say the bondholders and the stockholders each get a
quarter.
To make those assumptions
more concrete, suppose you're the manager of a corporation that employs one
black and nine whites, paying the black $60,000 and the whites $100,000 apiece.
That makes your total wage bill $960,000. The bondholders and the stockholders
each receive one fourth as much as the workers, thus each group gets $240,000.
So your payouts look like this:
(The
specific numbers in the preceding paragraph don't matter. If you assume 100
employees instead of 10, or wages of $6,000 and $10,000 instead of $60,000 and
$100,000, the conclusions to follow will remain unaffected.)
Now we can estimate the cost of your
discrimination. Notice first that discrimination must be quite common in your
industry; otherwise your black worker would have gone elsewhere long ago. That
means there are a lot of blacks working for $60,000 in this industry. If you
could put aside your racism, you'd fire your nine $100,000 white employees and
replace them with some of those $60,000 blacks--cutting your wage bill by
$360,000.
Where would the $360,000 in
savings go? The same place any corporate savings go--into the pockets of the
stockholders, increasing their earnings from $240,000 to $600,000--a 150
percent increase overnight. Your payouts now look like this:
When the
return to stockholders rises by 150 percent, so must the price of your
company's stock. That's enough to put you on the cover of Time magazine
as the financial genius of the century. To continue discriminating is to throw
away an opportunity for unprecedented financial success.
In fact, that same opportunity is available to every other
corporate manager in the industry as well, and they're rejecting it too
(remember that discrimination must be widespread or all blacks would move to
nondiscriminatory firms). So in order to believe that discrimination explains
the black/white wage differential, you must believe that managers throughout
the industry are so blinded by racism that they are willing to throw away a 150
percent gain for their stockholders, and the acclaim of all Wall Street for
themselves. Personally, I find that wildly implausible.
That's not an irrefutable
disproof that discrimination exists, but it's at least a calculation that needs
to be taken seriously. If we had come up with a number like 10 percent rather
than 150 percent, it would have been far easier to maintain a belief that
employers discriminate.
The figure
of 150 percent is based on numerical assumptions that are reasonable but not
ironclad. If you juggle those initial assumptions a bit, you'll get a number
other than 150 percent coming out at the end, and you might or might not
discover a scenario in which discrimination is plausible. (My guess is that you
won't, but then again, you and I might have different standards for what's
plausible.) Regardless of how that experiment turns out, it's well worth
performing. Without some such test, there is simply no way to know whether
discrimination is a credible hypothesis.
If we rule out employer discrimination, there
must be some other explanation for the black/white wage differential. Suppose,
for example, that there is discrimination not by employers but by customers,
who are willing to pay a premium for goods and services produced by white
workers. To advocate that theory convincingly, you'd have to estimate the size
of the premium and assess whether it's something that consumers would plausibly
pay. I invite readers to do their own arithmetic.
Alternative theories posit
that blacks earn less because they have fewer marketable skills. Like theories
of discrimination, these theories are best judged by quantitative criteria, but
now we have to go beyond what can be computed on the back of an envelope and
look, for example, at what we can learn from standardized test scores.
According
to recent research by Derek Neal of the University of Chicago and William
Johnson of the University of Virginia, black/white wage differentials are
largely explained by differences in skill levels which are already detectable
at an early age. (Richard J. Herrnstein and Charles Murray had previously
reported similar findings in their best-selling book The Bell Curve .) To
explain those skill differentials, one can try pointing either to training or
heredity.
Herrnstein and Murray argued that heredity plays a
substantial role, but Neal and Johnson's more recent findings tend to refute
that interpretation. For one thing, Neal and Johnson report that the
performance gap between blacks and whites is considerably larger for young
adults than it is for teen-agers. That's hard to explain if the gap is caused
by heredity (why should an inherent difference become larger over time?), but
not if it's caused by training (if blacks get inferior schooling, then it's not
surprising that the effects are greater after 10 years of schooling than after
six).
Much research remains to be
done, and is being done, and will be done. All of that research, at least when
it is useful, will be quantitative in one way or another. Some of it requires
sophisticated techniques and sophisticated measurements. But there are
cases--and discrimination is one of them--where the inherent plausibility of a
theory can be well tested with nothing more than the back of an envelope and an
open mind.
