One recent Sunday, I opened up the op-ed page of my local paper, The Arizona Daily Star, and read an editorial entitled "Ignorant Media are Being Manipulated about Income Gaps." Written by Herbert London of the pro-business Hudson Institute and syndicated by business news service Bridge News, the editorial was designed to counter a recent report by the Center for Budget and Policy Priorities. The CBPP's report, Pulling Apart, used yearly data from the Census Bureau to document the continued widening of the income gap between the richest fifth (or "quintile") and poorest fifth of Americans.
London's central critique is that "the report doesn't take the amount of people in each fifth into account." Specifically, he claims that "if someone's income improves to the point that he leaves the bottom fifth, the bottom fifth is unchanged. It is just smaller by one. But if someone in the top quintile increases his income by $10,000 he remains in the top quintile, and he raises by some level the aggregate income of those in that status. The consequence of this condition is that the bottom quintile always represents those earning under $10,000, while the top quintile is invariably an upwardly moving average. What this means is that a growing income disparity is not only likely but proves very little." London says the CPBB is therefore an unfair distortion of the truth that "takes advantage of the media's ignorance of mathematics."
Okay, let's cut through the verbiage and get down to the point of that quote. London says that the bottom income "quintile" -- or fifth of the population -- shrinks as people leave it by earning more money. The smaller pool of people left behind in the bottom fifth are just those few who still earn next to nothing. As a result, it always looks like the bottom fifth is getting poorer.
Herbert London's criticism becomes clearer with an example. Let's imagine an imaginary world (we'll call it "Herbert London's World") in which 25 people reside. To find quintiles, we simply put all the people in order of income from lowest to highest. The first five (1/5 of 25) go into the bottom quintile, the next five go into the 2nd quintile, and so forth. This leads to a perfectly sensible result: the average income of the bottom quintile is lowest and average income rises across quintiles, reaching the highest average at the top quintile. If we observe these folks' income over two years, we might come up with the following results:
Now, we've included two changes from 1999 to 2000, the kind of which Herbert London described. First, Adam in the bottom quintile got a raise in income from $5,000 to $7,000. Second, Ethan in the top quintile got a raise in income from $25,000 to $26,000. In this hypothetical case, there was a larger rise in income among the poor ($2,000) than among the rich ($1,000). Following London's directions, we now place Adam in the 2nd quintile with his income peers. Look at the result! Even though we know the poor gained more income than the rich, the average income for the bottom two quintiles drop, while the average income for the top quintile rises, making it look like there's a growing income gap when none exists. In Herbert London's World, Herbert London is correct.
Can any high school math students see the problem here? A fifth is a fifth is a fifth is a fifth. By definition, a quintile simply cannot shrink in proportion to other quintiles. A fifth of the population cannot change to a smidgen smaller or larger than a fifth of the population. Quintiles can't and don't shrink! In short, London's critique is pure nonsense.
The problem is best illustrated by returning from Herbert London's World to the Real World:
In the Real World, where quintiles are always arranged as ordered fifths of the population, a change in Adam's income means that Adam rises to the 2nd quintile - London had that right (London also had it right when he noted that Ethan's rise in income couldn't bump him up to a higher quintile -- Ethan stays put). But what London fails to recognize is that Adam's rise necessitates Bess' fall into the bottom quintile. When Bess is properly placed in this hypothetical example, the changes in quintiles' average income correctly reflects what we know about the good fortune of both the bottom quintiles and the top quintile. When used properly, the quintile method does not misrepresent changes in income gaps over time.
The Center for Budget and Policy Priorities' report is firmly grounded in the Real World. As the CBPP's report makes perfectly clear, in every year studied, each quintile makes up precisely one fifth of the population. It is the critic Herbert London who fails to grasp Reality.
While the substance of the editorial falls flat, the title remains apt: the ignorant media are clearly being manipulated about income gaps. London himself, as he put it, "takes advantage of the media's ignorance of mathematics." What is to be done to prevent this kind (either callous or careless) of manipulation? The answer's a no-brainer: check facts. The journalistic code of conduct is designed to prevent such fiascos by mandating simple fact-checking. Had the paper followed its profession's code, London's baloney would have never made it into print. Unfortunately, it ignored the code and descended into the realm of incoherent, self-serving blather. We can all get that from the presidential debates. We shouldn't get it from a newspaper.
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