Rising Incomes and Falling Income Statistics

by Don Boudreaux on September 8, 2008

in Data, Inequality, Myths and Fallacies, Seen and Unseen, Standard of Living

Here’s a letter that I sent recently to the Washington Post, in response to the same Robert Samuelson column that Russ blogged on:

Robert Samuelson helpfully explains why the data routinely cited to show the alleged economic stagnation of middle-class Americans are misleading (“The Real Economic Scorecard,” September 3).  In particular, he’s correct that average or median income can stagnate or fall even if everyone’s income rises.  Here’s how I explain this possibility to my students:

Imagine what the average or median income would be in a room occupied only by Bill Gates, Warren Buffet, and Bono.  Now imagine that I enter the room and accept their offer to become their full-time shoe-shiner at an annual salary of $500,000.  Because this income is higher than I earned before entering the room, I’m richer.  And because my entering the room does not lower their annual incomes, none of them is poorer.  But my presence in the room (with my new income still far below that of each of these men) dramatically lowers the room’s average income, and pretty significantly lowers its median income, even if the income of each of these men rises during the current year.

Everyone is richer, yet average and median incomes are lower.  As Mr. Samuelson points out, this possibility is not merely academic.

Sincerely,
Donald J. Boudreaux

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{ 8 comments }

Alex September 8, 2008 at 10:44 am

The assumption must be that the newest person in the room is the shoeshiner. Are there statistics that bear this out? Does America's immigrant population have an income lower than the mean or median? I would assume that to be the case, but is it?

dave smith September 8, 2008 at 11:18 am

It is not just the immigrants. It is also the new households formed by newlyweds, new college grads, the splitting of households by divorce, etc.

Their incomes are nearly all lower.

This whole income inequality debate should come down to the nature of the flow of new households into the pool.

And Don's letter illustrates that perfectly.

kebko September 8, 2008 at 11:29 am

Even without immigration, the newest people in the statistical pool would be 18-23 year-olds getting their first job, so that even if there were truly income stagnation on a national scale, the trend of income growth over a lifetime would mean that few individuals would actually be experiencing personal income stagnation. Of course, outside of special circumstances, young people entering the workforce today have much higher expectations than their parents did.
The statistical problem, I would suggest, is made worse by the fact that young people are staying in school longer & staying single longer, so that they have many years that show up as low household income, even though these are decisions that will be economically beneficial in the end. And, older people are living in semi-retirement or retirement longer, showing years of low income which are actually the result of the wealth they have accrued over their working lives.
It would be really interesting to see the numbers disected to see how much of the various levels of income are explained by these factors.

Atabrat September 8, 2008 at 1:36 pm

It's Simpson's paradox. The same issue came up when UC Berkeley was accused of discriminating against female applicants, when in fact it had a small bias against men.

http://en.wikipedia.org/wiki/Simpson's_paradox

Bryan September 8, 2008 at 10:22 pm

Actually if I walk into a room with 3 billionaires, the median income is unchanged and the average income falls.

Martin Brock September 9, 2008 at 2:47 pm

Conventionally, the median of three values is the central value, and the median of four values is the average of the two central values, so the median presumably does fall when you enter the room, unless the three billionaires have precisely the same wealth.

Bryan September 9, 2008 at 10:09 pm

oops I stand corrected!

notsneaky September 12, 2008 at 2:37 am

But Bryan's essentially right in the sense that with more than three people, like say 260 million more, the thing about the median is not likely to work, unless you're getting HUGE inflows into the income pool (or unless the income distribution is symmetric, which it ain't). Which is precisely why folks who look at these sort of things like to concentrate on the median and not the average.

And keep in mind that these are usually intertemporal comparisons, like 1975 vs. 2005. But there were folks entering the income pool in 1975 too, it's not a new phenomenon or anything (except possibly for immigration but then you gotta make that case with some hard numbers).

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