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September 28, 2006

Throwing off the curve

In a post below, Zach links to a web site that attempts to illustrate the distribution of income in the United States. However, one of the figures cited on the site doesn't pass the sniff test.

After representing the annual household income of $40,000 as a stack of $100 bills 4 cm high and the ~99.7th percentile mark of $1 million as a stack of Franklins 1 meter high, the site claims that "it keeps going up...it goes up 50 km (~30 miles) on this scale!" But on that scale, a 50 km high stack would represent an annual income of $50 billion. Bill Gates' net worth in 2005 was $46.5 billion, so obviously no one is making $50 billion a year in income.

If my math is off, someone please let me know.

Update: As was pointed out in the comments, the author of the site is counting a 1-year increase in Bill Gates' net worth as income. (Wikipedia confirms that Gates' wealth "briefly surpassed $100 billion in 1999".) I guess the author only counts positive income, because there's no 50-kilometer deep spike to reflect Mr. Gates' subsequent loss in net worth.

As an aside, I must say that my first reaction to the "L-curve" was to be surprised not at how insanely wealthy a very very small number of people are, but how relatively equally income is spread out for most Americans. The 95th percentile is making only a little more than twice the median income, and the 99th percentile is earning 7.5 times the median income. In my view, why obsess with bringing down that top 1%?

Posted by Eric Seymour at September 28, 2006 05:28 PM

Comments

The math seems fine, but it's your reading skills that apparently need some improvement. Here's the text, taken straight from the site on the most 'zoomed out' frame:

"Our frame is now 100 kilometers square. The exact height of the top of the curve varies from year to year, but the total amount of money in the vertical spike continues to grow steadily. Bill Gates "wealth" was at one point estimated to be over $100 billion. The red line represents his greatest "increase" in net worth in a year. At 50 kilometers, the pile of $100 bills extends beyond the stratosphere, more than 5 times the height of Mt. Everest. $1 million is the same proportion of this income as $1 to a person earning $50,000 per year."

The accompanying image then identifies that stack as, indeed, 50 billion dollars, and notes parenthetically: "(Bill Gates greatest estimated 1-year increase in net worth = 50km high stack of $100)"

So they are using a 1-year increase in net worth as a stand-in for income for (literally) the wealthiest of the wealthy. One can argue about whether this represents a good way of estimating the high-water-mark of U.S. 'income', but it doesn't strike me as unreasonable -- this isn't the sort of issue where distinguishing income strictu-dictu from other ways that one's net worth can grow. I also didn't poke around to see where they got that estimate from, so for all I know, the estimate is skewed in some way. But, _pace_ your sniff, the site is completely honest about what the number is meant to be.

Posted by: philosopher at September 28, 2006 06:42 PM | permalink

No need to get snippy about it, phil...

I didn't realize you could zoom out further than the football field which comes up when you first load the page.

Anyway, yeah, I'd say that including a remarkable 1-year increase in net worth in something called "a graph of the US Income Distribution" is highly misleading. Since Mr. Gates has apparently lost $50 billion dollars since then (ah, the joy of having most of one's net worth residing in stocks and stock options, etc.), shouldn't there be a downward spike at the left end of the football field that plunges into the earth's mantle?

Posted by: Eric Seymour at September 28, 2006 10:27 PM | permalink

This looks like a response, over at the L-curve site; he has a contact link there you may want to use, if this wasn't a reply to you already

----excerpt follows------


*Since I first posted this site, several people have quibbled over various technical points. Here are a few of the issues raised:

*

"Increase in net worth" is not the same thing as "income," according to one reader. However, I recently received a comment from economist John Maher who wrote, "I believe the first reader's comment is incorrect. Increase in net worth IS income according to the renowned economist, John R. Hicks in Value and Capital. Hicks is right."
*

The income of very wealthy people typically varies radically from one year to the next. Sometimes years of huge earnings are followed by years with similarly huge losses. I agree. I have added a comment to this effect in the main body of the text above. Those of us on the horizontal spike, however, find radical jumps in income much harder to achieve. The overall L-Curve pattern persists through it all.
*

The published wealth of billionaires is typically estimated by their holdings in their own companies. These estimates do not include their typically vast diversified investments.
*

Income on paper, from growth of investments, needs to be distinguished from "taxable income." It's true that there are differences among different kinds of income, so they aren't strictly comparable, but political and economic power derives from wealth, whether it is taxable or not.

My response to all of these kinds of questions, in short, is that the truth of my central thesis is not dependent on the exact height of the graph or shadings of definitions. As one correspondent put it, there is a "money spike" and there is a "population spike". There are two classes in this country. One class derives concentrated power from its concentrated wealth. The other class has power only in numbers. ...

---- end excerpt---

Posted by: Hank Roberts at August 30, 2008 01:19 PM | permalink

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