Saturday, October 04, 2008

Visualizing the Long Tail for Tax Policy

They say software is hard to understand because it's "invisible" - but aren't so many things? For fun, I downloaded the raw data on Obama and McCain's proposed tax policies from http://www.taxpolicycenter.org - they have it all in Excel form, which makes crunching it convenient and easy - and tried to construct what I considered a reasonable visualization. Their data is broken out to show the effective tax increase or decrease for the first quintile, the second quintile, etc, with the top quintile broken down to partitions of the top 10%, 5%, 1% and 0.1%. I wanted to show the range of salaries in each partition, the number of people in each partition, and the change in tax. I decided that it just can't be done - the ranges are just two broad to see on, without using hard-to-explain constructs like a loglog plot.

Here's a mental image that might help. Think of a football field, 1000 typical Americans, and some big stacks of money in small bills. Specifically, think of $1 and $5 shuffled together and piled up so that each pile contains about equal numbers of $1's and $5's. If I did the math right (they say a US bill is 0.043" thick) then a money stack one foot tall is worth about $10k - so the football field is $3M long and $1.6M wide, I'm about $57k tall, and my waist size used to be about $30k (but with my diet, I lost about $1600 around the middle).

Now to visualize income distribution, let's take those 1000 typical Americans, and let them walk down the gridiron like this: start at one goal line, and for every $10k of yearly income, walk one foot toward the other end zone...so if you make $90k/year, e.g., you'll end up on the three-yard line, and if you make $300k/year, you'll end up on the 10. Subject to that rule, space everyone out as much as you can.

The first 900 of those 1000 people will end up somewhere before the 4 yard line, because about 90% of Americans make about $120k or less.

Another 90 people will end up between the 4 yard line and the 8 yard line - that is, they make between $120k and $240k per year.

Another 9 people will end up between the 8 yard line at the 20 - they make between $240k and $600k per year.

That accounts for 999 out of 1000 people, but this is America, land of Bill Gates and Warren Buffett - so we're not done yet. The last guy will stand, on average, at the 94 yard line - with an average income of $2.8M per year. Remember this is income, not life savings.

Now, for the tax cuts. Let's start with McCain's. EIn his plan, everyone gets a tax cut, and we'll hand it out as stacks of money. McCain has a stack about 9 feet high to be shared by the first 900 people; a stack about 5 feet high to be shared by the next 90 people; another 9.5 foot stack to be shared by the next 9 people; and a final stack about 6.5 feet high - about the height of Ben Rothlisberger - that goes to that one lonely old man (surely, he's old?) down on the 94 yard line.

Above is a picture I drew of this...you can click to zoom in.


This is approximate, and loses some detail - which maybe I'll get to in another post - but it illustrates the main properties of McCain's plan: there is an extremely long tail in income distribution in the US, and as a consequence, an extremely long tail of tax-cut returns. If you imagine the money stacks are all the same (which is order-of-magnitude correct), then
  • For the bottom 90%, the per-person tax cut is about 1/10 that of people in the 90-99% bracket.
  • For the 90-99% partition, the per-person tax cut is about 1/10 that of people in the 99-99.9% bracket.
  • For the 99-99.9% partition, the per-person tax cut is about 1/10 that of people in the top one-tenth of one percent.

8 comments:

Tim Grossner said...

I haven't looked at your source data, but does it take into account that the taxes paid by each group are based off of percentages of the total taxable income of each person/group/etc?

William Cohen said...

tim: "I haven't looked at your source data, but does it take into account that the taxes paid by each group are based off of percentages of the total taxable income of each person/group/etc?"

I assume the answer is "yes" - since otherwise the numbers couldn't be accurate. To be honest I didn't look in detail at the way the numbers were derived - it's non-trivial and there are several variants. This analysis was widely cited by several MSM pubs when it came out, though, and it's the only detailed one I've seen.

Jon said...

have you done the same for the Obama plan? Any significant difference in the visualizations?

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