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Posted at 1:44 PM ET, 01/12/2011

Inequality among the rich in one graph and one thought experiment

By Ezra Klein

Catherine Rampell asked the hardworking folks at the Tax Policy Center to estimate the paychecks that correspond to different income percentiles. In other words, if you're the 37th percentile, or the 85th, how much are you making? Then she graphed the results. The only problem is, the incomes of the rich make the rest of the chart impossible to read:


"The line gets much steeper because at the very top of the income scale, the monetary divisions between percentiles grow much greater," writes Rampell. "Those who aspire to hop from the 30th percentile to the 35th percentile would need [to] increase their cash income by $4,000 annually (or by about 17 percent); those who aspire to hop from the 91st percentile to the 96th percentile would require an increase of $324,900 (or 171 percent)."

Someone in the 80th percentile is a lot closer, in dollar terms, to someone in the 20th percentile than to someone in the 95th percentile. But are they more like someone in the 20th percentile than someone in the 95th percentile? That's trickier. Kevin Drum posed a nice thought experiment to his readers the other day.

Let's say that you're in your 30s, married, two children, and you make $100,000 a year. I offer you a fair coin flip with the following possible outcomes:

Heads: You will be stripped of most of your assets and will earn $30,000 per year for the rest of your life. That's all you get, and neither friends nor family can top it up for you.
Tails: You will earn $1 million per year for the rest of your life.

Treat this as a serious question. Would you take me up on my offer to flip the coin?

Just about no one did. Drum didn't conduct a scientific survey, but "it's suggestive that in terms of lifestyle, if not political goals, a $100K wage earner actually feels somewhat closer to the zillionaires than to someone barely scraping by. We intuit, correctly I think, that life at the bottom of the working class is pretty damn tough, while life at the tippy top is more exciting, but perhaps not fundamentally different from life in the upper middle class.'

By Ezra Klein  | January 12, 2011; 1:44 PM ET
Categories:  Inequality  
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A logarithmic scale along the vertical axis would've solved the readability problem, Ezra. Still, I appreciate that you didn't pull an Al Gore and set the top of your scale below the maximum data point to exaggerate your claim. ("The rich's incomes are BURSTING off the chart!")

Cash income is an important component of income, but it would have been nice to see total income plotted instead, i.e. accounting for health and other benefits, welfare assistance, etc., to get a feel for how people of different strata are actually doing. I suppose if you're fairly well off and just want to compare salaries while ignoring benefits, this is a useful set of data.

I think if you plotted income tax collections on a secondary scale such that the highest income and highest tax data points coincided, You'd see how progressive the tax code is. The tax curve would be higher than the income curve at all average and higher percentiles. Even funnier would be a second tax curve for the what-if scenario of the Bush tax cuts not being extended. You'd see a lower share for the rich, and proof that the Bush tax cuts weren't actually directed at the rich the way the Left often and loudly complained.

Posted by: angrydoug1 | January 12, 2011 2:06 PM | Report abuse


Don't waist your time asking Ezra to graph anything that will discredit liberal arguments. This purpose of this blog is not to shed light on both sides of any issue, only the liberal progressive side.

Posted by: cummije5 | January 12, 2011 3:00 PM | Report abuse

Kevin Drum had an interesting experiment and I think I agree with the overall conclusion. But, I strongly disagree with saying $30,000/yr is "bottom of the working class." In fact, there are many people making less than that, including, for you conservatives out there, quite a few so-called "overpaid" government workers (GS-4 and below at the federal level, even some GS-5's). The fact that people making less than $30,000/yr appear to be viewed as "bottom of the working class" in opinion and policymaking circles may explain why the tax increase on those making less $20,000/yr was not considered to be a problem by policymakers when the Making Work Pay credit was removed and replaced with the payroll tax holiday. "Oh, they're POOOOR, people who work don't make that little, it doesn't matter," seems to have been the attitude. Speaker after speaker said they had to prevent the raising of taxes and vote for the compromise, but the compromise *did* raise taxes on the working class.

Posted by: jfung79 | January 12, 2011 3:10 PM | Report abuse

I suspect that a logarithmic scale on the y-axis would result in a 45 degree line of the y=mx+b form.

Which would, itself, be interesting.

Posted by: wiredog | January 12, 2011 3:19 PM | Report abuse

If you have to put a data set on a log-scale to see the differences, then something really is "off the charts!".

But the thought experiment is really the most useful part of the post. And the outcomes don't have to be as extreme. If you have two kids, are in your mid-30s, and have a job that pays $70k with a decent retirement, there is no way you would gamble on a coin flip that had a 50-50 chance of either doubling your income (to $140k per year) versus halving it (to $35k a year). $140k gets you some nicer vacations, a bigger house, probably some more college money for your kids and that's about it. But a family of four on $35k is really struggling. You almost certainly would have to move. Your eating habits would suffer. You most likely would give up any hobbies you can afford. Your kids would have to pay their own way through college for sure. And you'd be looking at a future where social security is the majority of your retirement income.

Fostering an entrepreneurial society indeed.

Posted by: willows1 | January 12, 2011 3:21 PM | Report abuse

Ezra, you once again provide quality information and absolutely lovely graphs!! I sincerely respect and look forward to what you have to say here, on twitter, and on tv. I especially loved you on Charlie Rose the other night - masterful! How in the hell did you get so smart being that you are clearly around 15 yrs old???? (LOL - kidding!) As a mother of a young son, I must say - your mama must be SOO proud!! :)

Keep up the good work!!!

Posted by: angiep1 | January 12, 2011 3:28 PM | Report abuse

I believe that is called "risk aversion"- it's more painful to lose something you have worked for than to give up something you never had.

Also, think of this: I don't make *that* much money every year, as I plow as much as I can into growth. One year, I will sell some or all of my company and recognize a lot of income in that one year. That's probably the only year I'll be near the $1M range, maybe near $10M if things go crazy well. This is how a lot of these lumpy earners look. I'm trading years of working all the time for a big payday. You have no data to indicate it's the same people making this money every year. A bunch of my peers sold off their companies this fall in anticipation of a 5% increase in the cap gains rate. That's probably their last year on the right side of the chart.

Before you do anything on wealth inequality, look at this:

Posted by: staticvars | January 12, 2011 3:46 PM | Report abuse

Cheers to the brilliant Rampell!

An Italian economist Vilfredo Pareto did something similar at the dawn of the 20th century. He showed that the wealth distribution in Italy follows a certain pattern (20% of society owned 80% of the wealth).

We now call this the Pareto distribution:


Posted by: chrisgaun | January 12, 2011 3:48 PM | Report abuse

It sounds like the thought experiment you describe has a lot more to do with "risk adversity" than somehow "feel[ing] somewhat closer to the zillionaires". Consider: if the coin flip payoff was framed as pay $500,000 or receive $5,000,000 I would still expect most middle class people would decline the offer because a $500,000 bill would be ruinous.

Posted by: walla151 | January 12, 2011 3:52 PM | Report abuse

As jfung79 says above, the bottom of the working class is $15,080, not $30,000: minimum wage earners ($7.25) working full time (40 hrs/wk, 52 weeks a year) make up a significant percentage of the American workforce. The interesting effect is that raising the minimum wage causes elimination of jobs, leaving the number of minimum wage earners relatively constant.

Nobody -- not even a minimum wage earner -- wants to be perceived to be at the bottom of the earning/food chain. "TANF Mammas" and "Medicaid Milkers" are the exception, trading the stigma of being federally subsidized for wages higher than minimum: this is especially true in some states (Massachusetts, etc.), where TANF Mammas and Medicaid Milkers receive subsidies greater than the median wage earners in other states.

Posted by: rmgregory | January 12, 2011 5:18 PM | Report abuse

I agree with staticvars and walla151 - it's not a very good thought experiment because humans are so risk averse about losing something they already possess. No matter how rational it would be to choose one option over the other, it's one way that humans are "predictably irrational".

Ezra, have you read the pop-econ book "Nudge?" If you haven't, I think it's absolutely essential reading for you and right up your alley.

Posted by: madjoy | January 12, 2011 5:31 PM | Report abuse

madjoy fyi loss aversion isn't the same as risk aversion. time to reread nudge, although ezra doesn't seem to favor libertarian paternalism (just plain old paternalism) (or even better, read against the gods) cheers!

Posted by: stantheman21 | January 12, 2011 5:45 PM | Report abuse

angrydoug and others: go here for the logarithmic version, which simply clarifies and reinforces the point that the line goes almost straight up after about $250,000:

Posted by: pjro | January 12, 2011 9:09 PM | Report abuse

Actually, Ezra, if you had plotted the graph so that the rich people are below the poor, it wouldn't be so left-leaning.

Posted by: dpurp | January 12, 2011 9:19 PM | Report abuse

Charts like that make a point if a person can see past their own bias, which most conservatives never will. The coin flip question has a big "it depends". If like most middle class, it takes 80k per year to pay the bills when you make a 100k salary then no way. But if all the bills are paid, including the house, someone could get by on 30k as an individual in some select cities. 1 million also may not seem like enough in some cities where that is a middle class apartment.
The value depends a lot on the situation. I personally would rather have all my bills paid and make 30k than make 100k and only have 100 bucks a paycheck for spending.
Give us poor indebted folks some inflation and help us pay our bills off.

Posted by: EducatingTheFools | January 12, 2011 9:52 PM | Report abuse

This is a Zipf distribution. Plot it on a log scale.

Posted by: chase-truth | January 13, 2011 9:05 AM | Report abuse

Stantheman, my bad. thanks for the correction!

Posted by: madjoy | January 13, 2011 11:38 AM | Report abuse

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