Monday, April 15, 2013

How to Lie With Statistics: A Recent Example

A recent post by Chuck Marr on a Huffington Post blog provides a nice demonstration of how to use true facts to support a false claim. It contains a series of charts with information on taxes, mostly federal. One of them is labeled: "Bush Tax Cuts Heavily Tilted to the Top," and shows that the percentage increase in after-tax income as a result of the tax cuts was almost three times as large for taxpayers with incomes of more than a million dollars as for those with incomes of $40,000-$50,000.

What it does not mention, but what one can see from other charts on the page, is that high income taxpayers pay in federal taxes about three times as large a fraction of their income as middle income tax payers. So if the tax cuts reduced everyone's taxes by the same percentage, the result would have been almost exactly what the chart shows. Indeed, the author could have made his claim even more striking by pointing out that taxpayers near the bottom of the income distribution got nothing out of the tax cuts—and neglecting to mention that the reason was that they were not paying any taxes.

Another somewhat misleading chart shows that it is possible for a middle income family with relatively little investment income to pay a higher tax rate than a high income family whose income is mostly from investments. It is clear if you read carefully that the author is not claiming this situation is typical--an earlier chart shows that, on average, high income families pay a much higher rate than middle income families. But the author does not mention that his calculation ignores corporate income tax, which arguably should be attributed to the owners of the corporations—the people receiving investment income. 

A final problem, not of dishonest presentation but of the difficulty in adequately analyzing the effect of taxes, is that all of the charts show who pays taxes, not who actually bears the tax burden. It is easy enough to describe situations where the result of taxing the income of group A is partly a reduction of their after tax income, partly an increase in their before tax income, ultimately paid by those who consume the goods or services they produce. To put it in conventional terminology, it is not clear to what extent a tax on A is passed on to B. That problem applies to corporate income taxes as well—the reason for the word "arguably" in the previous paragraph.

One other chart has a different sort of problem. It shows taxes as a fraction of GDP for a range of countries, with the U.S. near the bottom. The author does not mention that the federal government for the past few years has been going largely on borrowed money—at one point almost half of total expenditure—hence that the chart badly misrepresents the more important question, which is what fraction of national income each government spends.


Joey said...

Because the government is the rightful owner of all of our income, when they let us keep some of it, it is considered an "expenditure".

Hence, chart 9.

How's that for dishonesty?

David (not Friedman) said...

"Another somewhat misleading chart shows that it is possible for a middle income family with relatively little investment income to pay a lower tax rate than a high income family whose income is mostly from investments."

I think you meant "pay a higher tax rate".

David Friedman said...

To David (Not Friedman)

You are correct. Fixed.

Tibor said...

One thing I sure don't understand is why people like Warren Buffet go around saying they "pay lower taxes than my secretary" (ignoring the corporate tax, which is the highest in the USA of all countries in the world).

I can only think about it as a cheap way to gain popularity (although philantropy seems to be both more useful AND more popularity boosting to me).

Or if I get a bit paranoid, I would say that is his way to make friends in Washington who will "help" him with some insider information he can make a lot of money on.

Otherwise, I don't understand why it is not so popular for rich people to go around saying they should pay higher taxes...the funny thing is they can give money to the state as a gift if they really feel like, but they are not doing it :)

Peter said...

Did he account for inflation/nominal growth when calculating tax rates on investments? I would guess no, but I'm too lazy to check.

Glen Whitman said...

Comparing the federal government of the U.S. to the national governments of other countries is also misleading when those other nations don't have federal systems of government. It would be better to look at the taxation (or spending) at all levels of government.

Nightrunner said...

> high income taxpayers pay in federal taxes about three times as large a fraction of their income as middle income tax payers

David: Relative utility. You have more use for 10K than the "celebrity" for 100K on 10x your income. It will all be blown on coke anyways.

David Friedman said...


I believe the table in the page I linked to included state and local taxation as well as federal.

David Friedman said...


Declining marginal utility of income + wanting equal utility burdens of taxation gives you an argument for why rich people should pay more money than poor, but it doesn't imply that they should pay a larger fraction of their income, let alone that it should be larger by more than it is. That requires a much more specific assumption about the shape of the utility function.

David Friedman said...


The calculation on investments simply assumed that the high income taxpayer had 2/3 of his income from investments. It ignored the fact that income in the form of capital gains is at least partly fictional if there is a positive inflation rate between buying an asset and selling it.

Joey said...


The system you defend, in which a celebrity earns 10x as much and pays 10x the income tax is not our tax regime.

high income taxpayers pay in federal taxes about three times as large a fraction of their income as middle income tax payers

This describes a progressive tax.

Anyway, I don't believe anybody wants to live in a world in which we pass laws to confiscate money from somebody based on assumptions that another makes about their utility. That would result in a very non-utilitarian outcome.

Nightrunner said...

> it doesn't imply that they should pay a larger fraction of their income

David: Is it not what "progressive" tax rate is about? The more one makes, the higher is the tax rate and so the % of income.

Patrick said...


If we ignore the effects of the tax rate on people's behavior and treat it as a pure redistribution mechanism, then for the two assumptions:

1) if everyone has an identical utility function for money and
2) if everyone has diminishing marginal utility for money

it follows that the tax should be maximally progressive. Specifically, it should be set up to take money from the rich and give it to the poor so that everyone has exactly the same amount of money. This state is a global utility maximum, given assumptions 1 and 2, that we can only redistribute, and that our redistribution has no side effects.

To come to another conclusion, you have to reject one of the assumptions--number 2 is probably true, but 1 is not. There are reasons to believe that those who earn lots of money get unusually high utility from money for about the same reason that those who eat lots of apples get unusually high utility from apples.

Of course, you can also reject the assumption that taxes have no side effects: the harm from deadweight loss should be roughly quadratic in the rate, so this is another reason to avoid progressive taxes.

Tibor said...


Why do you suppose that everyone has the same utility function (for money)?
That is obviously not true.

Suppose there are only two jobs in the world available (for simplicity). The first if a job of a charter accountant, the second is a job of a musician.
Let's say the charter accountant earns twice as much as the musician (at least on average).

Why is that so? Because more people want to be musicians, since there are other non-monetary benefits to it. On the other hand, very few people find charter accountancy interesting (as testified by a number of Monty Python sketches about charter accountancy :)) ). Why would anyone want to do the job of the accountant if they earned the same as the musicians? There are only two ways of dealing with a shortage of charter accountants. The first is a command economy where someone is simply designated as a charter accountant whether he likes it or not. The second is difference in wages.

Let us say, there are 2 people identical in their skills. They can do both of the jobs. But one values things like yachts and rolex watches which are pretty expensive (after all, we are in a world of charter accountants and musicians only so noone is building any new yachts :)) ). The other one does not fancy these things but likes to have a job that is interesting (perhaps there can be people who find accountancy interesting, but I have not yet met anybody like that :) ). Then the first person will work as an accountant, while the second will become a musician - the difference is that the first values money much more than the second one.

Basically the mistake you are making is that you compare jobs (or not working at all) based only on the monetary benefits of it. Of course, almost anyone would prefer a higher paying job to the exact same job with a lower wage. But that is usually not the case. I know a lot of people myself who could do a better paying job, but prefer to do something else for other reasons instead. Myself for example. I will be finnishing my Ms. degree in 3 months. Then with my education it wouldn't be a problem for me to work in a company like Delloite or probably even McKenzie (I hope I spelled that right) earning a lot of money. Instead I am going to continue studying a PhD. supporting myself with some job just to get by and then working for probably less money but on something that I prefer to do - research...that is as long as will find a sutiable research positon. The possibly less interesting career in Delloite has to be compensated by a higher pay - after all, if the difference were even sharper, I would seriously consider that career too. So no, people don't have the same utility function for money. Not at all.

Anonymous said...

Buffett claimed he paid 17.4 percent of his income in taxes while his secretary paid a rate of 35.8 percent. But:

* Buffett omits the effect of the corporate tax.
* Buffett omits the effect of inflation for capgains.
* It's likely the 17.4% is Buffett's effective rate, while 35.8% is the secretary's marginal rate.
* To get 35.8% for the secretary, Buffett presumably added in Social Security and Medicare taxes. Yet, the individual eventually gets reimbursed for those payments, so putting them in the same class as general taxes (never individually reimbursed) is not quite fair. If Social Security is a net benefit for a person over his life, then what he gets back from it must be more than what he paid into it. So the secretary's Social Security payments would be cancelled out in the long run.

Here's another distortion. A person does not have a single "marginal tax rate".
If Buffett got another dollar in capgains, his tax would probably go up by 15 cents.
If Buffett got another dollar in earned income, his tax would probably go up by 30 cents, plus. (At least at the time when Buffett made his statements.)
A person really has at least two marginal tax rates, depending on what kind of income he will get next.
So Buffett has two distinct marginal rates for (1) capgains+dividends, and (2) earned income. And the secretary also has those two distinct marginal rates.
And, each of Buffett's marginal rates is probably >= the corresponding rate of the secretary!

Another comedy item: It was recently announced that Obama's effective tax rate is 18.4%. Note that Obama's rate is considerably below the secretary's alleged rate of 35.8%. While Obama earned less than $1 million, in formal terms, he received in-kind benefits (not necessary to do his job) that pushed him up to a billionaire-level life-style. His true tax-rate must be under 1%, when you factor in all those bennies.

Social Security and Medicare have been presented as wonderful things for us Americans. Yet, when it comes to Buffett's secretary, suddenly we're supposed to cry for her because she has to pay those onerous payroll taxes. So are those "Social Insurance" systems wonderful or not? I would like liberals to take a consistent position.

windwheel said...

David, you are an elderly and stupid man. Yet you keep going and going and you say more and more stupid thins like maybe young Landsburg said the same thing as Bork? That could be interesting? But, it didn't happen.
Who are you writing for?
People MORE stupid than you?
Guys, content yourself that TIBOR sucks your cock.
You literally can't make a coherent argument to save your life.
Friedman- you are totally shit. You could of been a Dentist- you cunt.

David Friedman said...


I specified "Declining marginal utility of income + wanting equal utility burdens of taxation"

Your argument assumes that the objective is maximizing total utility, which is not at all the same thing.

windwheel said...

Worthless cunt, I request and require that you kill your family and yourself. You are shite. Die you worthless turd.

windwheel said...

Oh, also I threaten to kill your children and stuff.
Fuck you Friedman.

Patrick said...


I do not think that everyone has the same utility function for money. I assumed that because I thought David was assuming it. (As David correctly points out, I misread his goal as maximizing total utility rather than equalizing the utility burden of the tax.)

The fundamental problem is interpersonal utility comparisons. You need to know at least *something* about how one person's utility compares to another to be able to add them together. Without an assumption like identical utility functions, it is hard to persuasively justify a progressive tax at all--what if people who earn a lot of money also value money so much more that it counteracts the effects of diminishing marginal utility?

But notice that in my post, I pointed out that the assumption I made for the purpose of the argument was likely false. People with more money are likely to value money more. I.e., if you compare what the marginal utility for money would be if a rich and a poor man magically had the same amount of money, the rich man's marginal utility would probably be higher. This is because people who more highly value the things money can buy are more willing to give up nonmonetary goods in exchange for money, so if you become rich, that is (some) evidence that you value money unusually highly.

In other words, my post was saying: here's what I think you're assuming, here's what you should conclude based on those assumptions, and here's why some of the assumptions are probably wrong. My mistake in interpreting David's goals muddied it a bit, I'm afraid.

Milhouse said...

What is a person's fair "share" of the "tax burden"? Why is it any different from a person's fair "share" of the "grocery burden", or the "housing burden"? Surely everyone recognises that that does not depend on the person's wealth, or utility for money, or anything but the benefit he gets. The more and better food he buys the more he pays; if he is a miser and buys the same as a pauper, he pays the same. If he lives in a mansion he pays more, but if he lives in a hovel he pays less. So why is it fair for one person to pay more tax than another just because he's richer, and has less use for money? In dollar terms, Warren Buffett pays far more than his secretary does; does he really get that much more benfit from the government?!

Now it's true that the benefit a person gets from the legitimate functions of government rises with his wealth. A poor person doesn't need much protecting, whether from burglars, foreign invaders, or embezzlers. So the rich should pay more than the poor. But I doubt that someone who makes 10 times as much as I do gets 10 times the benefit that I do. I could believe 6 or 7 times, maybe 8.

So tax rates, far from being "progressive", should actually be a bit "regressive". The rich should pay more than the poor in absolute terms, but a bit less as a percentage.

Tibor said...

Patrick: Oh, I see, my bad. I should have read your comment more carefully. Well, then we have to agree that we agree :D

Nightrunner said...


> That requires a much more specific assumption about the shape of the utility function.

You are right but our tax system is based on that assumption