Friday, April 20, 2012

How to lie with statistics

Along with David Leonhardt's interesting article "Taxmageddon," last weekend's  New York Times Sunday Review included this pair of graphs. These belong high up in the pantheon of "How to lie with statistics" (one of my favorite books) examples. 

These graphs are paired left and right in the original.  (I made them big and split them up so you could see them. They're even clearer on the Times' website)  On the left, is this graph:

Right next to it, is this one

(The graphs had little to do with the article, so I presume they are the work of the Times staff, not Leonhardt.)

It's damning, right? The rich got huge tax cuts (top graph) and so made a ton of money courtesy of the government (+528% change in income, numbers to the right of the first graph). The rich are also feeding at the trough of tax breaks (bottom graph). Outrage!


Now wait a minute here...The top graph is a tax rate, the percentage of income paid, while the bottom graph is total dollars. To say this is comparing apples and oranges is an insult to fruits.

In fact, wealthier people pay nearly all Federal income taxes. So it's not surprising that they benefit more in dollar terms from tax deductions -- except credits, which is money the government pays you even if you pay no taxes. 

If we expressed the bottom graph as a percentage of taxes, or a percentage of income -- the same units as the top graph -- you'd see a dramatic reversal of the implication. Since the lower percentiles have so much less income and pay so much less taxes, the graph would suggest those with less income get the largest (percent) benefits.


The top graph is even more misleading, at least for the Times' goal which is to back a raise in Federal income taxes for the wealthy.

Where does this 60 and 71% tax rate in the 1960s come from? The basic fact of the Federal taxation is that it raises about 20% of GDP despite wild variation in the statutory tax rates. In 1960 Federal tax receipts (NIPA table 3.2) divided by national income (NIPA 1.12) were 93.9/2013.9 = 19.8%. In 2004 this ratio was 2013.9/10534.0 = 19.1%.

Statutory tax rates in the 1960s were as much as 90% marginal rates on the highest incomes. (Remember George Harrison's "Taxman?" "One for you, 19 for me." He wasn't kidding.) But the tax code was so shot full of loopholes that the Federal government didn't collect nearly that fraction of income from anyone.

So where does the 71% come from? At least the Times gives their source, so you can go back and see what the heck the number means. These are estimates by Emmanuel Saez and Thomas Piketty of total Federal taxes -- individual income, corporate income, payroll (Social Security, etc.), and estate taxes -- divided by an estimate of income, which excludes Government transfers.  (The paper is here and a longer working paper version here.)

To what extent is this the statutory rate and to what extent is it actual money paid? I'm still tracking this down, but it appears to be some of each. For example, "We use the TAXSIM calculator developed at the National Bureau of Economic Research ... to compute federal individual income taxes." That seems to imply this is taxes the NBER thinks they should have paid, not what people actually paid.   But they do have individual level IRS data, so in theory know what people actually paid. On the other hand, it doesn't add up: Total tax recepits are 20% of income. So how can everybody's rate come down yet the total rate stay stuck at 20%?  How can the rate of everybody who has any money in 1960 be above 20%, yet the average is still 20%? 

But let's not get in to the depths of the sausage factory, as  it does not matter for the point here. (And my head starts to hurt anytime I delve in to the details of this kind of calculation.) 

The important point, for the Times is that graph has basically nothing to do with Federal income taxes. All of the action comes from Saez and Piketty's assigment of corporate taxes and estate taxes. They assume all corporate taxes are paid by stockholders and bondholders.  This is conceptually right -- it is not true that "corporations" bear any tax burden. Someone is paying, through higher prices, lower salaries, or lower returns to investors. Saez and Piketty assume it's all the latter.

Here is Saez and Piketty's breakdown of how taxes changed between 1960 and 2004 (source):

The actual individual income tax line has not changed much at all, other than to fall slightly for all income groups. Almost all of the Times' fabled taxes the rich were happily paying in 1960 comes from Saez and Piketty's assignment of corporate taxes to wealthy people and their calculations of estate taxes! (Estate taxes are notorious for the games the rich pay to avoid them.)

(It also appears to me that Saez and Piketty are a bit off here: If you charge corporate income tax against the rich, don't you have to divide that tax by an income measure that includes corporate income? In general, you have to divide taxes by pre-tax income not post-tax income. Dividing corporate taxes by individual income, and not including corporate income, can produce "rates" above 100%. On the other hand, if their "income" number attributes all corporate income as individual income to the wealthy, then the distribution of income is grossly overstated. Ok, we're not going in to the sausage factory, maybe for another post someday, but I'm still scratching my head.)   

As Piketty and Saez put the matter:
The larger progressivity in 1960 is not mainly due to the individual income tax. The average individual income tax rate in 1960 reached an average rate of 31 percent at the very top, only slightly above the 25 percent average rate at the very top in 2004. Within the 1960 version of the individual income tax, lower rates on realized capital gains, as well as deductions for interest payments and charitable contributions, reduced dramatically what otherwise looked like an extremely progressive tax schedule, with a top marginal tax rate on individual income of 91 percent.

The greater progressivity of federal taxes in 1960, in contrast to 2004, stems from the corporate income tax and the estate tax. The corporate tax collected about 6.5 percent of total personal income in 1960 and only around 2.5 percent of total income today. Because capital income is very concentrated, it generated a substantial burden on top income groups. The estate tax has also decreased from 0.8 percent of total personal income in 1960 to about 0.35 percent of total income today. As a result, the burden of the estate tax relative to income has declined very sharply since 1960 in the top income groups
Note the tiny percentages of total income involved. These are not going to balance anyone's budget.
Now, when we talk about the "Buffet rule," that is about raising the individual Federal income tax rate. If we calculate Warren Buffet's taxes this way -- including all corporate taxes paid by all Berkshire Hathaway companies (and why not property taxes, business taxes, business contributions to social insurance, and all other business-paid taxes), Buffet's tax rates would be correctly measured, and a lot more than his secretary's tax rate! 

This assignment of corporate taxes takes us into the dark territory of who bears the burden of taxes rather than who actually pays them. Saez and Piketty are assuming that rates of return on investments are reduced because corporations pay taxes, so rich people get less return than they would otherwise. Hence, it's "like" paying more taxes. Ok, that's how economists think about things, but why stop here? Who really bears the burden of the much larger wedge between what employers pay and what employees get? And all the other taxes,  that distorts prices and wages all over the place. And while we're at it, why not "who bears the burden of regulation?" through higher prices or lower returns?

Bottom line: It may be fine for Saez and Piketty's purpose, but I doubt any New York Times reader had the faintest idea they were looking at a graph that primarily said "rich people were hurt by taxes in the 1960s not because they actually paid more taxes but because we assume corporate income taxes drove down the rates of return on their investments!"

And, in case you think this all means  we should go back to the days of "Mad Men" taxation, Saez and Piketty warn:
The surge in top incomes since the 1970s has been driven in large part by a steep increase in the labor income component, due in large part to the explosion of executive compensation. As a result, labor income now represents a substantial fraction of income at the top. This change in composition is important to keep in mind, because the corporate and estate taxes that had such a strong effect on creating progressivity in the 1960s would have relatively little effect on labor income.
In sum, this graph has nothing to do with the main point -- establishing facts about who pays Federal income taxes.  It would be great if our national discussion were to broaden up and consider all taxes -- yes, proper attribution of corporate taxes (all corporate taxes); along with estate, excise, state and local income taxes, sales taxes, property taxes, and so on and so forth. And proper attribution of the burden of taxes. But it isn't.


Now, look at the nefarious pairing of the decline in (statutory) tax rate with the change in income on the right hand side of the top graph. We cut rich people's taxes and look how they got richer!

Here, the Times got too clever by half. The cause and effect insinuation here is actually a supply sider's dream, if you can read and add. The insinuation is, the rich got richer because they got to keep all that income that they're not paying to the government. Even that doesn't add up: a 528% rise is much more than (1-0.34)/(1-0.71) = 2.28 = 128% rise in after-tax income.

But the tabulated rise is in pretax income. (At least the labels are honest.) As tax rates came down, people went out and made an enormous amount more income in the first place.

A 528% increase in income is a lot. 71% x $100 = $71.00.  34% x $100 x (1+5.28) =  $213.52. So, using the New York Times' numbers, we would infer that lowering the tax rate on the top earners corresponded to tripling the tax revenue earned from that group! The rich are, apparently, paying much more in taxes than before.

If you take the Times' numbers seriously, Art Laffer's wildest dreams came true.


Update: Abel Winn notes it's worse than I said:

 The top graph’s y-axis is scaled according to position in the income distribution, while the bottom graph’s y-axis is scaled according to position in the distribution of taxpayers. Since only about half of income earners pay income taxes, being in the top x% of the income distribution means that one is in about the top 2x% of taxpayers. So when we see massive benefits going to the top 20% of taxpayers, that means the tax code was benefiting the top 40% of income earners. But that doesn’t fit very nicely into the 99% rhetoric that we’ve been hearing so much of late, and that the NYT graphs appear to be backing.


  1. There is a lot of stuff here but I wanted to point out that it is entirely possibly for everyone's tax rates to go down and tax collections to stay the same.

    Suppose that you have two people Adam and Bill. In period one Adam makes $110 and Bill makes $90. Adam pays 20% tax and Bill pays 10% for a total tax take of $31

    Now in period two Adam makes $180 and Bill makes $20. Adam pays 16 & 2/3% tax and Bill pays 5% tax for a total tax take of $31.

    However both taxes were cut

  2. I think what Karl was going for is the Simpson "paradox":'s_paradox

    that can explain why over time all rates drop (or increase), yet composition changes outweigh these effects, and the overall rate is higher (lower).

    I am not sure it can explain how the total is more than each individual rate.

  3. You are reading things into the charts that are not there - setting up one false implication after another and then knocking them down.

    The 528% increase in pre-tax income of the highest earners is the most striking point in the charts. Incomes for the middle class have stagnated while reported incomes for the top earners have surged ahead. There are two possible explanations, which are not mutually exclusive:
    1) reduced tax rates allowed the economy to expand - and most of the benefit went to the people at the top;
    2) with reduced rates, the wealthy reduced their level of tax avoidance and evasion resulting in increased reported taxable income but no real increase in their "economic" income.

    You seem to want lower taxes on returns on investment. The problem with that is: (1) a lot of the money in the markets is already effectively taxed at very low or nil rates because it comes through IRA's, pension plans and insurance companies; and (2) the world is said to have a glut of capital which suggests that there is no demonstrable need to reduce taxes on capital to encourage capital accumulation.

    Where is the pay-off to the middle class in agreeing to reduce taxes on capital when the immediate price of that reduction is a gutting of Medicare and the benefit of the reduction will flow almost exclusively to the already existing investments of the top 0.1%. Where is the incremental benefit to the middle class from the incremental investment that would result from a cut to the taxes on both existing and new investments?

  4. I wondered about these charts as well, what with self-contradictory labels.

    In point of fact, the top income tax rate in the 1960s to early 1970s was 90 percent---but I doubt anyone paid anything like that, even on marginal income above $1 million.

    Since then, the top income tax rate has come down a lot, while payroll taxes have radically increased. For people who make under $100k, payroll taxes are often the largest tax. This is why a lot of right-wingers love charts showing who pays income taxes---and do not like charts showing who pays payroll taxes.

    I am less concerned about who pays taxes, than with getting federal outlays and revenues down to 18 percent of GDP.

    That can be done--by raising Social Security retirement age, vouchering Medicare (and encouraging euthanasia), cutting Defense-Homeland Security-VA outlays by two-thirds, wiping out the USDA and ethanol, and eliminating HUD, Commerce, and Labor.

    Side note: The USA spends $80 billion a year in military R&D, in an era in which we have no military foes of any note. We can cut, and we can cut big time.

    1. I have trouble with attributing the word "tax" to SS and Medicare/Medicaid payments. This word got us to where we are today. If they had been correctly referred to as "forced deferred savings for income and medical care" plus "forced welfare payments for the poor's medical care", then perhaps these payments would have actually been treated that way by the government. But the long accepted unified "pay as you go budget" did turn these payments into a true income tax, rather than being downpayments/savings for the explicit social contract these payments were meant to fulfill.

      This is why we now call these payments "taxes" in the class warfare tax wars. The breaking of the social contract has caused the money to disappear and is disappearing at an ever faster rate. The "intergovernmnetal tranfers account" (the Orwellian named "lock box" with all those "IOUs" in it) is the amount spent using payroll "taxes" on things other than SS and the two MMs. That number now totals about $4-5 trillion and accelerating.

      "Right wingers" have little to do with this, except they have been complicit with the left wingers---this part of course is true---a true bipartisan money grab.

      Some portion of the population, including all government employees, have been scamming other portions of the population. Many of us even have been likely on both sides of the scam, less the vig the government literally takes.

      That money ($4-5 trillion) is long gone folks---never to return. Pretending otherwise is not healthy. One solution, among many plausible ones, is to start with eliminating the unified budget and prohibit payroll taxes from being used for anything other then what they are intended for. This would force a huge reduction in current spending---a rather good thing---plus force admission that the $4-5 tillion does not exist.

      But our pols do not like admitting such things----who wants to deliver that news? But stopping a bad thing is always better than continuing it---isn't it?

  5. This comment has been removed by the author.

  6. John-Re your last point, it's even more of a Laffer dream than you state. Starting at $100 in 1960, a 528 percent increase implies an income of $628 in 2004, not $528. This would imply tax collections of $213.52 in tax collections-a nearly 200 percent increase.

    1. Thanks for pointing out the rather embarrassing arithmetic mistake. I fixed it in the post.

  7. The available evidence is that the total amount of Federal Government receipts is a dependent variable tightly correlated (R^2 99.6) with median household income.

    And that this relationship has held unchanged for the last 40 years, despite dramatic changes in the tax code, and top marginal rates, from the 1954 Code with a TMR of 70% to the 1986 Code which has had TMRs that were as high as 39.6% and as low as 28%.

    I note that this relationship is stronger, and more causally meaningful than "Hauser's Law".

  8. Regarding the update, shouldn't 20% of taxpayers be equivalent to 10% (not 40%) of income earners?

  9. Agreed.

    "being in the top x% of the income distribution means that one is in about the top 2x% of taxpayers."

    Let x be 10% and 2x = 20%. The chart shows most of the tax cuts benefit the top 10% of income earners (not 40%).

    1. Ian and Charlie,

      You are quite right; I had it precisely backwards. How embarrassing.

      Mea culpa.

  10. "(It also appears to me that Saez and Piketty are a bit off here: If you charge corporate income tax against the rich, don't you have to divide that tax by an income measure that includes corporate income? In general, you have to divide taxes by pre-tax income not post-tax income."

    Good point. You should set a PhD student to looking at this for his dissertation. This would change a lot over time too, I imagine, with so many pension funds now investing in stock. What fraction of corporate income actually does go to the rich? (and do they take account of foreign stock holdings?)

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