How to Lie With Statistics: Tax Rates

A good deal of the recent rhetoric in support of Democratic proposals for raising taxes is designed to make it sound as though rich people pay federal taxes at a lower rate than everyone else. That, as one can easily check by looking at the published figures from the Congressional Budget Office, is not only false but wildly false. Most people in the bottom half of the income distribution pay no federal income tax at all, although they do pay payroll taxes and, arguably, some of the cost of corporate income tax passed on in higher prices or lower wages. On the CBO calculations, the ratio of total federal tax paid to income rises pretty much monotonically with income.

The less extreme claim, which has been getting a good deal of press of late, is that a quarter of the households with an income of at least a million dollar a year pay taxes at a lower rate than the ten percent of those with incomes of under $100,000 who pay at the highest rate. 

I have not seen any detailed explanation of how those numbers are calculated, but presumably they are based on income and tax for a single year. If so, although the claim may be literally true, it is also highly misleading—an elegant example of how to lie while telling the truth.

Income and tax liability vary for each individual from year to year. If you take a large capital loss one year, part of it carries over to reduce your taxes, but not your income, in the next year. If you have a large capital gain in one year, your taxes go up for that year but your average tax rate goes down, since capital gains are taxed at a lower rate than ordinary income. 

Some of the 25% of high income taxpayers paying at the lowest rate are people who regularly pay less taxes than most, some are taxpayers who happen to be paying a lower rate than average this year. Some of the 10% of middle income taxpayers paying at the highest rate are people who regularly pay more taxes than most, some are people who happen to be paying a higher rate this year than most years. So the widely reported calculation overstates, by how much I have no way of knowing, the spread of both distributions, both the number of middle income taxpayers who on average, year after year, are taxed at a higher rate than the bottom 25% of high income taxpayers and the number of high income taxpayers who on average are taxed at a lower rate than the top 10% of middle income taxpayers.

If the logic is not clear, consider betting on the races. Each day, a significant fraction of the bettors—say a quarter—make money. A few of them make money because they really are much better than most at guessing which horse will win. Most of them make money because that was the day that they happened to be lucky. If you looked only at the day's results, you would conclude that the top quarter make money at the races. If you looked at the year's results, you would come up with a much smaller number.

Just as, if you looked at the tax rates paid by any group of taxpayers over a period of years, you would get fewer paying a rate that was unusually high or unusually low than if you look at them for a single year.

And for readers interested in a more general account of how to lie with statistics, I have a book to recommend.

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P.S.

Here are two summaries of federal tax incidence, one from the Tax Policy Center of Brookings and the Urban Institute, one showing the figures from the Congressional Research Service. The former shows figures for the top one percent and top tenth of a percent. At least by its calculation, the effective rate rises monatonically with income.

P.P.S.

I linked to the figure showing the Congressional Research Service numbers, which I found on Google+. That apparently didn't, or at least doesn't, work. Here is the figure: