(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)
Mike “d3” Bostock writes:
Regarding the Vox graph on federal tax brackets, here is a quick-and-dirty visualization of effective tax rates for a given taxable income and year.
However, there is a big caveat: estimating the effective tax rate based on actual income is much harder since it depends on the claimed deductions. This could be estimated empirically, but the IRS doesn’t publish the data (AFAIK).
I’ve recreated the graphic [by Alvin Chang for Vox, criticized in my earlier post] below, substituting a log scale for the y-axis. It readily conveys the Reagan-era simplification of tax brackets, as well as the disappearance of tax brackets for the ultra-rich. (In 1936, the highest tax bracket applied to those making more than $83M in 2013-equivalent dollars!)
Yet fewer tax brackets do not imply the overall tax code is simpler; if anything, the tax code continues to get more complex. And looking only at bracket thresholds does not consider the effective rate at different income levels. . . . It is hard to estimate effective tax rates, especially now, because they depend greatly on the amount of itemized deductions. But ignoring that substantial caveat—and that this analysis only considers federal-reported income and not capital gains, the alternative minimum tax, and countless other forms of state and local taxes—we can compute the effective federal income tax rate for a given taxable income (after any deductions) and a given year.
Amounts are in 2013-equivalent dollars when filing as the head-of-household.
Here are some relevant principles of statistical graphics:
1. Static graphs can do a lot. Dynamic graphics are fine, but in some settings they do little more than add confusion.
2. The log transform really works.
3. No need to try to cram all the information into one graph. Bostock made one graph of tax brackets, another of tax rates. Someone could come along and make a third graph including other taxes, not just federal income tax.
Also, I don’t think graphics need to be so big. I display Bostock’s graphs above in a more compressed format than were on his page. I think that’s fine; actually I think these smaller versions are easier to read because I can see the whole graph more clearly in my visual field. In general I recommend that people make their graphs smaller, which implies that their labels should be larger relative to the original graphs. For Bostock, I’d actually recommend just putting x-axis labels every 20 years, percentage labels at every 25%, and income labels at 1, 3, 10, 30, etc. Some of this is a matter of taste, but I do think there are general issues of readability, and tradeoffs in that more labels make it harder to see the big picture but easier to identify exactly what is happening when.
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