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The 0% tax rate on qualified dividends and long term capital gains that are in the 10% or 15% tax bracket has not changed.

What has changed is that the inflation rate used to adjust the brackets will now be the 'chained' CPI, which moves up at a slower rate than the currently used 'fixed weight' CPI. That will make it harder to stay in the 2 lower brackets as time passes.

Actually, the bill also breaks the link between the tax brackets for qualified dividends and the tax brackets for ordinary income. According to the Joint Explanatory Statement,

The provision generally retains the present-law maximum rates on net capital gain and
qualified dividends. The breakpoints between the zero- and 15-percent rates (“15-percent
breakpoint”) and the 15- and 20-percent rates (“20-percent breakpoint”) are based on the same
amounts as the breakpoints under present law, except the breakpoints are indexed using the CCPI-U
in taxable years beginning after 2017. Thus, for 2018, the 15-percent breakpoint is
$77,200 for joint returns and surviving spouses (one-half of this amount for married taxpayers
filing separately), $51,700 for heads of household, $2,600 for estates and trusts, and $38,600 for
other unmarried individuals.
[Quote from the House provisions; the Senate and joint conference followed the House on this issue.]

But the top of the 12% bracket for ordinary income in 2018 is $77,400 for MFJ, $51,800 for HoH, and $38,700 for single. Just another gratuitous complexity to track, that can't have a significant impact on tax revenue. I kind of sort of understand how this happened in the sausage making process, but I'm still annoyed by the meaninglessness of the separate limits. It will still be 0% on qualified dividends and LTCG up to "about" the top of the 12% bracket, but it won't be precise.

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