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This morning I heard about how the new tax bill will be using "chained CPI" calculations instead of the traditional CPI calculations, and people seemed to be pretty upset about it. What is "chained CPI" and how does that affect my taxes?

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This Bloomberg article breaks it down nicely

...chained CPI adjusts for what’s known as substitution bias by recognizing that consumers tend to shift their purchasing behavior as the relative prices of things change. For example, when the price of Granny Smith apples increases, people may buy Gala apples instead. As a result, chained CPI shows a slower pace of price gains, or inflation, than traditional CPI.

In that way it is more accurate than traditional CPI, but CPI in general gets plenty of criticism. Chained CPI rates are typically lower than CPI rates. Inflation is used in taxes to adjust tax brackets each year, the intention was to make it so that you don't move to a higher top marginal bracket due to inflation alone. The difference in any given year between chained CPI and traditional CPI is very small, but over time the differences compound.

If actual traditional CPI was in fact higher than actual inflation rates, then the use of CPI was moving tax brackets boundaries up higher than intended, thus reducing tax revenue. Using a lower inflation rate means bracket boundaries will move up more slowly, and should increase tax revenue.

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    Adding on: CPI adjustments are reflected many things, like social security annual increases, IRS standard deduction levels, Personal exemption levels, etc. As it pertains to the IRS, they annually announce these new "adjusted for inflation" amounts - there were some 50 items that were changed for the 2017 tax season: irs.gov/newsroom/… – BobE Dec 29 '17 at 14:35

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