Monday, November 13, 2017

Tax math for dummies like me

The math is plain as day, and Senate Republicans have seized on it: According to the Joint Committee on Taxation, the nonpartisan tax policy counterpart of the Congressional Budget Office, the Senate tax bill cuts taxes on low and middle incomes more sharply than on higher incomes. Right?

Wrong, explains David Kamin, Obama's former Special Assistant to the President for Economic Policy.  The percent cut in your tax rate is very different from the percent increase in your after-tax income. Here is his chart  (with an adjustment at the top end for repeal of the estate tax, which JCT leaves out):


Surprise! The Republican tax cut is regressive.

If you're like me, this is not exactly intuitive. It's obvious that a larger cut in tax rate at the low end of the scale could mean a smaller bounty in dollars, since the dollars owed are so much fewer to begin with. But how can a larger percent cut in tax liability translate to a smaller percent increase in after-tax income?

To answer that, I had to set it as a problem. And of course it's true:

          Changes in tax liability and after-tax income

          $1 million income: rate drops 5%, from 40% to 38%
                 After-tax income rises from $600,000 to $620,000, up 0.33%

          $100,000 income: rate drops 7%, from 25% to 23.25%
                 After-tax income rises from $75,000 to $76,500, up 0.22%

So, why?  When you cut a larger number by a smaller percentage than you cut a smaller number, you still may cut more off the larger percentage. The distance between 40 and 38 is greater than the distance between 25 and 23.25.  Put more starkly, and using an equal percentage cut, if you take 10% off a 40% tax rate, you've cut four percentage points; if you cut 10% off 10%, you've cut one point (ten to nine). 

If no one but me needed that explanation sorry to have wasted your time. But Republicans are spinning the JCT numbers furiously. So if you're not mathematical, remember: the key comparative measure in terms of the impact on people's lives in different income brackets is the percent you raise their incomes, not the percent you cut their tax liability.

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