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Republicans Go to War Against Arithmetic; Or, a Tax Hike Too Far

Both House and the Senate plans zero out the personal exemption, now scheduled to be $4150 per dependent in 2018.

Both plans also increase the standard deduction from the $13,000 scheduled for 2018 to $24,000 (married filing jointly).

The first change hurts, the second helps.  The net effect is a matter of arithmetic.

All calculations below assume a family of four, with the children over 17.

Case 1: You were planning to take the standard deduction in 2018

The arithmetic is simple: under the Senate Republican plan, you have minus (4 * $4150) for the lost personal exemptions, plus ($24,000 – $13,000), for the increased standard deduction. In English, you lose $16,600 of personal exemptions, and you gain $11,000 of enhanced standard deduction.  So net, you lose $5600 in subtractions from taxable income.

Your tax hike, therefore, is your marginal tax rate (22.5%, 25%, 28%, or 33%, depending on which tax plan takes hold: the current regime, the House proposal, or the Senate proposal), multiplied by that $5600.

In sum, due to the changes in the personal exemption and the standard deduction, you pay between $1200 and $1800 more in tax, depending on which tax regime takes hold, minus any benefit from the lower rates proposed in some plans.

That’s the cost of removing personal exemptions, while raising the standard deduction by less than that dollar amount (for a family of four—note that for a family of three, the arithmetic would be close to a wash).

Arithmetic: a loss of $16,600 in exemptions must exceed a gain of $11,000 in deductions

Case 2: You itemized, and had more than $24,000 in deductions; but without state and local income tax, and/or property tax, your deductions would have been less than $24,000

To make this case concrete, assume a mortgage of $375,000 and interest rate of 4%; that gives the first $15,000 of deductions. In California, this house might incur $5000 in property tax; in Texas or New Jersey, $10,000. In Texas there would be no state income tax; in California, assuming an income of $150,000 more or less, there would be a state income tax of about $10,000; in New Jersey, perhaps $6,000.

So under the current regime, deductions look like this.

California Texas New Jersey
Mortgage $15,000 $15,000 $15,000
Property tax $  5,000 $10,000 $10,000
State income tax $10,000 $  6,000
Total deductions now $30,000 $25,000 $31,000


Given the same adjusted gross income, the Texan family currently pays one to two thousand dollars more in Federal taxes, because of fewer deductions; but their total tax burden will be less, because of the absence of state income tax.

Now if the Senate bill becomes law, and state and local taxes cease to be deductible, deductions look like this:

California Texas New Jersey
Mortgage $15,000 $15,000 $15,000
Property tax
State income tax
All take the new standard deduction instead of itemizing $24,000 $24,000 $24,000
Resulting increase in taxable income $  6,000 $  1,000 $  7,000


All take the new standard deduction, since they no longer have enough deductions to itemize.  Tax simplification!

Unfortunately, all now have an increase in taxable income, small for the Texans, substantial for the California and New Jersey residents.  In the 25% or 28% brackets (again assuming income of $150,000 or so), the increased taxable income will cost the California and New Jersey resident another $1500 to $2000 in Federal income tax.

Arithmetic: lost deductions must add to taxable income

The General Formula

The initial tax increase, before offsetting provisions, for a family of four, under the Senate Republican bill, will be:

  • Tax rate X (PE + excessD).
  • PE stands for the lost personal exemptions, @$4150 each in 2018
  • excessD is the extent to which state and local tax deductions, added to all other current deductions, cause total current deductions to exceed the greater of ($24,000, all other deductions)
  • tax rate will be 25% or 28% for these prosperous suburbanites.

For a numerical example, if the New Jersey family were in the 28% bracket, they lose $23,600 in exemptions and deductions, and would therefore suffer a tax increase of $6600.

This will be ameliorated if tax rates are lowered, and / or if they have children under 17, and can take the new child tax credit.

But still—you can see why a New Jersey Representative might be unenthused by the new Republican tax plan. Will his constituents vote to re-elect him, if he imposes a tax hike of thousands of dollars? Will they fail to do the arithmetic that reveals the hike?


In today’s tribal politics, it’s easy enough to oppose science—opposition was forged in the debate on Darwinian evolution, and honed on climate change.

And it’s not hard to oppose calculus, or any procedure that includes the phrase “least squares” (viz, John Roberts in the recent Supreme Court case on gerrymandering). After all, how many voters remember their calculus class fondly—or even their algebra class?

But to stand up and say two plus two need not equal four—surely that’s a bridge too far?

We shall see, as the Republican party goes to war against arithmetic, proclaiming tax cuts for the middle class.

Published inPoliticstax planning

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