### Any tax reform must keep deductions for state and local taxes

**Matthew Martin**3/27/2014 02:37:00 PM

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Martin Feldstein has a proposal for tax reform that, while reasonable in many ways, makes many errors. One of those mistakes is where he claims that the federal deduction for state and local taxes is a "tax expenditure." Not so!

Here's how Feldstein defines tax expenditures:

"Raising revenue without increasing tax rates requires eliminating or reducing the subsidies in the U.S. tax code. Such subsidies, for things as varied as hybrid cars and increased health insurance, are really the government spending through the tax code. That is why they are officially referred to as 'tax expenditures.'"So he defines tax expenditures and "tax subsidies" as tax deductions which, if eliminated, would increase revenue without increasing marginal tax rates. I concur. Now here's the offending passage:

"The big political challenge is dealing with the large tax subsidies to home mortgages, employer-provided health insurance and state and local taxes."See that, he just implied that the deduction for state and local taxes are a tax expenditure, and that therefore eliminating these would not increase marginal tax rates. FALSE!

We can see why using math. Let [$]Y[$] represent your annual income, let [$]f[$] be your federal marginal income tax rate, and let [$]s[$] represent your combined state and local marginal income tax rate. Under the current system, the federal government lets you deduct state and local taxes from your adjusted gross income for federal tax purposes. That means that if your unadjusted income is [$]Y[$], you only pay federal taxes on [$]\left( 1-s \right) Y[$] Which implies that your after tax income is [$]\left(1-f\right)\left(1-s\right)Y[$] which can be rewritten as [$]\left(1-f-s+fs\right)Y[$].

Now suppose we eliminate the deduction for state and local taxes. Your adjusted gross income is now [$]Y[$] for both state and federal purposes, meaning you pay [$]sY[$] in taxes to state and local governments, and an additional [$]fY[$] in taxes to the federal government, leaving [$]Y-sY-fY[$] in after-tax income. We can rewrite this as [$]\left(1-f-s\right)Y[$] to match the format of the deductible case above.

Now lets compare the two scenarios. When state and local taxes are deductible, your after tax income is [$]\left(1-f-s+fs\right)Y[$], while without the deduction your after tax income is [$]\left(1-f-s\right)Y[$]. Your marginal tax rate is how much less than $1 your after-tax income would rise if your pre-tax income rose by $1 (that is, one minus the first-derivative of after-tax income with respect to [$]Y[$]). Having written the after-tax incomes in this format makes marginal tax rates exceedingly easy to find: with the deduction, your marginal tax rate is [$]f+s-fs[$], whereas without the deduction your marginal income tax rate is [$]f+s[$]. So long as [$]f>0[$] and [$]s\geq 0[$], it follows that [$]f+s>f+s-fs[$]. That is, elimination of deductibility of state and local taxes would increase the marginal tax rates of anyone who pays federal income taxes. This violates Feldstein's definition of tax expenditures. The state and local tax deduction is not a tax expenditure.

Nor is this a trivial issue. We need to keep the deduction for state and local taxes. To see why, just consider the case, int he example above, where the state tax rate is [$]s=0.6[$] and the federal tax rate is also [$]f=0.6[$]. With the deduction, the marginal tax rate is 84 percent, meaning that increasing your pre-tax income increases your after tax income slightly. Without the deduction, your marginal tax rate would be 120 percent, meaning if you work more you earn less! The state and local deduction has to stay. In a previous post I examined this issue in a bit more detail, generalizing and extending it to implicit marginal tax rates generated by welfare incentives. The tax code must be hierarchical in such a way that taxes lower in the hierarchy are deducted from taxes higher in the hierarchy. Otherwise, interactions will cause the whole thing to blow up.