Impossibility theorem of marriage tax
It is well known that there could be marriage penalty or marriage bonus. For example, in 2019, if two people each make more than $306,175, then they have to pay more tax after getting married. In the worst case, they have to pay $8,165 more. Not that bad. However, if one person make all the money, and the other has no income, then together they will always pay a smaller amount of tax.
I always thought this is because the tax code is designed to advocate sole breadwinner in a family, and the other person is stay at home husband/wife. Recently, I realized it is just mathematically impossible to have anything other than a linear tax and preserve some other nice properties.
Indeed, this was shown by Lovell .
Let be the positive reals. Consider functions and . The first is for tax paid for a single person and tax paid for a married couple file jointly. The input for married file jointly is a single number, which is the combination of the taxable income of the couple. This is called horizontal equity in marriage.
Marriage neutral is precisely when . We define a few notions, it is not completely the same as the ones in Lovell’s paper , but it essentially demonstrate the same idea.
A tax function should have the following properties.
- Reasonable Tax: . Indeed, one should not tax people more than their income. The taxation system does not want to give free money to low income people either.
- Principal of Progressiveness: there is some such that for all . Basically, the rich should pay a larger proportion of their money to taxes.
For a marriage neutral system, the reasonable tax requirement would prove that for . It is easy to see we cannot hope to have principal of progressiveness.
Married filing separately is always no better than them being single and file their own taxes.
I personally think there should not be a marriage penalty at any income level to encourage marriage. Of course, people might disagree and think the rich should have a marriage penalty, since it is a small amount compare to their total income so they won’t care anyways.
Anyway, consider the world where there can only be marriage bonus. That is we have the property . An easy tax function is a function that has reasonable tax property, and is a piecewise-linear convex that has at least breakpoint larger than . This is strictly stronger than principal of progressiveness. This is satisfied by the current personal income tax function used by the IRS.
Let be a easy tax function, then we can obtain an easy tax function that always gives a marriage bonus. Indeed, let . is extreme in a way that any function greater than it at any point will cause marriage penalty. is the infimal convolution of and itself, which would also be piecewise-linear convex. If is the personal income tax function for 2019, then matches the 2019 IRS married file jointly function up to $612,350! For some reason I do not know, the IRS decide to cut this off at $612,350, and then impose a higher rate just to penalize families with two very high income earners.
 M.C. LOVELL, ON taxing marriages, National Tax Journal. 35 (1982) 507–510.