Income Taxes

 

I Paid My Income Tax Today

I said to my Uncle Sam
Old Man Taxes, here I am
And he
Was glad to see me
Mister Small Fry, yes, indeed
Lower brackets, that's my speed
But he
Was glad to see me

The rate in a tax bracket is the marginal rate, not the effective rate.

There is a world of difference between speed and acceleration.  We understand that acceleration is important for sprints, but speed is important for marathons. And there is just as much difference between the marginal tax rate (analogous to acceleration) and the effective tax rate (analogous to speed). No one expects a National Association for Stock Car Auto Racing, NASCAR, vehicle to win a drag race against a National Hot Rod Association, NHRA, vehicle.  And no one expects a NHRA vehicle to beat a NASCAR vehicle at the Daytona 500.  The tax brackets are only a way to compute taxes.  The rates cited in those brackets are NOT effective tax rates.

If marginal tax rates were uniformly zero, there would be a flat tax rate.  This would NOT be a  progressive tax rate, which mathematically would be described as a convex function.  By contrast regressive taxes, which decrease with increasing income  mathematically would be described as a concave function.

Math is hard.  But the answer is not to make math fit our expectations. Votes to make Pi equal to 3, (Don’t laugh.  In 1897, the Indiana State Legislature considered such a law) because the value of Pi is hard to remember might be  tempting. But such a law would result in computing the circumference and area of a circle incorrectly.  The correct course should be to change our expectations to fit the rules of math, not vice versa. 

For example the marginal rate for the 2020 married filing separately tax bracket for incomes from $207,350 to $311,025 is 35%, but the effective tax rate varies from 23% to 27%. Mistaking the marginal rate for the effective rate could lead to mistakes in policy.

The effective tax rates are progressive, which is necessary but not sufficient in determining if they are equitable.  The effective tax rates should also reflect the distribution of income.  The US Census reports on the distribution of incomes by quintile.  The distribution of incomes appears to follow an exponential function.  The taxes, and thus the tax rates, should also follow this distribution.  If the mean tax rate, say 20%, is set then the maximum tax rate can be computed from this distribution of income. The formula for the taxes which reflects the distribution of incomes is

Taxes=Income*Maximum Tax Rate*(1-exp (-Income/(Transient-Income))) 

If the distribution of income exactly followed an exponential distribution (not function) then the transient income would also be the mean income.  In this were the case, then the median income would be would be 69% of the mean income.  The maximum rate is not higher than the mean tax rate, because there is a bias against those with higher incomes.  It is the inevitable result of a progressive tax system.  With a progressive tax rate, the only way the mean rate could be the same rate for all incomes, is if ALL incomes were equal to the mean.  The maximum tax rate is a consequence of all incomes not being equal and that there are high incomes and low incomes.  The greater the variance in income, mathematically, the higher the maximum tax rate must be.  As Willie Sutton, the bank robber, once said, he did not rob banks because he had a vendetta against banks. He robbed banks because that is where the money is. If taxes on the rich are high then that is because they are rich, not because the tax system has a vendetta against the rich.