Our Messed-Up Federal Income Tax: Or, What is Your Marginal Tax Rate?

Last week I wrote about the failure of the Bush administration to apply some of that hard-earned political capital to effect Social Security privatization. Let me move on to another failure to apply political capital, this time to reform of the tax code. I do realize that an advisory group came out with some recommendations, but they did not strike me as cutting to the core of the problem. Here is the real problem.

One of my favorite things on an airplane is to ask people how much they paid for their seat. It is a great lesson in price discrimination and usually gets some good conversation going. Of late, I have been having more fun by asking my friends and colleagues what their marginal (federal) tax rate is. At best, I get an answer related to the 2005 Tax Rate Schedules in that favorite of all publications, 2005 1040 Forms and Instructions – that is, a relatively sophisticated answer is to give the statutory marginal tax rate for an individual’s bracket. The current tax schedule has six different marginal rates: 10%, 15%, 25%, 28%, 33%, and 35%.

The problem is that your statutory marginal rate is not your actual marginal rate because of three major effects and one overpowering effect. The three major effects are: phasing-out of exemptions; the phasing-out of deductions; and the Medicare tax which is 1.45% for the taxpayer no matter how high your income. The overpowering effect involves the AMT, the alternative minimum tax, to which I will return shortly.

Just a quick aside, I focus on the marginal tax rate as being key for incentives and therefore the efficiency of our tax system and of the whole economy. My average tax rate last year was, say, 23%, but that is not what should or did govern my decisions about working additional hours. If I have an opportunity to earn an extra $1,000 by working harder, what I should and do consider is how much of that extra money will end up in my pocket. If my marginal tax rate is 40%, I will get only $600 from the extra effort. My average tax rate might be 23%, but the marginal tax rate is what determines what is happening about additional money that I might be able to bring in. This is key. What we want to minimize to the extent possible is the “wedge” between what I am paid (the $1,000 from the above example) and what I take home (the $600 after-tax cash). The bigger this wedge, the greater effect the tax system will have on economic activity.

So how do we figure out our actual marginal tax rate? Given that my colleagues – business school professors! – could not tell me their marginal rate, I thought I would try to calculate my own. I had an estimate, but I wanted to see if I could pierce that complicated code and get it exact. Now one way of doing this, I suppose, would be to use Quicken or some such tax calculation software and simply do two hypothetical tax returns, one with my actual income and one with $1000 higher income. But I like to do things the old fashioned way – with equations and math. That way I understand a little better of what is actually going on.

Let’s get back to the three major reasons why the statutory marginal rate is not the effective marginal rate. The Medicare one is easy; that is simply an added marginal rate that is not part of the income tax but is certainly a relevant Federal tax. The second two major effects are more interesting, the phasing-out of exemptions and deductions. The key point here lies in those two tables that you have to fill out to complete your Form 1040, the table titled “Deduction for Exemptions Worksheet” and the “Itemized Deductions Worksheet.” As your income increases, the tax system allows you less and less of your exemptions and deductions to be subtracted from your income. As this increases your tax payable, the effects work just like a higher marginal tax rate.

Here is the math of it. I am open to corrections on this, as it is pretty complicated, but I think I have it right. There are a couple minor points not picked up by my equations, but they are not critical (for instance, I do discuss below the issue that deductions do not phase out entirely).

So let’s work with someone in the income bracket for their filing status that would give them a statutory marginal rate of 33%. Then I can write the total tax due, T, as

T = Base Tax + r*(AGI – AE – AD)

In this equation, r is the statutory marginal rate for the income bracket we are dealing with ( for a head of household taxpayer at 33%, this is for taxable income between $166,450 and $326,450). The base tax for such a taxpayer is based on the rates that apply for the first $166,450 of income, which for a single taxpayer would be $39,019.50. AGI is adjusted gross income; AE is allowed exemptions and AD is allowed deductions. Deciphering the tables that calculate AE and AD, we get:

AE = E – ((.02)*(AGI-y')/2500)*E)

where E is your dollar exemption amount before the adjustment and y' is a critical level of income, depending upon filing status (for a head of household taxpayer, y' is $182,450). To take an example, suppose someone has $250,000 of AGI and is filing as head of household, and also has five exemptions. For five exemptions, the statutory amount would be 5*3200 = $16,000. However, from the above equation, you can see that such a taxpayer is going to lose 54% of his exemption amount, leaving him with only $7353.60 of AE to subtract from AGI. Give that taxpayer another $10,000 of income and he is left with only 38% of his exemptions, or a dollar amount of $6073.60. Thought those kids were worth more than that, didn’t you??

Now if this is all getting a bit too complicated, I rest my case: our tax code is a mess.

The equation for AD is not quite so bad:

AD = D – (.03(AGI-y''))

Where AD is allowed deductions; D is statutory deductions; AGI is again adjusted gross income; and y'' is another critical level of income that is $145,950 unless filing status is married filing separately (in which case it is $72,975). (NOTE: I do realize that at worst, you will always get at least 20% of your statutory deductions. The equation above assumes that your income is not so high that you are at the extreme outcome where you will get 20% of your deductions and that is that. This is an interesting aspect of the effective marginal rates, which is that marginal rates actually fall as income gets really high because the phasing-out of exemptions and deductions is done.) Taking another example, let’s have our head of household with $250,000 of income and statutory deductions of say $30,000 (mortgage interest and local property taxes). Then deductions are going to get reduced for this taxpayer by $3125,50.

Now we have it. We can now write total tax payable as

T = Base Tax +r*AGI
-r(E - .02*((AGI-y')/2500)*E)
-r(D-.03*(AGI-y''))

Oh boy! Now we take the derivative of that with respect to AGI to get the marginal tax rate!

dT/dAGI = r + (.02/2500)*E*r + .03r

So the marginal rate depends not only on the statutory rate but also on the level of exemptions…because as your income goes up, the percentage of your total exemptions allowed goes down. Makes sense.

Take again our head of household filer with five exemptions, or an amount of $16,000 in exemptions, and in the 33% statutory bracket. This person would have a marginal income tax rate of

Marginal tax rate = .33 + (.02/2500)*16000*.33 + ,03*(.33)
= .3819.

So these two effects, the phasing-out of exemptions and deductions, increase this taxpayer’s marginal rate by 5.2 percentage points.

On top of that, we have to add the Medicare marginal rate of 1.45%, thereby making this taxpayer’s effective marginal rate a whopping 39.64% -- ah heck, call it 40%.

But now for the truly overwhelming effect. After going through all of good-old Form 1040, you get to the point where you have to fill out the Worksheet to See if You Should Fill in Form 6251! Form 6251 is the dreaded Alternative Minimum Tax, which in many taxpayers’ cases this year, it turned out they owed. So not only did they have to fill out the form to find out if they should fill in Form 6251, but they actually had to fill in Form 6251. In terms of the discussion here on the effective marginal tax rate, the Alternative Minimum Tax (AMT) really changes thing. In effect, the AMT broadens taxable income, by eliminating completely many deductions and exemptions, but at the same time it lowers the marginal tax rate -- to 26% or 28%. So in the end, the effective marginal tax rate this past year for the hypothetical taxpayer above was 28%, plus the Medicare rate of 1.45%, for a total effective marginal rate of 29.45%.

So she might have thought that she was going to get hit with a marginal tax rate of 40%, per my calculations above, but at the end of the year it would turn out that she should have anticipated getting hit by the AMT and having a marginal rate of only 29.45%. But tell me, how many people think ahead that much?

If anyone in Washington is reading this, can you tell me why we don’t just make the AMT the law of the land? The AMT is essentially a flat tax, with close to one tax rate (26 or 28%) applying to the whole base. Let’s do it and cut out all the confusion! More and more people are getting caught by the AMT. I would have thought that the Bush tax advisory panel would have just said, hey, if all these people are already under a flat tax rate system, let’s just make that the norm. Tell us what you made, with some significant adjustments for really low income taxpayers and to allow for some minor deductions, and pay the government 20-odd percent of it. How sweet and easy!