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# The "Buffett Rule's" Marginal Tax Rates

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I've been trying to figure out what marginal tax rates would be if the so-called "Buffett Rule" were passed. There's an actual Senate bill out there but, as with almost all bills, you have to look at previous law--and know how to read dense laws--to understand what it means.

Here's a little background on tax law and economics to explain what I mean. When tax economists talk about marginal tax rates, they distinguish between a "notch" and a "kink." Example: In 2010, Megan McArdle advocated eliminating "the tax-deductibiity of health insurance benefits for people making more than \$150K a year in household income, \$100K for singles." If we take her literally, she was advocating a notch. Here's my analysis at the time:

Imagine that you're a married person with a family and you're making exactly \$150K a year. Your employer pays \$10K toward your health insurance. Of course, it's not subject to federal income tax, state income tax, or Social Security or HI tax. You and your spouse make a total of \$150K, split roughly evenly, so both of you pay the marginal payroll tax rate of 7.65%. You also pay a marginal income tax rate of 25% and a state income tax rate of 5%. So your total marginal tax rate is 25 + 5 + 7.65 = 37.65%.

Now you earn one more dollar. What happens? That whole \$10K employer contribution becomes taxable and so you pay tax on it at 37.65% or \$3,765. You made an extra buck and you paid \$3,765 extra in taxes. Oh, yes, plus \$0.3765. So you paid \$3,765.3765 in taxes. Your marginal tax rate on that dollar: 376,537.65%.

That's a notch.

Now, my guess is that she didn't mean what she wrote literally but, instead, wanted to phase out the deductibility over some income range. That would convert a notch to a kink. [Why these terms? Imagine drawing the Marginal Tax Rate on the vertical axis against income on the horizontal. If there is no phaseout, you get a big jump at the \$150,001 point and then a big drop at the \$150,002 point. If there is a phaseout over some income range, you get the MTR line kinking and becoming steeper at the \$150,001 point.]

Rather than speculate about what she might have meant to say, let me turn to the Buffett Rule. If I take literally the way Obama talks about the Buffett Rule, then, once your taxable income hits \$1,000,000 or \$1,000,001 [I'm not sure which], your average federal tax rate on income becomes 30%. Now let's assume Buffett is right that there are a lot of high-income people paying, say, an average federal income tax rate of 20%. Imagine one of these people is making \$999,999 in taxable income and he is contemplating making an extra \$1 of income. Without the Buffett Rule, he pays \$200,000 [actually \$199,999,80] in federal income taxes. If he makes that extra dollar, getting him to the magic number of \$1,000,000 in income, he pays income taxes equal to 30% of his taxable income, or \$300,000. So he pays an extra \$100,000 in federal income taxes. His Marginal Tax Rate on that one millionth dollar is 10,000,000%.

Surely, Obama can't mean that, can he? It's hard to understand the proposed law, given how little analysis has been done. So let's turn to the Joint Committee on Taxation, which has done revenue estimates. Not surprisingly, they seem to be aware of this problem and contemplate a phaseout. They write:

The tax would be phased in for taxpayers with AGI between one million dollars and two million dollars (\$500,000 and one million dollars for married individuals filing a separate return).

So that's a kink, rather than a notch, for my hypothetical taxpayer at \$1,000,000 in taxable income. If he's at an average tax rate (ATR) of 20%, we can figure out his new MTR. Over the next million, he will move from an ATR of 20% on \$1,000,000 to an ATR of 30% on \$2,000,000. In other words, over that additional \$1,000,000 in income, he will pay an additional \$400,000 in income tax. [30% of \$2,000,000 minus 20% of \$1,000,000.] So his marginal tax rate jumps to 40%. That's bad, but not as horrific as it might first have seemed.

But wait; there's more. What about the person making \$1,999,999 in income who makes an extra \$1? For him there's NO phaseout. If he is currently paying 20% of his income in taxes, which is \$400,000 then, under the Buffett Rule, he would pay 30% of \$2 million, or \$600,000. So he pays an extra \$200,000 on that last dollar of income and his MTR is 20,000,000%.

This is as far as I've gotten. Has anyone looked at the details beyond what I have above?

UPDATE: My second last paragraph above, starting with "But wait; there's more," is incorrect. David W says why in the comments below:

The 1,999,999 taxpayer does indeed pay \$200K more - but that's the result of the change in law, not the result of the earning an extra dollar. Marginal tax rates are a question of the change in tax by changing your income, keeping law constant. What you're calculating is the effect of changing the law, keeping income constant. His marginal tax rate is certainly higher than current law, but it's also not what you state.

CATEGORIES: Taxation

dave smith writes:

You are correct, Professor. Regardless of any attempt to "phase in" the Buffet Rule, there will always be a "notch" where MTR are very, very high.

Here is why: our tax system is based on progressive marginal rates, but the buffet rule mandates a certain average rate. To switch regimes for a given taxpayer with the goal of making them pay more, there has to be huge singular jump in MTR.

David R. Henderson writes:

@dave smith,
Well put, dave. I think you’re right.

David W writes:

Your 'but wait, there's more' example is overstated. The 1,999,999 taxpayer does indeed pay \$200K more - but that's the result of the change in law, not the result of the earning an extra dollar. Marginal tax rates are a question of the change in tax by changing your income, keeping law constant. What you're calculating is the effect of changing the law, keeping income constant. His marginal tax rate is certainly higher than current law, but it's also not what you state.

As another way to look at this: if a law were passed that people named David had to pay an extra 200K in tax a year regardless of how much they made, that law would have a marginal tax rate of 0%.

The Buffett rule is worth opposing, but not for this reason. I would prefer to focus on things like enabling federal government overspending, giving in to envy as a driver of policy, and not likely actually raising much revenue.

Luke writes:

The whole thing is so odd, I'm having a hard time taking the proposal seriously. It seems more likely that the whole thing is a stunt designed to "prove" that conservatives show favoritism to "the wealthy" by forcing them to vote against "making millionaires pay their fair share".

John Voorheis writes:

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John Roccia writes:

That's why I don't get the concept of "income brackets" at all. Wouldn't it make more sense to just say that the first 40k of anyone's income is tax-free, the next 90k is taxed at 10%, the next 120k is taxed at 15%, and all money above that is taxed at 25% (or whatever the levels and percentages happen to be)? I mean, leaving aside all the other objections to progressive tax rates and even income tax in general, why tax the people who make income in different ways, instead of just taxing the actual income differently? Wouldn't this remove a lot of the "one dollar more" scenarios, and remove the incentives to make less money just so you don't get "bumped up into a higher bracket?"

JohnW writes:

If I understand the current system, the usual thing to do is for the marginal tax rate to be continuous, with the various "data points" connected by straight lines to phase the higher rates in.

The problem with the Buffet tax seems to be that people are talking about introducing an average tax rate into the current system based on marginal tax rates.

I would think the obvious solution would be to convert the Buffet tax idea into marginal rates. Basically, they would raise the current marginal rates at \$1M and above (or \$0.9M, or \$0.8M, depending on the phase-in desired), and possibly have the phase-in be very steep. Certainly not something I'd like to see, but at least it keeps the marginal tax rates continuous, instead of having discontinuous large jumps, as you mention in your post.

Ryan P writes:

John Roccia,
Right, that's what tax brackets do now. If you're a single person claiming the standard deduction, your first \$9750 in income isn't taxed at all, then your next \$8700 is taxed at 10%, the next \$28,650 at 15%, etc.

Even when a politician proposes something that sounds like an "atom of taxes" (where your total tax bill explodes discontinuously at a certain point), people at JCT and similar groups try to do their best to interpret the rule as phasing in over a range. Often you can't avoid having marginal rates be higher on some range than they are later, but you usually can avoid the ledge where earning a dollar costs you more than a dollar in taxes.

Keith Weintraub writes:

I don't think there needs to be a notch.

Imagine a graph with an X-axis of income and a Y-axis of ATR. Draw a line from (X,Y) of (1M,0) to (2M, 30%) and then continue it horizontally at (XX, 30%) for XX > 2M. The post-Buffet rule tax could be the maximum of your current ATR and this curve.

A notch is a discontinuity on this graph. A kink is a slope change.

The top marginal rate caused by the introduction of the Buffet rule in this hypothetical is 60%.

Airman Spry Shark writes:

@dave smith's point is only valid if you assume a constant MTR over the range of the phase-in

For instance,
MTR = 0.3 + 0.0000002 * (AGI - \$1M)
smoothly transitions from an ATR of 20% @ \$1M AGI to an ATR of 30% @ \$2M AGI, peaking at an MTR of 50% @ the 2,000,000th dollar. There are a couple of kinks (20% to 30% @ \$1M & 50% to 30% @ \$2M), but no notch.

Kevin Glass writes:

Two things:

-The Sheldon Whitehouse bill commonly known as the Buffett rule claims to have a phase-in between \$1 million and \$2 million - both CAP and the American Spectator reported this, so I think it's not as extreme as you make it out to be.

-The Tax Policy Center's chart of historical tax rates (here) lists the average effective rate for taxpayers in the top 1% to have hovered around 20% for the last few years; this to me suggests a much more substantial tax increase for these multimillionaires.

writes:

I think I agree with David W and Airman Spry Shark.

Let us formalize

```TR =
.2                if I < 1M
.1 * I / 1M  + .1 if 1M <= I < 2M
.3                if 2M <= I
```

Taxes paid is

```I * TR =
.2 * I                 if I < 1M
.1 * I^2 / 1M + .1 * I if 1M <= I < 2M
.3 * I                 if 2M <= I
```

Taking the derivative to calculate the marginal tax rate yields

```MTR =
.2               if I < 1M
.2 * I / 1M + .1 if 1M <= I < 2M
.3               if 2M <= I
```

We see that the Marginal tax rate is .3 at 1M and rises steadily to .5 at 2m, before falling back to .3 for all dollars after the 2mth.

To use math terminology, notches exist where the taxes paid is discontinuous, kinks exist where where the derivative of taxes paid is discontinuous.

David R. Henderson writes:

@David W,
You’re right. I considered the wrong margin. Thanks. That’ll teach me to write a long blog post in the early a.m. before a long day of teaching.

This thing is such a poorly written mess. If the goal is to raise taxes there are much simpler & easier ways to do that without introducting another layer of complexity to our already horrendous tax system.

Jim Glass writes:

Two thoughts:

1) The Buffett Rule is simple political posing for the election season. The Administration has made zero proposal to implement it. This is the classic form of political posing. If you actually want to do something, you make an actual proposal to do it -- but then the other side has something to criticize and shoot back at to score points of its own.

OTOH, if all you want to do is rally up votes without giving anything to the other side, you just make a "wish" proposal, and say "who could possibly argue with this?" And you don't propose anything concrete people *could* argue with. But while you may rally your troops this way, making zero effort to do what you are saying shows you are not serious. (As John Mitchell said in the Nixon years, "pay attention to what we do, not what we say".)

2) Buffett on Charlie Rose after making his tax proposal went on to list the amount of his SS benefits and say "People like me collecting Social Security and Medicare is absurd, this should be stopped".

Somehow, people pushing the Buffett Rule for taxes are ignoring the Buffett Rule for entitlements.

If not collecting enough taxes from "the rich" is bad, how is collecting taxes from the poorer plus running up the national debt to make transfers to the rich not much worse?

Again, proof the issue is not serious -- if cutting transfers to the rich is not on the table in Washington, then the politicians aren't actually concerned about the deficit at all.

If they ever become really concerned, this will be at the top of their list. Especially the the list of the Left -- for how can the Left argue to raise taxes on everyone else to protect transfers to the rich? (I'm looking forward to the day when Krugman declares *that* to be "progressive" policy.)

writes:

This is why we don't usually use average tax rates.

Tim Ozenne writes:

Have you considered the issue of charitable contributions? My quick read of the CRS summary suggests that charitable contributions may provide a way to avoid falling into the Buffet trap.

mark writes:

Right. The minimum effective rate across the full income is an embarrasment intellectually.

A more intelligent approach would be (1) for Congress to identify from available data the typical tax payment from someone who makes gross income of \$999,999 using typical deductions without limits; (2) to then impose a marginal tax rate for income above \$999,999 that, when applied to income between \$1 million and \$2 million produces a payment which, when added to the first payment, sums to \$600,000. In your example, if the effective rate is indeed about 20% below \$1MM, then the marginal rate is 40%. That rate applies to all income above \$2MM which frankly it should.

writes:

Might I suggest adding an update with David W's correction? I looked at this post and the problem jumped at me, but reading the comments, it seems lots of people don't realize the error.

David R. Henderson writes:

@PrometheeFeu,
Thanks. Good suggestion. Will do momentarily.

William Vaughn writes:

The Buffet rule is not addressing any of the real problems with the tax code. In fact, it would create yet another iteration of the AMT. One real problem with the tax code is that the marginal rate on capital gains in too low (15%) and that is why Mr. Buffet's effective tax rate about the same. We should phase-in a rule over a ten year period that brings that rate up to 25% or so. This can be done by increasing the percentage of capital gains subject to the standard progressive tax from 43% to 70%. (.15/.35 is approx. .43 and .25/.35 is approx .70).
The second problem that is exposed by your examples is the tradition of using "stair-step" or discontinuous marginal rates in our tax code. We should phase-in a continuous marginal rate system that eliminates these arbitrary income "boundaries". If you google "income tax rates" and "bracketless" you'll get to my blog entry that proposes a solution. Also "tax rates made simple" will get you there. The two-parameter system I propose would also simplify the discourse when discussing and comparing alternative tax systems. I think it's worth a look.

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