Tax Rascal

# Do Some People Really Face an 83% Income Tax?

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It’s a surprising claim, but Mankiw has at least done the math. He argues that for any new income, he’d invest it, and let his kids inherit it. Thus:

Let’s suppose Greg Mankiw takes on an incremental job today and earns a dollar. How much, as a result, will he leave his kids in T years?

The answer depends on four tax rates. First, I pay the combined income and payroll tax on the dollar earned. Second, I pay the corporate tax rate while the money is invested in a firm. Third, I pay the dividend and capital gains rate as I receive that return. And fourth, I pay the estate tax when I leave what has accumulated to my kids.

Let t1 be the combined income and payroll tax rate, t2 be the corporate tax rate, t3 be the dividend and capital gains tax rate, and t4 be the estate tax rate. And let r be the before-tax rate of return on corporate capital. Then one dollar I earn today will yield my kids:

(1-t1){[1+r(1-t2)(1-t3)]^T}(1-t4).

For my illustrative calculations, let me take r to be 10 percent and my remaining life expectancy T to be 35 years.

If there were no taxes, so t1=t2=t3=t4=0, then \$1 earned today would yield my kids \$28. That is simply the miracle of compounding.

Under the McCain plan, t1=.35, t2=.25, t3=.15, and t4=.15. In this case, a dollar earned today yields my kids \$4.81. That is, even under the low-tax McCain plan, my incentive to work is cut by 83 percent compared to the situation without taxes.

Under the Obama plan, t1=.43, t2=.35, t3=.2, and t4=.45. In this case, a dollar earned today yields my kids \$1.85. That is, Obama’s proposed tax hikes reduce my incentive to work by 62 percent compared to the McCain plan and by 93 percent compared to the no-tax scenario. In a sense, putting the various pieces of the tax system together, I would be facing a marginal tax rate of 93 percent.

What Mankiw is doing here is setting up a simple conversion rate between the dollars he earns and the dollars he spends. That’s fine, but he’s omitting almost every datum that would add to his return: he assumes a maximum marginal tax rate, that investments he makes will pay all of the corporate income tax, that investment he owns will be sold every year and will require full capital gains taxes, and all of his estate will be subject to taxes.

He also assumes that he values another dollar just as much as his kids do, which is not likely. Mankiw stipulates that he has all the money he wants, which is why he’d give his the money. But if Mankiw and his kids value the money equally, why give it to them in the first place? Why not assume that he’d give it to his most indigent or deserving relative, who would value it more highly than he would?

We can subject Mankiw’s calculations to some more realistic constraints: let’s imagine that 1) when he earns money, he gives it to each of his kids, in equal proportion; 2) he invests it on their behalf in very stable growth companies, turning over his portfolio every seven years rather than every year; and 3) he picks companies with lots of pricing power, so when taxes change, their customers pay rather instead of them.

In that case, Mankiw’s formula becomes (1-t1)(((1-t3)^(T/7))*(1 + r)^T. For the McCain plan, this yields a return of about \$8.10; for Obama, \$5.24.

These presumptions are differently (perhaps not equally) distorted, but they do demonstrate that a little prudence and planning could drastically increase Mankiw’s after-tax return for his children. Perhaps this is why he is an economist, rather than a financial advisor.

This exercise also illustrates something else: when you come up with alternative measurement systems, make sure they’re easy to convert back into the original. I used to try to figure out how long it would take to get somewhere by thinking in “New York Miles,” whereby two subway stops twenty blocks apart were ‘closer’ than a subway-less intersection three blocks away, because I’d waste less time in transit (subway-time isn’t wasted; you can read on the subway). It didn’t take long before I realize that this was a lot of extra work for basically no additional insight, and that tiny tweaks in assumptions could have an outsize effect on what conclusions I ended up reaching.

Mankiw is probably right that he doesn’t have a strong incentive to work, but he didn’t need much math to explain it. The answer was right there in his premises:

I am a pretty lucky guy. I have a comfortable, upper middle class life style that includes one house, two cars, three kids, a wife, and a dog. I am fortunate enough that I don’t have trouble keeping that going. I am also fortunate enough that I don’t crave much more than I already have. I don’t particularly want to own multiple houses or drive a Ferrari or wear Armani suits. You might say that I am close to being sated.

Mankiw’s work time isn’t ‘taxed’ because of the McCain or Obama plans; it’s taxed because he has better things to do with his time than work for more money.

### 3 Responses to “Do Some People Really Face an 83% Income Tax?”

1. Allen Taylor Says:

Allen Taylor

2. Alas, a blog » Blog Archive » By All Means, Greg, Take More Time Off Says:

[…] Mankiw’s argument, the base assumptions underlying his math are ludicrous1 (as you’d expect from someone who once argued that we could pay off the deficit […]

3. CR Says:

I don’t know if there is an academic consensus on the effective rate of tax but it seems strange to me that there shouldn’t be.
Anyway, on your technical points about investment taxes you sound like you are right (I don’t know much about these things).
I don’t think I agree with your subtle point about his valuing money the same as his children.
The way one should think about this is to give Mankiw a utility function over money at the end of his life – assumed to be a fixed point in the future for simplicity. That is determined by whatever he wants to will the money to. (Your points that he might give this before he dies and not face so much inheritance/capital taxes is well taken. Assume he is not allowed to do this for the sake of analyzing your argument.) There is no assumption that this utility function is the same as anyone else’s or that Mankiw cares about any one else’s utility. This is then just like a static tax model in which Mankiw works (a mulitidimensional choice of work over time) and gets a gross income and a net income. It is correct to say in this framework that today’s work faces a marginal rate of tax given by the sorts of calculations you and he are doing.

Your last comment is to be blunt badly worded and irrelevant. Yes it may be that Mankiw’s supply of work is not very price-sensitive (which is I suppose what you meant to say), but he wasn’t arguing at that point that it was.