## Sunday, October 26, 2008

### Greg Mankiw Tackles the Theory of Tax Incidence

Greg Mankiw laments the impact of enacting Barack Obama's tax plans on his personal work incentives:

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....

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....

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...
One problem with Mankiw's analysis here is that Mankiw assumes that all corporate stocks pay dividends. That's not true; I don't know the actual figures, but I believe the share of companies that pay dividends is a lot less than 1. This matters for the simple reason that dividend taxes aren't owed when no dividends are paid.

A second problem is that the capital gains tax is imposed only when gains are realized, not as gains are accrued. This means that for the part of Mankiw's income related to cap gains liability, the proper formula is [(1-t1){[1+r(1-t2)]^T}(1-t4)](1-t3). That is, the (1-t3) part doesn't get compounded, instead being applied after the gains have fully compounded. Plugging in Mankiw's chosen numbers, this fact means that under Obama's plan, a dollar earned today and invested in non-dividend paying stocks at a fixed return of 10% leads to \$2.27 (see update immediately below) when Mankiw leaves his money to his children, which is more than 25% higher than Mankiw's reported figure. (I leave it as an exercise to compute the corrected number for McCain's plan; I note also that assets that don't pay dividends will have to have a higher rate of capital gain than those that don't, other things equal).

[Update: David Levine points out an additional factual error of Mankiw's in the comments. When assets are inherited, the basis for capital gains taxation often/usually becomes the value of the asset at the time of inheritance, provided that this value is greater than the original purchase value. As a consequence, capgains taxes aren't owed at all on the return Mankiw receives before his death: the only capgains liability is whatever attaches after Mankiw dies, starting in year 36 in his example. Thus, for assets paying no dividends, t3 is 0 in all cases, not 0.15 or 0.2. This means that Mankiw's return to a dollar saved now would be something like \$2.84 under Obama's plan, not Mankiw's \$1.85. Another point I didn't note is that Mankiw will pay estate taxes under Obama's plan only if his estate is valued at more than \$7 million (I'm assuming Mankiw is married: there's a \$3.5 million exemption for each spouse). That's plausible, given the success of Mankiw's textbooks. But if he does have an estate this size, Mankiw will be very unusual.]

The above problems are factual errors on Mankiw's part. But he also makes a third error, one of economic analysis. Mankiw assumes that the entire economic incidence of capital income taxation is on suppliers of capital: they receive the same pre-tax return regardless of tax policy, and they write the entire tax check to the government. This combination of no change in the pre-tax price and full legal incidence on the supply side can occur only if the demand for capital is perfectly elastic, i.e., borrowers are willing to borrow an infinite amount of capital at 10% and not a bit of it at a higher rate.

[Update: It would also be possible for the full economic incidence of capital gains taxation to be on the supply side if the supply of loanable funds were perfectly inelastic, i.e., if the supply curve were vertical. But Mankiw says he will work less if the tax rate increases, so he must not believe this to be the case.]

I do not know what the actual elasticity of demand for loanable funds is, but I do not think it is infinite. I also do not think Mankiw thinks this elasticity is infinite. I would be interested to see him redo his calculations after taking into account the possibility that the demand for loanable funds slopes down, in which case the pre-tax rate of return to capital will be higher than it is under Mankiw's baseline, no-taxes assumption.

Fourth, I note that McCain's plan would increase the federal debt by more than Obama's plan (actually, taken by itself, Obama's tax plan reduces the debt on net). So, if McCain's plan were enacted, Mankiw's children would themselves have to pay higher taxes to make up for Mankiw's ability to earn a higher return now. It seems we should account for this fact somehow; I leave that as an additional exercise.

Final note: Mankiw concludes by writing that
If you are one of those people out there trying to induce me to do some work for you, there is a good chance I will turn you down. And the likelihood will go up after President Obama puts his tax plan in place.
Given the merits of Mankiw's analysis above, perhaps this is a threat whose promise we should all welcome.

Anonymous said...

And tell me when would Mankiw (or the typical investor) ever actually pay the corporate tax unless he was a venture capitalist? Say I buy stock for \$1, it goes up by 10% after one year, I pay my capital gains of 20% on the \$0.10, and I'm left with \$1.08 at the end of the day. Where does the corporate tax hit me?

bluememe said...

Would Maniw recognize the real world if he tripped over it?

http://bluememe.blogspot.com/2008/09/flunking-professor.html

David I. Levine said...

I do not believe you are nearly harsh enough on Mankiw's analysis. First, the last time I looked, prosperous people need not pay capital gains taxes on what they pass on to their children. The estate tax essentially forgives all capital gains taxes owed and "steps up" the basis for calculating future capital gains to the asset value at the time of inheritance.

Second, the tax rates Mankiw attributes to McCain are pure fiction and would lead to unsustainable fiscal deficits. Mankiw knows this fact, which makes it especially disappointing that he calculates work incentives based on McCain's promised but not sustainable tax rates.

unavailable said...

You are relying on your audiences ignorance of economic formulae.

Pretending you are correct on the accrual "error", McCain still provides more money for his kids than Obama in the same ratio as with the faulty formula.

Darko Svitek said...

I think the bigger problem is that in Mankiw's hypothetical non-tax world, he (and / or his children) would have to pay for things like the roads he drives his two cars on, something his analysis does not factor in.

Jonah B. Gelbach said...

david

good point on the step-up issue. i didn't mean to suggest these were the *only* problems with mankiw's analysis!

darko

also a good point. the proper baseline isn't zero taxes *and* a functioning economy: with zero taxes, we'd have no public-goods infrastructure, and also a lack of property-rights enforcement.

Steve Roth said...

I agree with many of the points made here about Mankiw's post, but I think the corp tax, cap gains, and dividend arguments are rather weak.

Mankiw will presumably, like other knowledgeable investors, follow the tenets of modern portfolio theory and put his money into a variety of index funds. Those funds parcel out the dividends and cap gains over time, so investors have to pay taxes on those.

And corporate taxes, of course, are deducted from the value of corporations, which reduces the value of funds holding shares in those corporations.

But: Most Americans invest via 401Ks, IRAs, and the like, so their taxes are long-deferred.

And: most will never have a large enough estate to be subject to the inheritance tax--even for their last dollars.

This 55% hit at the end skews the whole analysis.

Anybody care to run the numbers for Joe the Plumber?

He made \$40K in 2006. (Given that, his notion of buying the quarter-million-dollar plumbing company that currently employs him, and that presumably has annual profits of, say, \$80-120K, seems to be largely a fantasy.)

Anonymous said...

Darn, I thought I was going to cry after reading Greg's post. You've got to fill sorry for the guy who thinks he's going to get taxed like that. Perhaps, I could persuade my department to drop his principles text and help get him into a little lower bracket. Surely, we don't want to incentivize him into early retirement.

Anonymous said...

Nobody has mentioned that all this assumes that Mankiw's only incentive to earn income is to pass it on to his children. Does he not spend some of his income on consumption, charity, or whatever?

"Surely, we don't want to incentivize him into early retirement."

That was once true, but considering his output lately we'd be doing his reputation a favor if we did.

Paul said...

Economists argue about the degree to which human economic decisions are rational or emotional. Mankiw has put himself squarely into the "emotional" side on this issue.

Consider Adam and Betty. Adam is a median earner. He earns \$20 per hour, pays 15% tax, and takes home \$17 per hour. Betty earns \$100 per hour, pays \$50 tax, and takes home \$50 per hour.

If A and B are both rational, it's clear that Betty has the greater incentive to work. After all, \$50 an hour is nearly 3x \$17 an hour.

But, if they are emotional, they only look at the tax bill. The 50% "feels so bad" to Betty that she ignores the fact that she is still making 3x the median worker's income, and decides that "it just isn't worth my time" to work.

In this piece, Mankiw shows very plainly that his incentive to work is based entirely on his tax rate. He is completely indifferent to his after-tax income. Truly, we have met an emotional economist.

James said...

Jonah the Economist said...
"One problem with Mankiw's analysis here is that Mankiw assumes that all corporate stocks pay dividends."

Like all orthodox economists, he probably believes in the Efficient Market Hypothesis, and thus invests in index funds or passive ETFs. Therefore, the fact that not all corporations pay dividends is irrelevant. What matters is the dividend yield for the market as a whole.

Mankiw's argument may be weak (and selfish—he ignores the financial motivations for the majority of the U.S. adult population), but you don't do yourself a favor by using a weak argument in response.

Rob said...

"One problem with Mankiw's analysis here is that Mankiw assumes that all corporate stocks pay dividends."

Mankiw does not assume this. Mankiw expects an annual 10% return and it does not matter whether this return comes in the form of dividend or capital gains because they are taxed the same.