### Laffering All The Way

The Washington Post’s Ezra Klein had a great idea this week: He asked a bunch of economists and pundits to tell him where the Laffer curve bends. In other words, what is the marginal tax rate above which higher taxes lead to lower revenues? Meanwhile, coincidentally or not, Paul Krugman blogged on the very same question.

There’s a lot worth mentioning here, but let me start with one point that will be relevant below: Imposing a 20% income tax is not the same as cutting your wage by 20%. That’s because the income tax grabs not just a chunk of your current wages, but also a chunk of the future interest and dividends those wages enable you to earn. So a 20% income tax will, in general, discourage work more effectively than a 20% wage cut. This is important if you’re using data on wage cuts to predict the effects of income taxes.

That having been said, let’s see what we can learn from the responses:

• If your post-tax wage rate falls by 1%, your hours worked will fall by some percentage we can call e (for “elasticity”). Paul Krugman, having done exactly the same calculation I’d have done, concludes that the critical tax rate t is given by t = 1/(1+e).
• Emmanuel Saez, who has thought about these issues far harder than either Krugman or I, observes that our naive calculation implicitly assumes everyone’s in the same tax bracket. A more realistic assumption is that there are multiple tax brackets, and that our contemplated tax increase is concentrated at the top. This creates the possibility that a tax increase will cause people to move into lower brackets, which is something that Krugman (and I) ignored. This leads Saez to the conclusion that t is approximately 1/(1 + 1.5 e). At first, I couldn’t figure out where he got this formula, but then I found the paper that made it clear.
• Now that we have our formula, all we have to do is figure out what e is.
• Saez goes on to say that the reasonable estimates of e range from .12 to .40, with a best guess of about .25. This gives us a critical tax rate of about 73%.
• Careful now. That’s not a 73% federal income tax bracket; it’s a 73% marginal tax rate — which includes state income taxes, sales taxes, and so on. So the Laffer curve for federal taxes only peaks somewhat earlier; Saez says at about 69%. (I’d have expected this adjustment to be much bigger — pushing the peak substantially farther left — and am not sure why Saez says the adjustment is so small.)
• I have not digested the literature from which Saez got his estimates of e, but it seems to me that it’s possible they are partly estimated from data on wage cuts. If that’s right, then — because income taxes take a bigger bite than wage cuts of the same size, per the second paragraph of this blog post — the Laffer peak is probably somewhat further to the left.
• Ezra Klein divides his respondents into “The Tax Experts”, “The Left”, and “The Right”. The guys on the left guessed 70%, which is probably not far off (unless we need a substantial correction per the bullet point directly above). The guys on the right guessed ridiculously low.
• Greg Mankiw made the excellent point that it matters whether we’re talking about short-run or long-run effects. If I cut your wage by 20%, you probably won’t change your hours very much right away — but eventually you’ll look for a different job with different hours. So the long-run Laffer peak is probably well to the left of the short-run peak.

But Martin Feldstein gave the best answer of all, which was, in essence, that the whole question is stupid. Nobody, not even the most way-out leftist, thinks that the goal of tax policy should be to maximize government revenue. We also care about things like, you know, the quality of life.

Asking “what tax rate maximizes government revenue?” is like asking “what conscription rate maximizes the size of the army?”. Who cares? The right question is: What tax rate, and what conscription rate, will make us happiest in the long run? There is more to life than feeding the government.

#### 23 Responses to “Laffering All The Way”

1. 1 1 Henry

I believe the Laffer Curve argument possibly hurt the case for tax cuts by framing the debate as tax revenue maximisation. Most people probably support Kaldor-Hicks improvements to at least a limited degree (such as making a wealthy person \$100,000 better off by making a middle class person \$1 worse off), but “tax revenue maximisation” appeals only to Pareto improvements, and only a subset of them as well.

2. 2 2 Henry

Expanding on my above post: it is possible that Pareto improvements can be made from the maximum of the long run Laffer Curve. At that point, any decrease in taxes will require less spending. But that doesn’t mean we need to cut all federal government spending slightly, rather, we can cut the most marginal program that mostly benefits the rich. Since the Laffer Curve is presumably close to flat near the maximum, a small decrease in taxes should only reduce revenue a tiny amount. A minor cut in farm subsidies to the wealthiest farms could be more than made up for by the tax cut the farmers receive, so no-one is worse off from the spending cuts.

3. 3 3 thedifferentphil

I agree with Martin Feldstein that the goal of taxes is not to maximize revenue. But, the Laffer curve is still relevant if we are on the right-hand side of the bend, because it is very difficult to argue against a tax cut that increases tax revenues. Obviously, though, he believes that we are on the left-hand side of the bend. Many politicians, though, routinely argue that tax cuts will lead to revenue increases (esp. in GOP primary races), so Klein’s question is relevant if it helps establish that we are on the left of the curve.

By the way, he classifies Joel Slemrod with the left. Is that correct? My sense has always been that he is a very rigorous, but Republican scholar.

4. 4 4 Laszlo

Hi,
I am sorry to say, you just missed a (perhaps slight) revision of the most important paper you read and cited: http://elsa.berkeley.edu/~saez/saez-slemrod-giertzJEL10round2.pdf

Also, let me quickly note that the optimal tax literature is not as stupid as it would want to maximize government revenue for its own sake. Saez’s arguments about the asymptotic tax rate are clear : if (!) in the limit (!) the government cares only infinitesimally about the effects on welfare of earners above that (very high) level from income above that (very high) level, the optimal marginal tax rate is essentially where the government breaks even (where the “curve bends”). If you are so inclined, say that the welfare weights never go that low, or that this level of income is not in the millions but the (tens of?) billions, but the argument is not vapid. We would not collect the government revenue for its own sake but to collect less from other parts of the income spectrum. And it is a limiting result.

5. 5 5 Douglas Bennett

thedifferentphil-

Slemrod was the second one in the ‘experts’ section, the ‘left’ section began directly after him. I was confused by the placement the first time I read it too.

I’m not sure whether he’s left or right, but in my experience he does seem to be quite thorough. However, in ‘Taxing Ourselves’ he equates tax cuts to subsidies, which frustrated me because I can’t throw a book at the wall and read it simultaneously.

Still, it was better than Gruber’s “Public Finance and Public Policy” that I was reading for the same class.

6. 6 6 thedifferentphil

Do you mean tax expenditure types of tax cuts, because those really are subsidies. For example, I may get a new furnace this year, and that would allow me to get a “tax cut” of \$1,500 off of my federal income tax bill. That is identical to me paying my standard income taxes and then having the government send me a check for \$1,500 as a subsidy for buying a furnace. Ditto my child tax credits of \$1,000 a kid. The government could just send me a subsidy for having kids of \$2,000 and not have the IRS broker it as a tax cut. The same goes for many other “tax cuts,” that aren’t straight-up decreases in marginal tax rates.

7. 7 7 Steve Landsburg

Laszlo:

Also, let me quickly note that the optimal tax literature is not as stupid as it would want to maximize government revenue for its own sake.

Of course not, and I hope I didn’t imply this. Journalists have a tendency to ask this question for the wrong reason, which is the context in which I called it a stupid question.

8. 8 8 ryan

One thing that’s kind of interesting about Saez’s research is that he makes clear how sensitive the “optimal tax function” is to the thickness of the right tail. The reason why he comes up with a U-shaped tax function with very high rates where Mirrlees had a nearly flat one (slightly decreasing in fact) isn’t that Saez weights the poor more, but that Mirrlees says the income distribution is approximately log-normal while Saez says the right tail is Pareto.

Which I admit is kind of orthogonal to everything said above :-)

9. 9 9 Steve Landsburg

Ryan:

Which I admit is kind of orthogonal to everything said above :-)

It’s also very helpful and insightful. Thanks.

10. 10 10 Fake Name

I thought the point of the Laffer curve was that the marginal tax rate at which government maximizes its revenues is on the right of the marginal tax rate at which economic growth is maximized.

11. 11 11 Steve Landsburg

Fake Name: I thought the point of the Laffer curve was that the marginal tax rate at which government maximizes its revenues is on the right of the marginal tax rate at which economic growth is maximized.

This is certainly true, but not terribly helpful, since the revenue-maximizing point is so very far to the right of the growth-maximizing point that identifying the former doesn’t tell us very much about the location of the latter.

Of course, growth might not be exactly what we want to maximize either, but it’s a far better approximation to any reasonable goal than government revenue is.

12. 12 12 Douglas Bennett

thedifferentphil-

I still would have trouble viewing that as government spending. You could just as easily reword your example such that you must pay some amount in income tax each year, and if you don’t buy a furnace you must pay an additional \$1,500. When someoene buys some good that is subject to a deduction it moves their tax rate somewhat closer to zero, but it is still positive. Yes, this will cause too many furnaces to be bought, but that is only one characteristic of a subsidy.

Suppose furnaces were so important that it could be possible/reasonable to buy so many furnaces each year that you reduced your tax burden to zero. Suppose everyone did this. Further, suppose furnaces were the only thing the government ‘spent’ its money on. After all that spending and no revenue collection, how much debt has the government racked up? When will I or my children be required to pay for all of my reckless furnace purchases on the public dime? The answers are none and never, respectively, because the government never actually spent any money- it just allowed me to live my life in peace, untaxed, with a plethora of furnaces (furni?).

Now suppose an alternate scenario where the government will pay some portion of the purchase price of every furnace, with no impact on one’s tax burden. In this scenario, we again end up with too many furnaces, but the government debt will increase and I or my children will eventually need to pay more in taxes, because we haven’t yet paid for the furnaces that we purchased. They were bought with taxpayer money that the government likely hasn’t even collected yet (hence the borrowing). But in this scenario, someone will eventually need to pay for the furnaces, and it may or may not be the people who bought them.

If all goods and services were subject to a full deduction from income tax, income taxes could potentially be reduced to zero for everyone. The tax expenditure view would consider this as a massive case of government spending. But if that is the case, then how much was the government ‘spending’ before the income tax was enacted? How much is the government ‘spending’ now by allowing us to breathe, blink, or pick our noses untaxed? When will we have to pay for all of this reckless spending?

Maybe the distinction is that I don’t think the government has some natural right to acquire resources for the sake of acquiring resources, and that it should only do so if it can put those resources to better use than those from whom they were taken. In that framework, failing to tax is in no way equivalent to spending. However, if you believe the government has a right to seek out more resources, regardless of its purpose, then viewing a failure to tax as equivalent to spending could make sense. I just choose not to put the sovereignty of government above that of the people it ostensibly represents.

Yes, there are a lot of suppositions in the examples. Peel them back one by one and the general case still holds- its just easier to write in terms of furnaces than in terms of all possible goods and taxes.

13. 13 13 ryan

@Douglas Bennett,

In the second case, there’s no marginal impact on your tax burden when you buy more furnaces, but there’s an effect of collective purchases — if you were the average person, you pay as much in income taxes as you get in furnace subsidies. This is exactly identical to the first case.

The reason why you’re saying there’s debt only in the second case is that in the first case you (of necessity) measured taxes after all transactions were completed. If you’re going to count that debt and use that pre-April 15th moment, you need to also count the fact that in the second case, you’re (on April 14th) richer by exactly the amount of the debt. But this accounting illusion obscures more than it tells us — a better comparison is to compare all distortions. And in fact, all distortions are identical — too many furnaces, too few other goods, same effect on labor supply, etc.

14. 14 14 Douglas Bennett

ryan-

I admit that my scenarios each glossed over different details.

However, there is still an aspect in which the second scenario is worse than the first. In the first scenario, every single individual pays exactly as much in taxes as they receive in subsidies (as you stated).

In the second case, everyone /on average/ pays exactly as much in taxes as they receive in subsidies.

In the aggregate, these could be seen as identical, and I agree that both will lead to too many furnaces. The difference is that the second scenario allows for the allocation of furnaces to people who did not and will not be able to pay for them, funded by other people who received less in subsidies than they paid in taxes. Both distort the price and thereby land at the wrong quantity, but the second scenario then exacerbates that problem by allocating those furnaces inefficiently.

On further thought, I should never have assumed furnaces were the only good for either example. With multiple goods where furnaces are the only ones subject to a deduction, then the furnace market is distorted only in the sense that it is the only undistorted good in a distorted market. In other words, “too many furnaces” is shorthand for “not enough of everything else, thereby leading to more furnaces than desirable.”

15. 15 15 ryan

The reason it’s true for everyone in the first case is (only) because you assumed in the first case (and only in the first case) that everyone buys the same number of furnaces. If you had merely assumed that government budget constraint binds (as in the second case), you’d have gotten the same result — zero average net tax, same product distortions, same allocations.

As an aside, I don’t think your example suffers from too few good types. As a default, I think most people figure (or at least I do) that at least some income comes from working, so boom, leisure is already your second good (and two really is the perfect number). However, I don’t think furnaces per se are distributed inefficiently in this case. Yes, lots of distortions, but conditional on the (new) distribution of wealth, they go to those who value them most. (In other words, you could improve on efficiency, but not via frictionless ex-post moving around furnaces, whether by fiat or voluntary trade.)

16. 16 16 DividedLine

Steve,

“This leads Saez to the conclusion that t is approximately 1/(1 + 1.5 e). At first, I couldn’t figure out where he got this formula, but then I found the paper that made it clear.” LOL, easy for you to say…

Still parsing through the paper, but I do find it interesting that as U.S. income concentration has increased in recent decades, the Pareto parameter a has correspondingly fallen from about 2 in the 1970s to about 1.5 in most recent years. In other words, as income polarizes, the maximizing tax rate at the top would increase, which would seem to lend some credence to the behaviorist claim that it isn’t just income, it’s also income relative to the Jones that motivates.

I’d like to reserve the right to think about this a lot more, and I’ve never been a big fan of the Laffer curve, but if the theory were valid it would seem there is no real incentive to work less until t’ –Which could be used as an argument to increase taxes for people at the top in the same way as using quit rates as an indication that some people are paid too much.

Really interesting set of articles, thank you for bringing them to our attention.

17. 17 17 Douglas Bennett

Finally did what I should have done originally and drew some lines on a piece of paper. Ignore the vast majority of my previous posts on this subject. I’m not totally convinced that tax expenditure = government spending, but I’ll need to invest more thought into it.

ryan- thanks.

18. 18 18 Cos

I came here to say basically the same thing as thedifferentphil, and I want to stress it: As important as “the right question” at the end of your post may be, that doesn’t make the Laffer question unimportant, *because* we always have some politicians arguing that cutting taxes will increase government revenues – or arguing against raising taxes as a way of reducing government budget deficits by claiming that it’ll do the opposite. If we’re on the left side of the curve – as we almost certainly are – then these arguments are wrongheaded, and that needs to be more firmly established in public policy and media coverage.

19. 19 19 Laszlo

By the way, here is something even better and more accessible about the new public economics (ungated): http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.24.3.183

20. 20 20 Seth

I’m in full agreement with Feldstein. I made a similar comment on McArdle’s blog.

Seems like the questions should be how much do we need to fund the government functions and what’s the least painful way getting those funds. The main problem is agreeing on what functions the government should perform, but I’d rather have that discussion than the Laffer curve discussion.

But, I have to admit, having the left estimate 70% is much better than having them dismiss the idea of the Laffer curve outright, isn’t it? Am I wrong, but wasn’t it en vogue by the left to dismiss the LC as absurd?

21. 21 21 Joe Calhoun

I just ran across this post but have some thoughts.

The idea of the Laffer curve is very old having been mentioned throughout history. Some examples:

“It should be known that at the beginning of the dynasty, taxation yields a large revenue from small assessments.
At the end of the dynasty, taxation yields a small revenue from large assessments.” The Muqaddimah 14th Century

impositions, two and two never make more than one.” Jonathon Swift 1728

“High taxes, sometimes by diminishing the consumption of the taxed commodities, and
sometimes by encouraging smuggling, frequently afford a smaller revenue to the government than what might be drawn from
more moderate taxes” Adam Smith Wealth of Nations

“On all items which duties can be imposed, there is a point in the rate of duties which may be called the maximum point of revenue.” John C Calhoun 1842

In the equation above used to calculate the tax rate that yields the maximum revenue the only variable is elasticity for work. It seems to me that this maximum revenue tax rate is dependent on quite a few more variables than just the desirability of work. Would the rate not be different in 1842 when my ancestor opposed Tariffs than today? It would be dependent on the cultural attitudes of the time concerning the imposition of taxes and on whom they were being levied. It would also be affected by the difficulty of evading the tax which would surely be different today than in the nineteenth century. Should there not be a variable for the elasticity of tax evasion? Furthermore, this variable would seem to be different across countries. Is this revenue maximizing tax rate different in Greece and Italy than the US? The answer would seem to be pretty obviously yes.

I would also think the rate would be affected by citizen attitudes regarding the government. If the public has a low opinion of their law makers – as we do today – one would expect them to seek ways to reduce their tax bill, legally or otherwise, at a lower rate than if they believed them to be virtuous and trustworthy.

I would also point out that despite faulty memories to the contrary, no one in the Reagan administration ever said that reducing tax rates would raise revenue. Laffer himself only said that revenue would recover over a number of years due to higher growth. That is quite a bit different from claiming that a reduction in rates would yield an immediate rise in revenue. Surely there have been stupid politicians (an oxymoron if ever there was one) who claimed differently but that notion was never promoted by Laffer, Bartlett, Wanniski, Mundell or the other promoters of the classical, supply side approach of the time.

As for the exact revenue maximizing rate, surely we are currently taxed at a lower rate. How much lower is hard to say but I suspect it is a constantly changing number anyway and will never be discovered. Or at least I hope not.