I don't know what the copyright issues are and so, rather than assuming I have the right, I'll simply give this link to an excellent exposition of the Laffer Curve by Tim Groseclose. It's titled "Do High Taxes Raise More Money?" but, of course, as you'll see from the exposition, it should really be titled "Do High Tax *Rates* Raise More Money?"

I reviewed another important piece of Groseclose's work earlier and found it quite good.

Near the end, Tim makes a controversial statement. He says, at about the 4:30 point, that the Romer and Romer study implies a revenue-maximizing rate of 33%. He doesn't say that *they* say that. Rather he says, "if you do the math, the results imply that the hump on the Laffer curve occurs where the tax rate is around 33%." Yet, if James Kwak has it right, some later work by the Romers says that the revenue-maximizing rate is well over twice that. Would the Romers disagree with what Groseclose says is the implication of their earlier study? I must admit that when I look at the study, I can't tease out of it what Groseclose does. I don't even know how to do it based on their study and it seems to me as if one can't. But that could be my failing. Groseclose is very good and so it's quite conceivable that he found something I didn't.

The answer matters a lot. My own gut feel is that the revenue-maximizing tax rate, which would clearly be above the welfare-maximizing rate, unless high-income people's welfare is weighted by zero, would be somewhere in the mid-40s. But, as I admit, that's a gut feel. Even if he's wrong, by the way, his exposition up to the controversial part of the video is beautifully done.

HT to Jeff Hummel.

**UPDATE**: MatthewH, in a comment below, gives a link to the cite where Groseclose gives the proof. The proof makes sense to me. I told you that it's quite conceivable that he found something I didn't.

Are 'revenue' & 'welfare' transposed in this statement?

Thanks for the kind words! Folks can find the math to which I refer here: http://ricochet.com/main-feed/The-Laffer-Curve-and-New-Evidence-that-Taxes-Stifle-Economic-Output

@Airman Spry Shark,

Oops. Yes. Thanks. Correction about to be made.

I really don't buy his 33% number. Even if that is what is implied by the Romer and Romer paper, it seems a horrible idea to base our policy expectations on a single paper. I'm guessing a meta-analysis of papers estimating the peak of the Laffer curve would put it somewhere between the 33% and 70% number, probably a bit closer to the latter.

I would be less skeptical of a claim that the curve is quite a bit flatter after 33% than before. And I completely agree that the welfare-maximizing rate (for most reasonable social welfare functions) would be well below the peak.

I don't have the time right now to watch the video and see what he explains or doesn't. But he explained the gist of the math on Ricochet a couple days ago.

David, as James Kwak states, the Romer and Romer paper examines the effects of marginal tax rates on "the super-rich." Isn't this the group that is mostly likely to derive most of their income from other sources, such as capital gains? Therefore, is it not surprising that we would find a low elasticity for these earners because of how they are earning their income?

Part of the problem with estimating the peak of the Laffer curve must stem from the fact that we don't have a single tax rate. In particular, the progressiveness of our tax system implies that the marginal rate is very different from the average rate.

It seems plausible that we could simultaneously be above the peak of the Laffer curve for those paying at the top marginal rate and below the peak for others.

Derivative v elasticity:

James Kwak already makes the point about the elasticities not necessarily have to be the same for different groups/subets -- thereby countering Groseclose's claim that

-- but there is another point in his argument I take issue with: Groseclose says that the derivative dY/dt is -3 Y(t). However, givenhisphrasing I was more inclined to use the elasticity (yes, actually his phrasing, I am not familiar with the Romer-Romer study itself). Hence, it would be thatdY/dt * t/y = -3.

Taking the derivate of the revenue r(t) = t*y(t),

dr/dt = y(t) + t*dy/dt,

setting it to 0 and substituting the expression t*dy/dt with -3*y(t) (from the elasticity) would lead me to

-2*y(t) = 0.

Which obviously isn't that helpful... However, it leads me to two questions:

1) Am I right in using the elasticity instead of the derivate?

2) What did I do wrong to get this result?

Dr. Groseclose appears to make a rather fundamental error of omission in the second half of his explanation on Ricochet.

He refers to top marginal

Federalincome tax rate as 35%, and then refers to the various State and Local tax rates, as well as fees and consumption taxes as additional. Rightly so. But he omits the payroll tax - normally 15.6%, although slightly lower now with temporary "stimulus" payroll tax cuts in place.Since the 15.6% payroll tax is applied to the very first dollar of ordinary income (ditto self-employment tax, for sole proprietor businesses) - portions of which are subject to maximum limits - that should be considered for all income tax brackets.

The key point in context with Laffer Curve analysis being, the actual government-revenue rate is substantially higher than tax bracket rates would indicate - for ordinary income.

Additionally, some commenters have noted the "Warren Buffet" (and Mitt Romney) effect of lower tax rates on capital gains and dividend distributions - applicable to the higher-income groups. That perspective, of course, ignores the fact that such incomes are taxed twice - once at corporate earnings level and again at distribution/sale.

Correction and Clarification:

Referring to Federal Publication 15, Employers Tax Guide for 2012 ...

The employee/employer Social Security tax rate is 4.2%

eachon wages and tips earned before March 1, 2012, and reverts to its previous (non-stimulative) level of 6.2%eachfor all wages and tips paid after February 29, 2012. And the Social Security portion of that payroll tax is applicable to all ordinary gross earnings up to $110,100.(Currently, 12.4% total, subject to the $110,100 limit.)

The Medicare portion of payroll tax for employee/employer is 1.45%

eachfor all ordinary gross income - with no maximum limits.(2.9% total - not limited).

So the actual current payroll tax is 15.3%, instead of the 15.6% I stated above. And that "drops" to 2.9% for all ordinary incomes above $110,100. Note also that these payroll taxes are applicable to every dollar earned of ordinary income, and are not subject to any exclusions or deductions under current law.

With respect to this discussion on Laffer Curve tax rates, the payroll tax is significant. The individual

tax bracketsof course are subject to the exclusions/deductions/credits embedded in tax law, but the overall tax rates - including payroll taxes - are substantially higher than tax brackets would indicate.A quick look at the tax brackets indicates that wage earners in the central 25% bracket are actually paying a tax rate of 40.3%, for example. The lower portion of the 28% bracket are subject to tax rate of 43.3%.

And the top marginal wage earners tax rate is actually 37.9%, plus $13,652.40 - ($110,100 * 12.4%).

@David,

Dan Mitchell and others at Cato have elaborated on your suspicion that the revenue max rate would be higher than what you call the welfare max rate. This link http://danieljmitchell.wordpress.com/2012/04/10/the-laffer-curve-shows-that-tax-increases-are-a-very-bad-idea-even-if-they-generate-more-tax-revenue/

provides a good summary and cites some interesting research -- one of which looks at quantifying the trade offs between exacting that additional amount of taxes and letting the money grow in the private sector.

I think Mitchell summarizes it the whole issue well:

"Yes, the politicians usually can collect more revenue"...(raising rates to a revenue maximizing rate..."but the concomitant damage to the private sector is very large and people have lower living standards. So that leaves us with one final question. Do we think government spending has a sufficiently high rate-of-return to justify that kind of burden? "

I think that he is only saying that if the total tax of everyone's combined income was more than 33% you get less revenue but you still might be able to collect more taxes by taxing the top earners at above 33%.

Revenue maximizing?

How about growth maximizing?