StanCollender'sCapitalGainsandGames Washington, Wall Street and Everything in Between

Go Find Me the Peak of the Laffer Curve

02 Aug 2010
Posted by Andrew Samwick

My New Year's Plea from 2007 has been getting some attention in the recent discussions over whether cutting tax rates will raise revenue.  In this post, I'd like to follow up on the last line of that plea, which I have not seen recently quoted:

If I'm wrong, show me the evidence ... and tell me why the tax cuts were so small given their effects on revenues.

Restated, if these tax cuts raised revenue, then why not keep cutting them until the point at which revenues actually begin to fall?  I presume the reason is that none of the proponents of this line of argument have any idea what the revenue-maximizing tax rate is.  They only like to assert that we must have been past it because tax revenues eventually went up at some point after the tax rates were cut (ignoring the obvious counterfactual that it was economic growth unrelated to the tax cuts that pushed revenues higher and that they would have been even higher at the higher tax rates). 

So the next question is simply, "What do the experts on your staff tell you that the top marginal tax rate should be in order to maximize tax revenues, leaving everything else about the tax code the same?"  Journalists should relentlessly ask it of the Republican leadership in Congress who continue to make fallacious claims, and the Democratic leadership in Congress ought to ask it politely in a letter to CBO Director Doug Elmendorf. 

In both cases, we'll get some interesting responses. The Republican leadership will have to admit that they have no idea or give some ridiculous answer. CBO will also have to take a serious look at how it allows for potential supply side responses to changes in tax rates and take a stand on the issue.

Check for the beam in your own eye first...

Conservatives have been asking liberals for years to identify how much taxation is "enough". We never got an answer.

That's funny

Seems to me John Maynard Keynes gave you an answer on that about 60 years ago.

Reading him is your responsibility.


Nice Try

You know that not everyone bows at the feet of Keynes.

How much taxation is enough?

How much taxation is enough? This is a meaningless question by itself. We can't determine how much taxation is enough without knowing how much we want to spend, as well as the prospects for economic growth, which may hinge on any number of factors apart from tax policy. If we decide that it is in our best interests to pay for prescription drugs, new roads, or a a larger military, then all else being equal, we're going to need higher taxes. If we enact policies that manage to improve growth and productivity, we may be able to get by with a lower rate.

Taxation is "enough" when we have long term fiscal stability, given our public spending preferences.

Again, clearly wrong

Taxation is inherently a moral issue, because force is used to collect it.

Taking 100% of someone's income is indistinguishable from slavery, so no matter how much revenue you think the government needs, there *is* a rate that is morally indefensible.

You haven't been listening

The only reason for tax revenue is to cover government expenditures. Thus "enough" tax revenue occurs when revenue = expenditure.

To be truthful, us Liberals are a little more nuanced than that. We argue for tax revenue = government expenditures over the business cycle.

Now some will claim that we should shoot for debt being a constant % of GDP; that allows revenue to be less than expenditure in an expanding economy. I'd argue (especially after Iraq War, Afghanistan War and the Great Recession) that unanticipated negative shocks will occur and it is those events that should cause us not to plan to fully use the credit available to government.

how political debates go

Conservative politician: tells blatant lie
Person interested in rational debate and policy: "I'm not sure there's any factual support for that view."
Conservative rank and file: "LIBERAL POOPYHEAD!"

Too true.

ROFLMAO. Too true.

What really happened here

Conservative: posts a rebuttal
Liberals: respond with insults

Where was the rebuttal? I

Where was the rebuttal? I seem to have missed it.


It simply boggles the mind. I mean if cutting taxes raises revenue then umm, do it? I don't think any of them really have any idea what the right thing is to do now, no matter what party you belong to.

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Maximizing tax revenues is

Maximizing tax revenues is not what we should be striving for.

Presuming that you actually

Presuming that you actually do mean that you don't want the optimal tax rate, knowing WHERE the peak is still very important. Besides the peak, every amount of tax revenue can be supported by two tax levels, a low one and a high one. Without knowing where the peak is, you can't know for certain which side of the curve your on, and if the same revenue could be supported by a lower tax rate, wouldn't you want to know that?!

Finding the maximum is just about figuring out which side of the curve we're on. If we're on the left side, then the Laffer argument doesn't apply, if we're on the right, it does. All this post is asking is, "hey, tell us at what point it switches from left to right." Solving the maximization problem tells us that point.

Regardless of what one thinks tax revenues should be, it should be simple enough to understand how this mathematical problem is crucial to all arguments based on the idea of the Laffer curve.

Economists are very used to talking to people that consider a simple optimization problem to be a very basic idea. Is it simply that you're not in a line of work that requires you to know basic calculus and you're just confused by this whole concept of why the identification of the peak is so critical to the argument?

I agree that people in

I agree that people in congress probably should spend more time talking to experts, but it's not the job of any person in congress to know all of the information that might pertain to any decision, even decisions as important as tax law. Furthermore, given that experts almost certainly disagree on the peak given different assumptions on peak variables, it is almost certain that the ability to spout a number is almost useless for law makers. This is like saying that, because of the importance of nuclear energy, law makers should know the number of proton collisions each second necessary to sustain a nuclear reaction.

The number isn't the key piece of knowledge here. The key knowledge is that the government provides services, and needs to pay for those services or eliminate them, and that any choice (paying, eliminating, or running up debt) has consequences... but that real honest data can be used to predict a point that minimizes the impact of those consequences now and in the future, and that they should have several experts on their staff in different fields regardless of their committee affiliations who can help them understand good data and make informed conclusions.

Maximizing Tax Revenues

Guess some people have trouble with simple words as they're stated about...The laffer curve is about optimizing or maximizing if you like, tax rates/revenues.

If that's too complicated for you, you're dismissed.

Republicans are responsible for the vast majority of our national debt today.

12 years of : Reagan/Bush 1 (8 years) and then Bush/Quayle (4 years) quadrupled the national debt, a feat not accomplished again until Dubya/Cheney at the very least doubled it and set the ground work for massive debt through unfunded wars, Plan D and tax cuts for the wealthy.

Here's Reagan's supply side miracle

09/30/1988 2,602,337,712,041.16
09/30/1987 2,350,276,890,953.00
09/30/1986 2,125,302,616,658.42
09/30/1985 * 1,823,103,000,000.00
09/30/1984 * 1,572,266,000,000.00
09/30/1983 * 1,377,210,000,000.00
09/30/1982 * 1,142,034,000,000.00
09/30/1981 * 997,855,000,000.00

Re: Check for the beam in your own eye first...

"Conservatives have been asking liberals for years to identify how much taxation is "enough". We never got an answer."

There is no definitive answer to this question. It depends on the level of government services you want to pay for. So different folks will have different answers to this question.

But, and this is Andrew's devastatingly simple point, there is a point at which revenue from the Laffer curve turns negative. My guess is that it's actually at a point somewhere between 80-90% tax rates, but I would be interested to see the conversative case explaining why they believe we're already at or near the point at today's rates.

All of this excitement...wish I could bottle it...

ANOTHER one. Man, all this excitement and adrenaline oozing toward the objective of higher taxes. It has to be some kind of psychological disorder. It isn't a desire for a balanced budget, we know that from the increased spending by the very same people who want to raise the taxes.

The Republican leadership will have to admit that they have no idea or give some ridiculous answer.

I suggest you wait for them to do that, then write this column. Whoopsie, too late.

As I recall, the ORIGINAL

As I recall, the ORIGINAL premise of the Laffer curve was that as you reduce tax rates ( up to a point )you increase revenues due to greater compliance; revenues rise because people avoid paying taxes less. not because of economic stimulus due to tax cuts.

Which peak?

There is the rate which maximizes total federal income tax receipts.
There is the rate which maximizes total tax receipts of federal, state, and local income, sales, property, and other taxes (including the NPV of the death tax).
There is the rate which maximizes net tax receipts when you subtract mandated social spending.
There is the rate which maximizes net tax and bond receipts at constant interest rates.

In practice, every tax cut includes big cuts and credits for lower and middle incomes which will significantly reduce tax receipts. It is very difficult to isolate receipts from the top marginal rate from total receipts of all taxes. Also the slope of the Laffer curve at the peak is zero, so the signal to noise ratio near the peak will be very small. The signal of the Bush tax cuts has been completely clobbered by the noise. It is impossible to find anything conclusive from noisy real world data.

In theory, Laffer's napkin is wrong, the curve is asymmetric. Tax rates at and above 100% will collect zero taxes, so the slope of the curve at 1. must be zero. The asymmetry suggests the peak is below half. The peak of [x*(1+cos(pi*x))/2], which looks OK, is under 42%. Using Bush 35% + 0 death + CA state (10.3% deductible) I am at that peak. Add the rest of the taxes and I am over. Since most high earners live in high income tax states, federal income tax rates should to be lowered. I estimate the top federal income tax rate to maximize total net receipts is around 28%.

There is a Laffer curve for bond receipts. At 100% taxes there is no taxable income to borrow. At 0%, a significant percent of GDP can be sustainably borrowed. Higher interest rates will collect more bond money. If we are over the peak of taxes and bonds, tax cuts will cause interest rates to decrease and/or spending to increase (reverse starve the beast). We have definitely observed this. Holding spending and everything else constant, we should cut taxes until interest rates stop decreasing. If all government spending was cost effective, then we should seek a budget balanced between taxes, borrowing, and spending such that changing that balance in any way would reduce long term growth.

"Tax rates at and above 100%

"Tax rates at and above 100% will collect zero taxes, so the slope of the curve at 1. must be zero"

But the same logic applies to 0% as well as 100%, so by your same logic the slope of the curve at 0 is also zero. So no reason to invoke an asymmetry. Your equation is impressive, but if you didn't simply cut and paste that from somebody else, and actually understand it, then you should also realize that 0 & 1 will be inflection points on the curve, and therefore the derivative (or slope) is actually undefined.

The more salient point however, is that attempting to applying a smooth, integrable curve to this issue is utter nonsense. Too many variables to approximate with a curve. And whenever math geniuses try to apply mathematical equations to economic problems, we always wind up with financial implosions.

Negative tax rates will cause

Negative tax rates will cause negative tax receipts, so the slope at zero is positive. Boundary conditions and extremes are informative. The curve is just a gui
de to draw a better Laffer curve on a napkin.

How can anyone claim

How can anyone claim republicans are a deficit reduction party after Bush and Reagan? They cut taxes, spend huge amounts on defense, or whatever they feel like (medicare drug benefit).

Just because dems proclaims they favor domestic spending rather than military hardly makes them the only party that spends. Both parties have agendas that require government funding to execute, one compensates for this spending with tax cuts, and the other with tax increases...

The laffer curve tells you which strategy is best from a debt perspective.

More hypocricy

And then Obama and the Democratic Congress comes in and the spending and deficits shoot up even higher, yet you have not one bad word for them.

Ain't that funny?


"Together with the economic downturn, the Bush tax cuts and the wars in Afghanistan and Iraq explain virtually the entire deficit over the next ten years"

Nice try

Projected deficits are meaningless, since Congress changes what is spent every year.

That graph is already out of date, since the Obama administration has admitted after that graph was produced that this year's deficits will be larger than projected.

Actually, just about every

Actually, just about every Democrat I know is critical of Obama's policies to continue increasing defense spending. Cutting defense spending in half (to the levels that existed before we decided going after every non-Christian religious fundamentalist in a cave anywhere in the world was a policy worth bankrupting the nation to achieve) would more than offset the ARRA, it would more than compensate for TARP (a Bush program) over just two years (even ignoring the money that was paid back from TARP), and would pay for the first decade of the health care bill in a single year.

That's the general difference between liberals and conservatives (and unfortunately also the reason conservatives are so successful). Libs don't blindly support people just because they say they're "one of us". Bad policy, like bankrupting the nation to smoke out fundamentalists living in caves on the other side of the world, is bad policy, even if "one of our guys" is doing it. That's why Dems are doing so bad in the polls right now. Dem voters are unimpressed by the performance of the Dem leadership, too many bad existing policies are still being carried out. Of course, that doesn't mean the answer is to bring back the idiots that created most of those bad policies and want to make them even worse, but that seems to be what we're going to get...

Here's the picture:

The Laffer Curve, at historical rates of taxation, is very nearly a line.

Misleading with statistics

That graph doesn't correct for any other variable that has an effect on gross tax receipts, like the business cycle. Garbage in, garbage out.

The woeful state of math education

I don't know whether to laugh or cry after reading the comment by "Yet Another Budget Wonk" saying that the Laffer curve is very nearly a line. His comment is one of the best arguments I have seen for improving math education in our society.

First, the line that he is referring to would actually be an argument in favor of higher tax rates in order to reduce the deficit. Is that what you are arguing for "wonk"?

Secondly, the data points that are being used in this graph do not give any indication that the line drawn is correct. In fact for that matter the data points do not even indicate that a line is the correct shape. It would be more reasonable to assume there is little to no correlation between tax rates and revenue from this data.

Pythagorian, 1) Yes, higher


1) Yes, higher tax rates do indeed tend to reduce the deficit. That's exactly the point.

2) I'm sorry that a regression analysis doesn't give a "correct" line in your opinion. It's merely the line of best fit, I suppose. And there is a significant correlation, R-squared=0.38 (as I believe my chart indicates).

By saying it's very nearly a line, what I mean is that in the range of actual policies that the United States has tried over time, the relationship between the average effective tax rate and tax receipts as a % of GDP tend to move together linearly. Which the numbers make a very compelling case for.

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