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July 14, 2007


It's at times like these I wish I'd taken economics in college.

Incertus: the Laffer curve in a nutshell: If the tax rate was zero, the government would collect no revenues. If the tax rate was 100%, it would also collect no revenues, since no one would bother engaging in any kind of economic activity. We are somewhere between zero and 100%, and our tax revenue is positive, not zero. Therefore, somewhere between 0 and where we are, the amount of revenues we would take in must rise (to get from 0 to what we take in), and somewhere between where we are and 100%, the amount of revenues we would take in must start to fall as tax rates rise, in order to get from what we take in now back to zero.

Of course, this implies nothing of any practical use absent a lot more information, like what this curve looks like (in detail), and where we are on it. However, it was used as a justification for saying: if we cut taxes, revenues will rise! (Which must be true at some point on the graph, but not necessarily at the point we're at.)

But all you really need to know to see how stupid the WSJ story is is: how to draw the best line through a set of data points. Thoma's is pretty good: it shows the actual trend that the data points seem to support. The WSJ's, by contrast, seems to be just plain made up in order to support their point.

I actually think my "WHEE!!!" graph is better than theirs, as a line suited to this data. Not that that's saying all that much.

I actually think my "WHEE!!!" graph is better than theirs, as a line suited to this data. Not that that's saying all that much.

I tend to give it more credibility though, because it is by the Hilzoy.
Is that a self portrait BTW?

OCSteve: No. Then again, given the difficulty of doing lines drawings with a mouse, I'm not sure how much of a difference it would have made if it had been.

damn you hilzoy -- i was thinking of doing the whole face-in-the-graph thing but i lacked the photoshop skills (was this photoshop?) and gave up. though i hadn't thought of the "whee", which was great. as is the bubble dialogue. although you could have one that says "Epstein Rulz" or "Democrats Suck"

publius: it's a little mac program calledd graphic converter, which has such advanced tools as: the eraser (makes the line disappear), the pencil, and text. Not much skill required.

It has many other things that are somewhat advanced, but I don't know how to use them.

I also really like the cheerful loops leading up to the lolcat quote, even if it makes the graph disfunctional.

If you believe the laffer curve is fundamentally true (0 at the ends and positive in the middle) it would make more sense to fit a parabola to the data than a straight line.

No, wait. They're looking at tax revenue as percentage of GDP. What shape laffer curve would you expect for that scale?

With no tax you'd expect tax to be 0% of GDP. And with 100% tax you'd expect tax to be 100% of zero GDP. And if the laffer curve concept is right you'd expect not a line but a bent line -- as you passed the point of diminishing returns, increasing the tax rate would reduce GDP more than it would increase revenue. So tax as % of GDP would rise fast.

How would that work?

revenue= rate * GDP
rate= revenue/GDP

And they graph rate versus revenue/GDP.

There you go. If "corporate tax rate" is rate on GDP instead of on profits or something, then this should be a linear function and not a parabola, much less this tilted parabola.

But wait! "Corporate tax rate" is a tax on profits. So the higher the tax the more it makes sense to change the accounting to hide profits, and suck out the juice some other way. So we'd get a higher GDP with lower aggregate profits and lower revenue from taxes on those profits. This is a confounding variable because people want to maximise GDP a lot more than they want to maximise creative accounting.

At any rate, whatever model you use, the scatter of the data might give some indication how reliable the laffer curve is for predicting results.

I briefly thought of doing 'ALL UR TAXE BASE R BELONG TO US!!!', but for some reason decided against it.

JakeB: function is for little people. The WSJ and I scoff at such petty constraints.

The graph is truly a mystery. Even without the absurd curve, I don't see why you would want to graph corporate tax rates against revenue as a % of GDP.

First of all, corporate rates by country don't tell us a lot, I think, about the overall tax burden. Corporate taxes are just a part of the tax system.

Second, the whole Laffer idea is that tax cuts increase GDP and revenue. If you buy all that the effect of a tax cut on tax revenue as a percentage of GDP is ambiguous. Even an honest version of this graph isn't going to tell you anything.

This is bizarre.

Awesome post. Wish I was teaching undergrads data analysis so I could show it to them.

Wow. The fact that I laughed out loud for a LOLcatz type joke...But it was pretty hilarious.


What amazes me is that all of this is so reminiscent of Martin Gardner's last Scientific American column from 1981.

hil... you've outdone yourself. bravo!

(Mind you, I'm not implying that Hilzoy is plagiarizing Martin Gardner, just that people seem to be driven to this type of conclusion by the data.)

Matt -- Gardner's is great. (I hadn't seen it before.) I did, at one point, have something similar, but got distracted by other possibilities. I still regret that my attempt to superimpose a very complicated line drawing of a dancing Hindu deity surrounded by various lotuses, etc., on the graph came to nothing, since I couldn't figure out how to superimpose it with a transparent background, rather than just obscuring the original graph with it.

Btw, shouldn't that be "Sklavenmoral"?

Dammit! A post on taxes and I have company arriving imminently. More commentary later if I haven't had too much to drink (or maybe even if I have).

David Cay Johnston has an article in the NYTimes in the past day or two on some of the private equity tax stuff, no time to dig up the link.

This is a classic. A true "Laugher" curve. Congratulations, Hilzoy!

rilkefan: with a capital S? Probably. Or is there some other typo I'm missing?

Clearly the WSJ is obeying that old adage that every engineer and scientist learns in university lab courses: "First draw the line, then plot the points."

I also love the way they don't mention that in Norway, oil companies pay a special tax of 50% on oil profits, on top of their 28% corporate tax. Strangely, the WSJ doesn't seem to be suggesting that America should follow that example.

Completely OT, but it's important to me:

HAPPY Bastille Day

Allons enfants de la Patrie
Le jour de gloire est arrivé!

to my french family, happy independence day.

Yup, capital S, unless that's some philosophical term which has been annexed by English without my knowledge, which is perfectly possible. Not sure why I quibbled.

Good point, Bernard. No one but fantasy liberals is interested in maximizing revenue as a percentage of GDP. What would be the point? The privilege of rubbing your hands together evilly and chortling about how great a percentage your were able to rake in?

Maximizing the revenue itself, on the other hand, while it's not something to actually do, is useful to think about because it's useful to know where the maximum is reached, so that you don't raise taxes and find yourself reducing revenue. Not that we're likely to get anywhere close to that point.

Of course, you can't very well compare across countries if you're using absolute revenue, but comparing across countries is ridiculous anyway, because of all the other differences between the countries that aren't being controlled for.

Bernard Yomtov and KCinDC are dead right. The idea that you are going to get a tight fit in the relationship between corporate income tax and tax revenues as percentage of GDP is really silly (and bordering on statistically illiterate).

The Laffer Curve is stated usually over aggregate income, not corporate income. Why? Because aggregate income = GDP. So a hypothetical 100% tax on income is, in effect, inescapable.

But raising the corporate income tax doesn't have the same chilling effect on business activity, because there are alternatives to reporting corporate income, namely, retaining earnings, not organizing as a corporation to begin with, etc.

KOnDC, when I thought about it, if they made a graph showing revenues against tax rates the data points would be all over the map because of big countries versus small countries. So revenue/GDP would give you a simple way to weight GDP size -- if you were willing to assume that GDP was independent of tax rate. But of course the assumption is that GDP is not at all independent of tax rate.

J Thomas: the problem just seems twofold (1) they picked a really ridiculous curve fit (running it through the outlier Norway!) with a shape that has nil to do with the data points (2) revenue/GDP might weight GDP but it doesn't account for either the different contributions of corporate activity to GDP in those countries or the character of that corporate activity. An old-line oil company is much more likely to be paying corporate income tax than a big growing tech firm, even if each makes the same contribution to GDP.

Wait a bleepin' minute. There's another point here. It might be in some sense easy but besides the point to show that we're on the wrong side of the Laffer curve for any given tax.

I remember reading an article long ago about lowering the capital gains tax. I am not sure when or where this was, but the point I am going to make is very general. The first few years after the tax was lowered, revenues from the tax spiked. Laffer curve advocates declared victory. Then, after a couple of years, revenues flattened out to a level lower than what they were before the decrease. The point is that people often have a choice of how to pay a tax and when to pay a tax. Lowering some tax just makes it more appealing compared to the alternatives. What happened back -- people speculated -- was that lowering the tax encouraged people to liquidate their capital gains at a higher rate. Once that stock of "unfreezable" capital gains was depleted, we saw revenues more in line with the actual consequences of the policy.

So: easy to be on the "wrong side" of the Laffer curve for some particular tax, but besides the point because what we should look at are the implications on total tax revenues, not just collection on that particular tax.

i like the idea that govt revenue is a function of one variable, r = f(t).

but why is there even a field of study called "economics", if the whole thing boils down to one equation ? shouldn't there be some kind of job opportunities for people who can plot the results of other single-variable functions? where are the Tangentists or the Logrithmists ?

Ara, clearly the WSJ graph is indefensible. All the various arguments against it here look right to me.

As you point out, they ran their curve through their single outlier. They were probably trying to draw a parabola but the shape of their curve is rotated so they don't get a function. One axis has corporate taxes as a percentage of something-or-orther (probably claimed profits) while the other has revenue/GDP, neither is what you'd expect.

Someone who hoped to get anything useful out of this would probably have to make the assumption that profits are a constant fraction of GDP. With that assumption you can interchange profits and GDP (with a fudge factor) and it all works out.

Then a parabolic laffer curve implies that profit (and GDP) decline linearly with tax rate.

So if you measure tax rate against revenues divided by GDP (or profit). Revenues *are* tax rate times GDP (or profit). So the result is to compare tax rate against tax rate.

The result should be linear, just like Thoma's inear curve-fit.

The scatter in the data indicates how closely the assumptions fit reality.

According to Mao there are at any time 5% traitors in the population (independent of purges). Obviously according to supply side economics the ideal tax rate is always 5% lower than the actual tax rate ;-).
(In that case let's put it at 105%!)

While indeed the formula(+) gives tax rate against tax rate effectively (=>linear), it does not when GDP approaches 0. The 0/0 cannot be removed from the equation because in the vicinity of that even minute fluctuation can have an infinite response.

revenue= rate * GDP
rate= revenue/GDP

I think the vertical axis is mislabeled, and is actually intended to be corporate taxes as a % of GDP. Total tax revenues are much higher than 10% of GDP in these countries.

I did poorly in Economics 101, and it probably shows in this question, but why wouldn't you weight GDP against population instead?

The general rule here is when the WSJ editorial page says something about taxes is that its either (a) flat out wrong; or (b) highly misleading.

They have repeatedly claimed that Bush's tax cuts were "progressive" by comparing what percentage of income taxes are paid by the top X% both before and after the Bush tax cuts, noting that after X went up after the tax cuts. Conveniently ignoring how much more money the rich were taking in in the latter years. This graph is just more BS from them, as if the only thing that has an impact on corporate tax collections is the marginal rate.

I was just curious, so I tried fitting a least-squares quadratic (since the Laffer curve is often drawn to look like a parabola) to the data points, not forcing the curve through (0,0). The peak occurs at about 27%, but only the linear coefficient is statistically significant at the 90% level. R-squared is miserable.

I bet you can get decent R-squared by fitting a 26th-order polynomial.

My guess is the WSJ drew a spline with something like Adobe Illustrator. Note that a didn't say that they "fit" a spline to the data, but that they simply drew the curve they wanted over a picture of the data.

I think this may be the single worst scatterplot diagram ever created.

Since I took my nick to 'honor' Laffer and folks who 'believe' him like unthinking politicians and fools on the WSJ editorical page, I noted that the WSJ also chose to use ancient -- 2004 -- data. The AEI, which provided the bogus graph has some explaining to do with their fake chart, and the Editorial Page folks of the WSJ have proven once again that they are totally unconcerned about reality. Let's see what it looks like if they have Norway's tax rate properly calculated and use 2005 or 2006 data.

NFL, I don't really care what it looks like, even with better data, because the whole idea of the chart is bogus. The y axis is just wrong. If you're dividing the tax revenues by GDP, then it's not even theoretically supposed to produce a Laffer curve. If the claim is that at some point increasing the tax rate will decrease the GDP, then it's innumerate to normalize by GDP. Rather than having 0 tax revenue at a 100% tax rate, as in the Laffer curve, you'd expect an undefined tax/GDP ratio at a 100% tax rate.

KCinDC, I understand your point, but the problem of the WSJ Idiotorial is much easier for most people to grasp when you point out that the tax rate that they attribute to Norway understates the actual tax rate, making the supposed curve (which we all know was not fitted to the posted data) even more erroneous, and that it chose a year that happened to have relatively low corporate income in the USA. I agree with your complaint as well. Laffer's fantasy is doing as much damage to America as Marx's economics as interpreted by the Soviet Communit Party did to the USSR.

Amusing and educational!

If it's a Laffer curve, instead of "Wheee!" it should say "Ha!".

Just de-lurking to thank Hilzoy for the link to Despair Inc. This is brilliant:

AT DESPAIR, INC., we believe motivational products create unrealistic expectations, raising hopes only to dash them. That's why we created our soul-crushingly depressing Demotivators® designs, so you can skip the delusions that motivational products induce and head straight for the disappointments that follow!

I saw that posters that Despair Inc. is mocking all over the place when doing temp work a few years and they made me want to scream at the banality of them all.

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