Yesterday's Wall Street Journal has a *spectacular* example of really bad math.

The WSJ is, in general, an excellent paper with really high quality coverage of economic issues. But their editorials page has long been a haven for some of the most idiotic reactionary conservative nonsense this side of Fox News. But this latest piece takes the cake. They claim that this figure is an accurately derived Laffer curve describing the relationship between tax rates and tax revenues for different countries; and that the US has the highest corporate tax rates in the world.

There's an idea in economics about taxes called the Laffer curve, which is based on the extreme value theorem. What the Laffer curve describes is the relationship between tax revenues taken in by the government and take rates. Naively, you might assume a linear relationship between taxes and revenues: raise the tax rate, and the amount of money that the government brings in increases.

But reality isn't so simple. When you increase tax rates, you reduce the amount of money available to people and businesses for investment. So it's not a simple linear thing; the size of the pool of taxable profits can be altered by changing the tax rate, because a higher tax rate reduces the amount of money that can be invested in growing a business, which can slow the growth of the business, which reduces its taxable profits. The Laffer curve is a model for the relationship between tax rates and tax revenues. It starts off roughly linear, and then the revenue growth rate starts to slow, until it reaches an inflection point, and revenues start to *decrease* as tax rates increase. The figure to the right is a drawing of the standard Laffer curve borrowed from Wikipedia.

What people like the WSJ editorial page like about the Laffer curve is that one of the implications of it is that if your tax rate is *past* the inflection point, then you can *increase* tax revenue by *decreasing* the tax rate. So they constantly argue that our tax rates area on the downward-trending side of the curve - and that therefore, lowering takes isn't just good because it means that people get to keep more of their money, but it's in some sense free, or even *better than* free, because it will have either no impact or a positive impact on government revenue.

The catch, of course, is that for that to be true, you need to be on the far side of the curve, where revenues are dropping because the rate is so high that it's stifling investment. The WSJ editorial board constantly argues that we're on that side. And they argue it in stupid, sloppy ways.

Which brings us to the subject at hand: the WSJ's latest effort to support their argument that we're on the wrong side of the Laffer curve. They take a scatter plot of tax revenues as a percentage of GDP against take rates for a selection of countries, and then argue that it's an illustration of the Laffer curve. The thing is, it's more of a laughable curve than a Laffer curve. If you look at the data, what you see is a scatter that looks an awful lot like a typical noisy linear curve. It's got one extreme outlier, which the WSJ chooses as an inflection point, and then they curve fit on either side. The resulting curve is blatantly ridiculous - the tax rate smoothly increases in an almost linear way up to almost 25%; slows to crest over about 3%, and then falls into an almost perfectly vertical line over the next 4%. It's a terrible curve fit, which is just simple foolishly wrong.

In fact, it's an example of the same kind of nonsense that I wrote about in the very first post on the original GM/BM back at blogger, where the Geiers were analyzing autism rates, and *wanted* to show an inflection point, so they inspected the data, picked an outlier, split the data around it, and then argued for an increasing slope on one side, and a decreasing slope on the other, even though a single linear regression with a shallow increasing slope matched the data better than the double-curve with their chosen inflection point.

That's exactly what's going on here. For *some* reason, Norway is an extreme outlier in this data. Eliminate Norway, and you've got data that looks awfully close to either a nice linear slope, or to a very shallow Laffer curve. But drawing the curve not as any reasonable mathematical curve fit, but instead building it specifically to pivot on the outlying point, they've created an artificial and ridiculous curve. Sure, it supports what they're arguing for: it was artificially and dishonestly created to do exactly that.

Here's an interesting fact, which the WSJ folks certainly know about. In mathematical curve fitting, where you try to use some kind of regression method *honestly* fit the curve to data, you *never* wind up with a curve that intersects the most extreme outlier. The fact that this curve does just demonstrates its dishonesty.

The data underlying this is also definitely not honest. Calling the US corporate tax rate 34% without any qualification isn't honest at all; it neglects to mention the fact that the US has one of the most ridiculously loophole-ridden tax codes in the world, and that the actual average rate actually paid by American corporations is dramatically lower. (Just for example, the WSJ cites the average state tax rate at 4%; actually statistics show that the state rates really paid were under 2.5%, and the larger the business, the lower the rate they paid. In 2003, for example, Boeing and ATT paid *no* state taxes *at all*.)

I don't know where we fit on the Laffer curve. Frankly, I think our tax code is so distorted by random loopholes that it's probably impossible to make a blanket statement; for some businesses, we're probably taxing them enough effectively reduce the tax revenues received from them; for many others (can you say oil company?), we're clearly *not*.

But the idea that this curve produced by the WSJ folks has *any* meaning at all is simply laughable.