Best Curve-Fitting Ever

From Mark Thoma, via Brad DeLong, comes what will henceforth be my absolutely favorite example of twisting data to fit your theories. Observe the following graph of corporate tax rates vs. revenue in units of GDP:

thoma2.png

Pretty straightforward, really. As you raise taxes, the government collects more revenue. Norway seems to collect more than its fair share, which might be interesting to dig into, but the trend seems clear. But there’s something nagging at the back of your mind — aren’t there people out there in the world who believe that raising taxes actually decreases revenue past some certain not-very-high tax rate? “Supply-side economists,” or something like that? People who exert a wildly disproportionate influence on U.S. tax policy? What would they make of such a graph?

Yes, Virginia, there is such a thing as supply-side economics, and you can find its practitioners in such out-of-the way places as the American Enterprise Institute and the editorial pages of the Wall Street Journal. Here is how such people view these data:

thoma1.png

No, I am not being unfair. I did not draw the “Laffer Curve” on top of those data in order to embarrass the WSJ or AEI. They did it themselves; the second graph is how the plot was actually published by the Journal, while the first one was Mark Thoma’s subsequent reality-based-community version of the plot. As Kevin Drum says, it’s “like those people who find an outline of the Virgin Mary in a potato chip.”

Among other features, we note with amusement that the plotted curve implies that tax revenues hit zero at a corporate tax rate of about 33%, and become dramatically negative thereafter. As of this writing, it is unclear what advanced statistical software package was used to fit the Laffer Curve to the data; the smart money seems to be on MS Paint.

66 Comments

66 thoughts on “Best Curve-Fitting Ever”

  1. Philip Walker,

    Good point. Way too many people fall prey to the fallacy of reversal, where an argument with some flaw is assumed to have no merit at all. They sometimes apply this to “crank” ideas. In this case, I agree that the really important thing (for our understanding, but it is still important to flag bad presentations) is not the hokey high-peaked curve, but the rough clustering between 15-35% rates, which could thus ideally be considered a “reasonable range” for liberal democracies that want to raise “adequate” revenue without oppressing business. However, the real trick here is that so many companies pay less, or are even given net payments, due to loopholes and lobbied rigging of the tax code. The percent figures, as a practical matter, are therefore dubious to begin with.

  2. It’s certainly easy to poke fun at other disciplines, especially those that are a little removed from one’s own.

    I was going to write some cogent argument pointing out that Economics is viewed as the dismal science, not because its practioners are charlatans, but because it is so hard. First principles are a little tricky to pin down… But in the light of this sort of ‘analysis’ (the graph) I probably better not bother.

    I’m not quite convinced by Brian’s (39) argument that business would continue under a 100% tax regime. I can’t imagine many of them would bother…

    I supose that every field has it’s unfair share of contributions from people with little knowledge of the subject but a powerful urge to talk about it anyway. Physicists and astronomers have IDer’s, nutjobs with perpetual motion machines and economists have everyone that knows the world would be a better place if everyone was more left/right wing.

    I’m glad I’m a software engineer. Everyone likes us. Or something.

  3. It’s sort of amusing that in a post where you’re ridiculing someone’s ability to fit a curve, you make the classic blunder of assuming a linear fit is appropriate without any justification. Both plots are obviously ridiculous.

  4. Isn’t it amusing, though? Here’s the thing: the first plot was not a “fit” to the data, it was just a way of indicating the perfectly obvious fact that there seems to be a general upward slope in these data. Nobody claimed that the curve would never turn over, or that these things were the right axes to be plotting, or that higher taxes are always better. Any suspicion that those things were being claimed is more reflective of your inner mental state than any point I or anyone else was making using these curves.

    The point is that the AEI/WSJ curve was laughably ridiculous. A decent supply-sider could argue “Wow, that particular curve is egregiously bad, and they should be embarrassed; but a better analysis, with more appropriate data, would nevertheless show a turnover.” Such a person, whether right or wrong, would be “honest.” The actual people who seem to be showing up here are choosing instead to ignore the ridiculousness of the published curve (the point of this post), and to make fun of straw men that they are choosing to construct. That’s what we call a “hack.”

  5. Brian (#39), what if the tax rate is 110%? 200%? Do you think there is a point along this curve where tax revenue declines? I do (far below 100%, at a guess).

    The higher the tax rate, the greater the incentive to plan your taxes carefully. Even for whatever companies would remain under a 100% regime, presumably few accounts would show a net profit, and even fewer a substantial one.

  6. AJ on Jul 14th, 2007 at 9:19 am

    “Did anyone bother to look up the fact that this line is not being fit to the data?”

    It’s just there for decoration?

    “It is merely a curve which indicates ‘good’ ratios are below the curve and ‘bad’ ratios are outiside the curve.”

    Um, could you repeat that, in a way which makes more sense?

  7. Hahahahah!

    Great job! It seems that someone actually wanted to discredit Laffer curve and could not find a better way to do it than manipulating these data.

    Who’s worst? Economists doing science or scientist doing business? I wonder

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  9. Take UAE and Norway out as outliers, what is the confidence level of there being a correlation? Looks like random scatter to me.

  10. An interesting point made over at Crooked timber with regards Norway as an outlier.

    In science, outliers are often easy to dismiss as measurement error, equipment etc. But how can you ignore a REAL country with REAL people?

    so you reply well they’ve got oil etc. so we just can. so what about all the other countries with oil or special ‘resources’ or exceptional state of affairs?

    read here for more:
    http://crookedtimber.org/2007/07/14/outliers/

    m

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  14. OK. Does anyone have the original data, because this one is just begging for a treatment with Akaike Information Criterion. You have a bunch of very noisy data, a simple model (linear trend) and a (very, very) complicated model that looks almost, but not quite parabolic–maybe a weibull of some sort. I’d bet the linear trend kicks serious tuckus.

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