Gauging the water level
Exception to the rule

Mid-week entertainment: dogma

Wsj_laff1This chart from a Wall Street Journal editorial has been making the rounds lately, being ridiculed left and right.  A number of you have been leaving comments here so I'm putting it up and center as our light entertainment for the week.

The chart is being used to justify this economic concept called the "Laffer Curve" which claims that lowering tax rates can increase total tax receipts (for example, because fewer people will cheat the government.)  As far as I know, it is dogma, and has never been proven empirically.

I also agree with Prof. Gelman's skepticism about using countries as experimental units to inform domestic policy.

Fire away!

Further reading:

Junk Chart readers

Economist's View
Tufte blog
Gelman blog

And more:

Cosmic Variance
Brad DeLong


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Mike Anderson

How the heck did they fit that curve? Laffer's basic idea is that there must be a "sweet spot" somewhere between 0% and 100%, and it's good policy to find it. What the chart shows is more of a Laugh-er Curve, with a built-in zero intercept (maybe reasonable), and a maximum that completely ignores at least 3 data points directly below it. Without the assumption of a zero intercept, it's not even clear that there IS a curve. I'd run a loess line through the data before I even started thinking about curvature, let alone some bogus maximum. Then I'd address Dr Gelman's concerns, maybe by looking at historical rates and receipts, or states and municipalities. And I'd be really careful about making any statements about p-values or confidence intervals. In the meantime, this chart belongs in the encyclopedia illustrating the entry for "Junk Chart."


A reasonable model would be linear, with variance some function of the mean. Maybe there is a plateau effect, but more points would be needed. Otherwise the variation will be explained by other tax policies, for example capital gains and sales taxes. Norway's revenues from oil will be the explanation for its position.


I considered it for Junk Charts, but I couldn't think of a way it was actually junk as a chart. Apart from the values, it's actually not a bad design.

I'd give it fewer numerical labels on the abscissa, but that's a common complaint of mine.


Reading Tufte's book on statistics, I think I remember it to be an important principle to always try to explain outliers, or extremes.
And Norway is quite simple; they get all their money from oil (and gas). Damn does norwegians! (Coming from a Swede)


Where does one start? The line doesn't represent a statistical function that I've ever seen (it certainly doesn't minimize the sum of squared errors). There's no obvious, non-ideological reason to use a curvilinear shape rather than a linear one (Occam's Razor, anyone?). The dependent variable is all wrong (Laffer curves are supposed to be about the abolute amount of revenue collected at a given rate within a country, not the share of taxes as a fraction of GDP). The graph doesn't specify whether the dependent variable is only corporate tax revenue or all taxes together as a % of GDP. And, of course, there was no obvious reason to pick 2004 and only 2004 for the data, ignoring longitudinal, within-country differences in revenue. I'll have to find a way to use this in my Political Economy course in August.


It is bad design as a chart because the line is what draws most of your attention, and yet it's based on nothing. As Brad De Long said, it doesn't go through the data, it goes above all the data.


It is bad design as a chart because the line is what draws most of your attention, and yet it's based on nothing. As Brad De Long said, it doesn't go through the data, it goes above all the data.


Talk about one outlier driving the curve.



abbamouse, had the dependent variable been the proper total of revenue instead of the percentage, there would have been a good theoretical reason for the curve to be not a straight line, but at least a curve capable of passing through the origin, reaching a maximum, then declining.

Such a curve models three common sense outcomes that most people agree with: zero tax revenue for zero tax rate; low tax revenue for 100% tax rate; and some value of revenue that is greater than the 100% tax value, at some tax rate that is less than 100%.

The controversy is in the details :-)

David Gorsline

If this is the Journal's idea of good reporting, then maybe the Murdoch acquisition will mean an improvement in journalistic standards at the paper.


Here's a quadratic fit to the data, showing a shallow peak around 25-30% and a small decline at 30-35%. I have not constrained the quadratic to pass through the origin. The correlation coefficient is 28%, not very inspiring. As noted, though, it must be repeated that the revenue as a percentage of GDP is not what supply-siders seek to maximise when invoking the Laffer curve. If anything, they seek to minimise that.

What they say is that a reduction in corporate and wealthy personal taxes will bring an increase in total government revenue, thus arguing that cutting taxes on the rich will not harm social programs. So this data set isn't even appropriate to the question.

(on the famous Laffer peak itself, I don't doubt for a moment that it exists: I simply have seen no evidence that the US government has ever taxed any activity on the far side of it, unless the purpose of the tax was deliberately to discourage that activity, not to extract revenue from it)

Still, for what it's worth, this is more like what the WSJ graph should have looked like. Note, as I said above, that I haven't done much to it as a graph, because as a graph there's not a lot wrong.

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