Outrageous Data Illiteracy
The Wall Street Journal has an opinion piece on corporate tax rates, national tax revenue and the Laffer Curve. Accompanying this editorial is the following authoritative graphic:
Wow, I guess we better change our tax rate.
...
Wait a second, doesn't that fit line look a little suspicious? Like, maybe it fits too well? Or maybe it's been pulled up by Norway? Or maybe there isn't even a statistically significant line to report? By eyeballing the data off the chart, I ran a binomial fit and got these results:
To the extent there is a parabolic fit to this data, it's not what the WSJ shows. It's a much lower curve with an R2 of less than 0.2, meaning it predicts at most 20% of the variance in tax revenue based on tax rate. Other factors account for more than 80%. This fit did better than the linear regression, which fails to produce a statistically significant linear relationship.
So, perhaps the data shows a binomial trend. Maybe there is a Laffer Curve. But it is not the curve the Journal drew in the paper. The editorial does not describe how it derived its impressive graph, but I'm highly skeptical it involved any more math than "let's draw the curve we want to support our policy hypothesis."
It reminds me of undergrad, when we crunched decades of national data to find the "Phillips Curve," the legendary tradeoff between unemployment and inflation. Like the Laffer Curve, it sounds very sensible at the end points. Phillips suggested that high unemployment means low inflation (no need to pay higher wages to hire more employees) and if there were low unemployment, there would be high inflation (must pay increasingly higher wages to get employees away from old jobs). Laffer suggested that if there were no taxes, there'd be no revenue and if there were 100% taxes, there'd be no revenue; therefore, there is a revenue optimizing sweet spot. Anyway, long expose, short point: we crunched all the Phillips data and found no statistical relationship. None.
These macroeconomic concepts make fuzzy sense, but a lot of macroeconomics starts breaking down on close analysis. And yet - in California's one required high school semester of economics, we teach macroeconomics, not microeconomics.
Last thread of the rant: newspapers only get away with publishing wildly misleading graphs because people accept them without scrutinizing the details. Sadly, people don't trust a newspaper's ability to report facts (which its reporters have a specialty in), but will then take their graphs on faith. Don't. For more on accurate data presentation, I present all things Tufte.
Back to regularly scheduled studying.
PS: I have to add the caveat: the corporate tax rate is incredibly stupid and should be abolished. But not because of "the Laffer curve." Because it leads to double taxation and inefficient cost distribution. For more, take Rakowski's Income Tax (which there are many good reasons to do).
DISCLAIMER: Yes, the Laffer Curve does not have to be parabolic. It could be any curve with a maximum between (0, 100). I used a parabola because I wanted a curve that fit the data in a statistically meaningful way. The stark difference between my graph and the Journal graph to me suggests that there is no mathematical basis for the curve they drew. Why does it top out at Norway? Maybe it can go higher! Much higher! My point being: without a mathematical model to justify the curve you draw around the points, there's no basis for suggesting it would have such a steep slope just to the left of where America is now.
Wow, I guess we better change our tax rate.
...
Wait a second, doesn't that fit line look a little suspicious? Like, maybe it fits too well? Or maybe it's been pulled up by Norway? Or maybe there isn't even a statistically significant line to report? By eyeballing the data off the chart, I ran a binomial fit and got these results:
To the extent there is a parabolic fit to this data, it's not what the WSJ shows. It's a much lower curve with an R2 of less than 0.2, meaning it predicts at most 20% of the variance in tax revenue based on tax rate. Other factors account for more than 80%. This fit did better than the linear regression, which fails to produce a statistically significant linear relationship.
So, perhaps the data shows a binomial trend. Maybe there is a Laffer Curve. But it is not the curve the Journal drew in the paper. The editorial does not describe how it derived its impressive graph, but I'm highly skeptical it involved any more math than "let's draw the curve we want to support our policy hypothesis."
It reminds me of undergrad, when we crunched decades of national data to find the "Phillips Curve," the legendary tradeoff between unemployment and inflation. Like the Laffer Curve, it sounds very sensible at the end points. Phillips suggested that high unemployment means low inflation (no need to pay higher wages to hire more employees) and if there were low unemployment, there would be high inflation (must pay increasingly higher wages to get employees away from old jobs). Laffer suggested that if there were no taxes, there'd be no revenue and if there were 100% taxes, there'd be no revenue; therefore, there is a revenue optimizing sweet spot. Anyway, long expose, short point: we crunched all the Phillips data and found no statistical relationship. None.
These macroeconomic concepts make fuzzy sense, but a lot of macroeconomics starts breaking down on close analysis. And yet - in California's one required high school semester of economics, we teach macroeconomics, not microeconomics.
Last thread of the rant: newspapers only get away with publishing wildly misleading graphs because people accept them without scrutinizing the details. Sadly, people don't trust a newspaper's ability to report facts (which its reporters have a specialty in), but will then take their graphs on faith. Don't. For more on accurate data presentation, I present all things Tufte.
Back to regularly scheduled studying.
PS: I have to add the caveat: the corporate tax rate is incredibly stupid and should be abolished. But not because of "the Laffer curve." Because it leads to double taxation and inefficient cost distribution. For more, take Rakowski's Income Tax (which there are many good reasons to do).
DISCLAIMER: Yes, the Laffer Curve does not have to be parabolic. It could be any curve with a maximum between (0, 100). I used a parabola because I wanted a curve that fit the data in a statistically meaningful way. The stark difference between my graph and the Journal graph to me suggests that there is no mathematical basis for the curve they drew. Why does it top out at Norway? Maybe it can go higher! Much higher! My point being: without a mathematical model to justify the curve you draw around the points, there's no basis for suggesting it would have such a steep slope just to the left of where America is now.
posted by Tom Fletcher at 8:06 AM
9 Comments:
How's the studying going, Tom?
Go-ood.
Sometimes I get bored though.
It's even worse than you say it is, Tom. The data on which the graph is based is poor.
The x-axis data, corporate tax rates, fails to account for the effect of base erosion. Numerous gaps, carveouts, and exceptions for special industries can make the effective tax rate much lower than the stated rate.
The y-axis data, tax revenues as a percentage of GDP, include both personal and corporate taxes, as far as I can tell. Unless you believe that each of the listed countries collect individual and corporate taxes in the same proportion, the y-axis doesn't state anything meaningful about corporate tax receipts.
Finally, the data doesn't account for the effect of worldwide tax systems, which tax the state's residents on their worldwide income and is used in the U.S., as opposed to territorial tax systems, which tax only income earned within the state. The graph uses GDP, which is a territorial measure. The effective of using GDP, in the context of the U.S., is to overstate the amount of tax we collect.
sorry to break up this graphing party, but does anyone know what the texas law school blog is? I want the scoop on David Gamage, who is apparently visiting from UT and teaching income tax I next semester
I hate Mack Brown
Here's some more coverage of the WSJ's dishonesty with links:
http://www.fair.org/index.php?page=22&media_view_id=9066
Money quote:
The WSJ editorial crew are "like those people who find an outline of the Virgin Mary in a potato chip." Also, the links reveal the curve was originally drawn by the American Enterprise Institute. Big surprise there!
http://www.usnews.com/usnews/edu/articles/070617/25gender.htm
I wonder how Justices Johnie and Sammie feel about too many ladies going to college in light of their recent opinions?
Probably fine with it, so long as no one is taking bong hits.
There's an argument that can be made that the estimate of a Laffer curve should not be a "best fit" estimate, but rather an "outer envelope" estimate.
Take, for example, an estimate of a PPF. A PPF is supposed to measure the frontier of production possibilities--the outer limit showing a perfectly efficient manner of production for a fixed level of inputs. A "best fit" estimate doesn't make sense in that scenario unless you're specifically interested in actual production rather that efficient production (i.e., you're not interested in the PPF).
Similarly, when concerned with estimating the highest possible tax revenue which can be achieved from an array of tax rates, a "best fit" approximation might not be terribly meaningful. It might make sense to force any estimation form (parabola, line, whatever) through the most outside point. However, doing that would destroy degrees of freedom and so you lose predictiveness elsewhere--that would be the reason that the shown parabola can't also go through the "frontier" points down in the corner where the US point is.
All I'm saying is, there could be an economic reason for forcing the fit through Norway. To wit, Tom's fit, in contrast, does a very very very poor job of answering the following question: what's the maximum achievable tax revenue from an array of possible tax rates. Tom's estimate would not include Norway, which is, in fact, THE empirical maximum.
Note: I did not look into the WSJ article at all to see if that's what the authors of the graph did. Just saying that data illiteracy is sometimes in the eye of the beholder.
Speaking of dubious news sources, this man is my hero: http://en.wikipedia.org/wiki/Greg_Packer
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