I know we're not all scientists here, but anyone who has even glanced at the graphs in a few scientific papers will instantly recognize that trying to fit a curve to the following data is prima facie
I'm not going to go into the reasons why picking an inflection point at the one outlying data point on this graph is so, let us not be delicate--dumb
--that you don't even have to understand the math to sense why this is wrong. Mostly because Mark Chu-Carroll, a software engineer at Google and author of the always excellent blog Good Math, Bad Math has already done it for me
, and much better than I could have:
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.
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.
The reason this matters, by the way, is that this kind of "evidence" is often used to back up the notion that we should lower taxes on corporations. I'm not arguing that either way--merely pointing out that if this is the justification for such policies, it's a completely flawed justification.
PZ Myers of Pharyngula Mark Thoma of Economist's View (via Pharyngula)
has a nice image
of what an honest curve fit to that data would look like if, say, this data were to be published in a reputable scientific journal.
I hope he doesn't mind my borrowing it...
And, being the gentleman he is, he's granted me permission to display it here:
Check out Dr. Thoma's full explanation of his modified graph--and his take on this story--after the jump.
From a letter from Dr. Thoma (who, coincidentally, has been a staple of my Google Homepage for some months now, and should be in your RSS reader, too, if you're the least bit interested in economics):
1. As I noted in my original post on the topic, I didn't actually estimate the line (I didn't have the data), I just eyeballed that line as a rough approximation. I was just making the point that it is pretty clear that there is an upward linear trend in the data, and that it would have a much better fit than the silly thing they drew, but I made sure to note it wasn't formally estimated. When the line is estimated, as many have done since, it looks pretty much like I sketched, but the slope coefficient does not turn out to be significant.
2. Many people rebut a straight line model by noting that if you add a quadratic term, you will get a peak somewhere between 30%-40%.
However, as Brad DeLong at Berkeley notes, the Norway observation is not plotted correctly. He says:
"One more point, with respect to "omitting Norway": Personally I see no need to omit Norway. I do see a need to plot the Norway point on the graph correctly. The revenues plotted on the vertical scale include oil excise taxes levied on corporations. The tax rates plotted on the horizontal scale do not--hence the Norway "tax rate" of 28% rather than the correct 52%. Move Norway out to its proper position--with the same tax concept on both axes--and everything is fine."