[From Bill Powers (2009.10.03.0717 MDT)]
Rick Marken (2009.10.02.2000) --
I wrote to Barro asking for the evidence that "tax rate reductions
will increase real GDP". I hope to hear from him soon.
But in the meantime I took a quick look at the correlation between tax
rate (upper bracket) and GDP (annual from 1948 to 2008) and found that
the correlation is -.85! That's a correlation that even Bill Powers
might like (a little;-).
At that correlation, the odds are a shade less than 5 to 1 that a decrease in upper-bracket tax rate (of any size) will go with some amount of increase in GDP rather than a decrease.
Is there any way of finding a record of how much taxes the largest earners actually paid? That is, not the tax rate from the tax tables, but the actual percentage of income paid as taxes by those in the highest tax brackets. When you can hire the best tax advisors you don't really have to pay the highest rates. That's why you have congressmen on your payroll, too, to create the loopholes.
You're getting pretty good at finding the data and analyzing it!
I realized that the increase in GDP could just be a result of the
increase in population that occurred over the same period while the
decreased tax rate is a result of policy changes during that period.
So I computed the partial correlation between tax rate and GDP
factoring out population. The result is that the correlation between
tax rate and GDP goes almost to zero (-.076). So when you factor out
population there is not even evidence of a relationship between tax
rate and GDP, let alone a negative causal one.
I think we need an additional piece of data here, though I could be revealing my ignorance about statistics. The correlation shows how much scatter there is in the data, but the regression line shows what the slope of the assumed linear relationship is, as I understand it. You might have a regression line with a slope of -1.0 going with a correlation of -0.076, mightn't you? This would seem to tell you that one variable has a relatively large effect on the other, but the low correlation says that this is an almost totally unreliable conclusion. I'm thinking of Richard Kennaway's ellipses, in which the long axis is tilted to indicate the regression line, and the ratio of major axis to minor axis, or one minus that ratio, indicates the correlation (both indications being approximations). A correlation of -0.075 tells you that the scatter plot is almost circular, but doesn't tell you what the slope of the major axis is -- or does it?
What are the slopes of the regression lines?
Recall that the correlation between tax rate and dGDP/dt (growth) was
.28 for the same period (1948-2008). When I factor out population
growth from this correlation the result is a correlation that is
somewhat higher, .36. These correlations are still small and I am
completely puzzled by the difference in the correlation of tax rate
with GDP vs GDP growth.
With that correlation, the odds that an increase in d(GDP)/dt will go with an increase in tax rate rather than a decrease are only about 1.5 or 2 to 1, meaning that if you make many predictions of the rate of change of GDP from observations of tax rate, you will be right only 60% to 67% of the time. Might as well toss a coin if you have only one chance, especially since you're only predicting the sign, not the magnitude of the effect. Your ten-dollar investment might earn you only 10 cents even if you're right.
But this exercise was useful to me. First, it shows me where
economists get the idea that increasing taxes is recessionary. It must
be based on that huge, artifactual correlation between tax rate and
GDP. Apparently, the economists don't want to deal with the
correlation between tax rate and GDP _growth_. Second, the fact that I
see all these puzzling relationships convinces me that, once again,
Bill Powers is right; there is no way to make sense of the data
without a model.
Thanks for that. Your results tell us that growth in GDP is due to something other than taxes. Common sense models tell us that it's certainly not due to population growth; having a baby does not increase GDP unless something else happens at the same time to give the parents more income to spend for the next 18 or 20 years. Even a delayed correlation doesn't help. When the baby gets a job and starts earning money to spend, where does that extra income come from? So there is some as-yet-unknown factor that makes GDP increase with time, and perhaps changes the tax rate, too. I know what it is! It's the change in the distance to the moon (it increases by about 38 millimeters per year). That must be a very powerful influence, since such a small change alters GDP by billions of dollars per year. Astrologers were right!
Statistics can't teach us anything, though it might tell us that we don't know something. The universe remains totally mysterious when seen only through statistics -- everything happens because it happens. Human beings are to chimpanzees as modeling is to statistics. Both have been evolving for the same length of time, so they are both well-developed examples of their species. But one has a lot more useful abilities than the other has. Of course in some areas each has advantages; for example, if a human being wanted to eat termites, chimpanzees could teach him or her how to use a stick to get them out of the mound.
Best,
Bill P.