1: The data fails to separate changes in tax policy with changes in deficit spending. In most cases, tax cuts are not paired with similarly-sized spending cuts, nor tax increases coupled with similar-sized spending increases. What happens in practice is that tax cuts are often paired with spending increases, thus causing a big increase in deficit spending. However, this makes it impossible to determine whether it was the change in tax policy that caused changes to economic growth, or the deficit spending itself, which seems like an obvious candidate for the causal factor. Of course you can goose your short term economy with borrowed money.
2: The data fails to account for reverse-causality. As often as not, we change tax policy in response to economic changes, not vice versa. So even if you find a weak correlation between lower tax rates in growth, it might be because we tend to cut taxes vigorously in response to economic slowdowns, allowing them to correlate to the rebound without causing it. Likewise, we seem to pass the most tax increases at the height of bubbles, when the populace is more flush with cash than usual and more tolerant of paying additional taxes.
However, there is one tax that suffers neither of these problems - Social Security (OASDI). First, Social Security spending and revenues have been pretty close together as the program was phased in over over 50 years starting in 1937, thus giving us a rare example of more or less simultaneous tax increases and corresponding spending increase.
The exceptions to this can be found in the 50's, 80's, and 90's, where there were slightly faster increases in revenues than spending. However, these changes were slight, and given the fact that these were all economic boom years, are hardly evidence that an increase in tax rates harm the economy.
The other great thing about Social Security is that the tax increases were planned years ahead of time and phased in slowly. Hence, we can be certain that these tax increases were not a response to economic conditions. If there is a correlation, the causality must run the other way. Additionally, there has been little political fiddling (until recently) with the OASDI system. Other than the gradually phased-in tax increases, its structure is the same now as in 1937.
So what does the data look like? Well, we can first look at a simple chart of OASDI revenue vs the statuatory tax rate. If the famous "Laffer Curve" is correct, revenues should not keep up with the tax rate - a 10% tax should not bring in twice the revenue of a 5% tax.
Is that what we see? Nope. Not at all. In fact, revenues correlate perfectly with the tax rate. No evidence of a "Laffer Curve" appear at all. It appears people aren't trying very hard to dodge the OASDI tax, despite it amounting to nearly 6% of the economy and constituting our single largest tax.
But wait! What if Social Security is harming the economy? We wouldn't see that in the above chart, so we have to look elsewhere. So I have prepared the two charts below. Both consist of one data point for each year, with the horizontal axis being the change in OASDI tax rate relative to the prior year. The vertical axis are the change in GDP growth, with the upper chart being the difference in growth in the subsequent year less the growth in the prior year, and the bottom chart being the growth in the three subsequent years minus the growth in the three prior years. Positive values on the vertical axis indicate accelerating growth. Most values fall at zero on the horizontal axis because most years saw no change in tax rate.
So there you have it. Our experience with Social Security shows no evidence at all of even a hint of a "Laffer Curve", or having an effect on economic growth, despite it being our largest individual tax. This is all the more compelling because the Social Security system is a rare example of a tax increase coupled with a corresponding spending increase AND not being a response to the current state of the economy. In appears unlikely that at anything approximating our current tax rates, further tax increase or tax cuts would have a substantial effect on the economy if those tax changes were coupled with a corresponding change in spending.