When straightening up my office at the end of the semester, I ran across a paper by Alan Blinder and Mark Watson that came out this summer. It points out that since the 1940s the American economy has grown faster under Democratic presidents than under Republicans--a lot faster. If we restrict it to the complete presidential terms in the data (starting with Truman 1949-53 and ending with Obama's first term), per-capita GDP growth has averaged 12.4% per term under Democrats and 5.7% under Republicans.
The ranking of individual terms is shown below--the worst performance among Democrats (Obama) is almost equal to the Republican average.
GW Bush-1 7.4%
GHW Bush 2.8%
GW Bush-2 -2.4
As Blinder and Watson observe, the difference "while hardly a secret, is not nearly as widely known as it should be." Ironically, the magnitude of the difference is probably part of the reason that it's not well known. Given that the American economy is large and complex, and that presidents don't have total control over government policy, it's hard to believe that presidents could make this much difference. So any reasonable person has to say that a lot of it is "luck"--growth varies in mysterious ways, and the Democrats just happened to be there when growth was stronger. Once you've allowed a lot of it was luck, it's easy to assume that it was all luck. So even people who know this fact don't talk about it, because they assume that it's just a fluke (that was my first thought when I encountered it in Larry Bartels's Unequal Democracy).
But this is not a reasonable conclusion. The reasonable conclusion is a compromise--that the observed difference is partly luck and partly "real" (that is, the result of differences in economic policies). More precisely, you can obtain a Bayesian estimate by specifying a distribution that represents your prior beliefs and combining it with the evidence of the data. For a prior, I took a normal distribution with mean 0 and standard deviation of 1. That amounts to assuming about a 67% chance that any real effect over a term is less than 1%, 95% chance that it's less than 2%, and almost no chance (less than 1 in a billion) that it's as large as the observed difference of 6.7%. So this distribution amounts to a strong prior belief that any difference will be small. Since the normal distribution is symmetrical, the chance of an x% difference in favor of the Republicans is the same as the chance of an x% difference in favor of the Democrats.
Given this prior distribution, after observing the data there is about an 85% chance of a real difference in favor of the Democrats. The most likely value is a 0.9% difference in favor of the Democrats. That doesn't sound like much, but for someone earning $50,000 a year, it would mean they could expect to earn about $450 more at the end of a Democrat's term than at the end of a Republican's term (and given that growth compounds, $450 a year more for the rest of their life).
On the other hand, there's a 15% chance of a real difference in favor of the Republicans--that is, that Republican policies were more effective in producing growth, but because of bad luck they ended up with worse performance. So the data don't give a definitive answer, but if you're betting, 85% sounds pretty good.
Of course, you don't have to accept my prior distribution, but the point is that luck vs. a real difference isn't all-or-nothing choice.