This is largely just to keep track of this post from Krugman if I want to find it again.
One common viewpoint on the economy is that the rich spend less than the non-rich, so the more income inequality we have, the weaker our aggregate demand will be. This would help explain why our 2 depressions of the last century have occurred when inequality was high. And it was one of the first thoughts I had around explaining why our economy does noticeably better under democratic presidents than republican ones.
But as Krugman points out in the link above, that idea is hard to square with the correlation of private savings rates and inequality in the past. Here's a graph of our private savings rates over the past few decades:
Income inequality began rising some time in the 70s, with a temporary halt in that trend in part of the 90s. But the savings rate trend is basically the opposite; when inequality was increasing, savings has mostly gone down (therefore private spending went up). I think this pretty much discredits the theory that income inequality leads to lower demand and higher unemployment. There could be some explanation of how it can still be true, but I think it's best to go with the simplest thing that the evidence suggests unless we have a REALLY good reason to suspect otherwise.