Note: The specific relationship that they find is that startup creation is associated with home prices. This makes sense in the US, as home prices are a good proxy for middle class wealth. Here's a quick not fully vetted interpretation of this finding: When the middle class is relatively rich, they start businesses. When it is relatively poor, they don't. The aspirational income inequality that Graham posits doesn't immediately jump out when looking at year by year new startup numbers on a graph. I'm currently analyzing these numbers, but it's pretty clear that they don't support Graham's assumptions.
Note 2: The FRBoSF analysis isn't perfect for answering this question, but at least it's a good start, unlike the pure logic approach (despite the easy availability of good longitudinal Census data on the subject) that Graham published.
Note 3: The Graham essay is an essay on income inequality that came out before the atomic bomb that Picketty dropped on the subject. It really shouldn't be dragged out now because the research landscape on the field has been completely changed since it was written.
Final Note: I know that every time the word startup is used on HN, it spurs a 'No True Scotsman' debate about what qualities invalidate a new business from the label startup. Not remotely important. The FRBoSF article notes that new businesses have faster job growth than older businesses and that's the larger subject in question. Trying to throw companies out only serves to move the conversation from fact based to conjecture based by throwing out a perfectly good source of facts relevant to the matter.