There's a fair amount of research in economic history on almost exactly this topic. Two recent papers http://www.nber.org/papers/w12328.pdf and https://drive.google.com/file/d/0B4s_WKe-US99LV9XVTNVNzFxYW8... have looked at how measures of the artificial-ness of borders (how straight they are, how often they cut through the territory of ethnic groups, ratio of a country's area to the area of its convex hull) are correlated with various measures of welfare (e.g. GDP/capita, lack of conflict). The papers are often controversial because they often claim something approaching causality (see recent Twitter war https://twitter.com/bill_easterly/status/753252113510268928).
Who are these people discussing on Twitter? Are they the researchers who publish papers on the topic? (I do not mean these same papers you linked to, just asking if they are serious academics.)
Easterly is an economist at NYU (who published one of the earliest papers on the subject), I'm not sure about the others. However the discussion is a good representation of some of the debate that's gone on regarding interpreting correlations between regular-ness of borders and GDP (i.e. is it that having artificial borders was disruptive, or was it that borders were drawn artificially in areas that had fundamental characteristics which have caused them to have lower GDP today).
The two Olds papers both use clever triple difference designs (e.g. you're using change in entrepreneurship amongst those who've just become eligible for food stamps in one state relative to those who were already eligible as the treatment group, and the change in entrepreneurship amongst those same types of people in another state that didn't have a change in eligibility laws as the control group) which are hard to find fault in. It seems like a lot of people are arguing "other countries have strong welfare states, but less entrepreneurship", but that's a different question - most of the papers cited are arguing that in the United States, a strengthening of the welfare state leads to increased entrepreneurship. That does not mean that this would be true in other countries, nor that moving to a proper guaranteed minimum income would increase entrepreneurship, nor that entrepreneurship is the best measure of dynamism in the economy. But it is pretty convincing evidence that giving potential entrepreneurs the ability to fail at starting a business without too severe of consequences increases the rate at which they'll start businesses.
One question I had was whether the overall rate of entrepreneurship increased. As you note, the papers seem to focus on rates within the population that receives the benefits, but the typical conservative argument is that the cost of those benefits in taxes retards economic growth overall. I'm not suggesting that they are right (as far as I know no substantial link has yet been found between low tax rates and economic growth), but it's a question worth addressing in the article and it was not.
My personal interpretation is that a lot of this effect is driven by the fact that income (which I think we tend to think about as a proxy for standard of living, including quality of school system and safety of neighborhood, and not just what their family can buy) is often difficult to measure, and parental education might actually offer a much better measure of "standard of living" children experience (which is why it may show up as significant, while income may not, in those analyses).
Wealth is a poor indicator of education. Usually the questions will be how much do the parents earn, rather than where they live or their standard of living. My Dad has a doctorate in physics from a top university, yet he's pretty much given up normal employment and lives a happy sustainable life. Measured by annual income alone, he's probably below the poverty line.
On an individual scale, wealth is a poor indicator of education, but in the aggregate the correlation is very strong: http://www.bls.gov/emp/ep_chart_001.htm
Doctoral degree-holders are unique in that they're the only group that earns less than a lesser-educated group (professional degrees).
A professional degree isn't exactly "less" than a doctorate, though. Traditionally speaking, Medicine and Law are doctorates... and they both rank ahead of the Doctor of Philosophy (but behind a Doctor of Divinity, which is the highest doctorate).
> Traditionally speaking, Medicine and Law are doctorates... and they both rank ahead of the Doctor of Philosophy
No, while medical doctors and lawyers (civil doctors), were recognized uses of the term "doctor" for quite some time, traditionally the professional degrees in both fields have been baccalaureate degrees (the MBBS in medicine/surgery and the LL.B. in law), outside of certain Scottish universities, and the change to make the degrees generally doctorates were fairly recent (19th Century) US innovations.
