I see that "improve your WB ease of doing business score" policy advice has cropped up again on the interwebs (I'm lookin' at you, Alex T.).
In my own special bombastic way, I've had a lot to say on this topic so I thought I'd collect much of it here and expand on the issue/problem.
1. To the extent there is a correlation between the "doing business" index and per-capita GDP, it is a very loose relationship whereby countries with very similar scores have very different outcomes.
Sadly, this is true of almost all institutional indicators, as Hausmann, Pritchett and Rodrik showed us lo these many years ago.
2. Even though there may be a historical correlation between "doing business" and incomes, it is far from clear that it is either causal or exploitable. The exploitability point is kind of a Lucas Critique point. If we see such a reduced form relationship in historical data, treating it as exploitable (i.e. targeting index improvements as a path to higher incomes) is pretty risky. Incredibly, some countries are making improving their scores a policy goal. Ricardo Hausmann has a nice piece on why this can be problematic. And, Matt Andrews has written a book about how countries are adopting "good looking" but not actually good, governance.
3. As Dreimeier & Pritchett show, it is often the case that the outcomes reported by the index, which is compiled by surveying "experts" are not really related to the actual experience of business people in the country under study. This is the usual de facto vs. de jure issue that plagues many expert compiled indices.
People, we know that North Korea is poor and South Korea is rich. We know that East Germany was poor when West Germany was rich. But we really do not know in any reliable way, what macro policy advice will ensure development success. Really and truly. "Adopt the observed policies and forms of the rich countries" has been offered as advice by the IFIs for decades with very uneven results. Measures of institutions across countries are converging, but per-capita output across countries is not.