Explanatory is a subset of relevant. Furthermore, using a correlated factor as a proxy for the explanatory one is perfectly legitimate if you are attempting to make an unrelated comparison.
(I.e., if "European descent" is correlated with "good home environment" or other exogenous predictors (the data shows it is), and you are comparing EU schools to US schools, it's utterly reasonable to control for "European descent" if data on those exogenous predictors is unavailable.)
As for PPP numbers, the gap often becomes larger when you compare like to like. The same blog did a very good job of this (focusing on not only European Americans, but actually narrowing down to Swedish Americans) a while back:
I don't understand "explanatory is a subset of relevant". If it does not (partially or not) explain the observed result, how can you decide whether it is relevant ?
As for the other links, I don't see numbers related to PPP, but maybe I misunderstand those graphs (I don't understand income per unit of consumption). I also don't see how he can deduce the difference is coming from gvt differences. I am only familiar with statistics, so I may be missing the subtlety of a field I am unfamiliar with (economy), but those analysis seem quite superficial to me. Certainly, they don't warrant such strong conclusions.
(I.e., if "European descent" is correlated with "good home environment" or other exogenous predictors (the data shows it is), and you are comparing EU schools to US schools, it's utterly reasonable to control for "European descent" if data on those exogenous predictors is unavailable.)
As for PPP numbers, the gap often becomes larger when you compare like to like. The same blog did a very good job of this (focusing on not only European Americans, but actually narrowing down to Swedish Americans) a while back:
USA vs Sweden: http://super-economy.blogspot.com/2010/03/income-distributio...
Swedish-USA vs Sweden: http://super-economy.blogspot.com/2010/03/super-economy-in-o...