Your argument seems to be that, "yeah but the US household incomes are under reported." so the whole comparison is invalid....
I didn't use the word invalid. I do think that if you use bad data you will often have incorrect conclusions. Do you disagree, or do you think we should all reach conclusions knowing that our data is very poorly constructed because we quickly read something and it supports our world view?
Well, since inter-generational mobility is the key, and the US demonstrates the lowest inter-generational mobiity .. that would mean that despite slightly higher incomes than Gini calculates there still isn't mobility in the US.
Could that be because medical inflation and the cost of education have increased far more than incomes ? And its those two key factors that allow for poor kids to work out of their born circumstance.
Or it could be that Biloxi and Boston are more different than Copenhagen and Odense (that would have had more zing if I could have found another Danish City beginning with a "C".) One of your studies tries to normalize for that and it totally changes the results.
BTW, your study shows that the UK has less social mobility than the US. What is wrong with their health care and educational system?