The income inequality research is the worst I have ever seen by economists searching for agreeable political solutions. All the data I have seen is provided in the gross by the Bureau of Economic Analysis. The assumption must therefore be that the national economy is a singular system. But, every economist will agree that the national economy is divided into sectors.
The rash and false assumption is that each sector has an identical mean and distribution, or something close to it. It is easier to use that assumption if the results justify the prior political beliefs of the holder. The fact of the matter is that different sectors clearly have different means and medians and different total incomes per capita.
In addition, each sector attracts income and capital from foreign economies in varying amounts in total and per capita. This means as well that in each sector the decile and quintile borders differ.
Interclass mobility is usually observed as movement within a single sector and not across sectors. Let us examine one sector. The financial sector can be blamed for many recent wrongs -- crashing the housing sector and causing a rational major change in behavior in the household sector among them.
A great deal of income and thus wealth was created within that sector. If the data for this sector alone could be separated it would, I believe, show a significantly greater mean and median income than the economy as a whole. The quintiles themselves would be at different levels. Thomas Piketty and the rest need to disaggregate the data by sector to measure income levels and inequality -- and opportunity in each sector. It is so much easier to swallow BEA data whole.