Reducing Global Inequality At The Cost of Raising National Inequality?

Branko Milanovic has a provocative article hinting at the possibility that the reduction  in global inequality may come at the cost of raising national inequality. Here's the key chart:



While the Asian middle class and the top %1 have seen an increase in real income, the US and Western lower middle class have not seen as much gains.

Brankovic's larger point is that people care more about national inequality than global inequality. Thus they are unlikely to accept a reduction in global inequality if it comes at the cost of increasing national inequality.

I'm reminded of some studies that show it is not the absolute wealth people care about but the relative wealth. (I can't find any references at the moment.)