The IMF has published information on the effectiveness of progressive taxation in reducing inequality . The chart shows the redistribution effect in different countries. 

Notice that the economies above which are least able to redistribute income through taxes are Chile and Mexico. This is probably because they collect taxes relatively more through sales taxes (which act regressively), while the base for an effective income tax is too narrow. Poorer countries, such as Indonesia and Honduras, would face even more difficulties in trying to make their tax systems progressive.

Can anyone explain why Korea and China also have relatively low levels of redistribution through taxes?

The IMF article continues with suggestions for further redistribution, such as transfer payments, minimum wage legislation, and training/educational programs.

Source : https://blogs.imf.org/2017/04/24/chart-of-the-week-sharing-the-fruits-of-growth/?utm_medium=email&utm_source=govdelivery