John Sides in The Monkey Cage has an excellent post that points to the distinction between the progressivity of taxation and the level of inequality.
This paper by Moinca Prasad and Yingying Deng has an excellent graphic of the progressivity of direct taxes, as measured by the Kakwani index of taxation (a measure of the progressivity in the distribution of taxes among different categories that controls for the impact of income concentration on the concentration of the tax burden), in many advanced countries.
However, given its relatively higher Gini coefficient, America's progressivity of taxation does not translate into lower income inequality. So what gives? The aforementioned paper shows that the high progressivity in America's taxation system is matched by the low level of income redistribution through welfare policies. In simple terms, it is America's welfare policy that needs immediate attention than its taxation policy. The graphic below highlights the role played by income redistribution in lowering inequality.
The Scandinavian countries achieve twice as much inequality reduction (as measured by the lowering of their respective Gini coefficients) by redistributive policies than the Anglo-American nations. It is not a coincidence that these countries have much higher levels of taxation as measured by their higher tax-to-GDP ratios. It appears that higher redistribution goes hand-in-hand with higher levels of taxation.
Interestingly, the association between tax progressivity and overall re-distribution through taxation across countries is negative.
Though the study speculates on several political economy reasons, none of them are satisfactory enough to provide a good explanation for this surprising inverse correlation.
These graphics are an excellent empirical illustration of the importance of enlightened public policy in lowering inequality and poverty. It is also a strong reminder to free-market evangelists that unfettered markets fail to achieve the desired conditions necessary to promote growth and reduce poverty and inequality.