Here's the interesting thing: the fact that QE and lowering interest rates almost to zero has worsened inequality, does not mean that raising interest rates will help reduce inequality.

The Fed has a lot of power in the economy because it has a big impact on the supply and cost of credit, that is, interest rates. It also plays a key role in supervising banks and historically has seemed to take it easy on the banks when it shouldn't have, such as in the lead up to the financial crisis.

Increases in interest rates normally worsen inequality, at least partly by reducing employment and wage growth.

The Fed needs to adopt new tools, on its own and perhaps in cooperation with the other parts of the US government, to improve the economy from the bottom up. This includes increasing facilities for debt forgiveness for under-water mortgages and excessive student loans; increased credit facilities for small businesses and cooperatives; helping to underwrite mechanisms for creating affordable housing in cities; and more restrictive enforcement of financial regulatory rules to help rein in excessive banker risk and pay.

The impact of QE on generating more lending by Wall Street to Main Street and in generating more employment and increasing overall investment in the economy is quite modest. QE probably limited the initial collapse of the economy in 2008, and likely had a very small positive impact on economic growth, but its broader impact on jobs and growth in the economy seems not very big.

QE and other aspects of Fed policy increased inequality pretty significantly. This is reinforced if you take into account all the other non-standard measures the Fed used to bail out the banks early on in the [2008] crisis.

Many of those on the right distrust the Fed and want to eliminate its power in the belief that the private economy, including the private banks, will be much more efficient, productive and even democratic if they are left to themselves: in other words, the criticism of the Fed really reflects a desire to cripple the government in the service of increasing the power and authority of the market.