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.

There is no doubt that the Fed's large-scale asset purchases have caused major increases in a number of asset prices in the economy. This is especially true of mortgage backed securities and corporate bonds, and quite possibly of equities as well. For those people and institutions holding those things, the run up in prices has been a wealth bonanza.

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.

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.

Bankers themselves govern the Fed to some extent, and then there's the classic revolving door where Fed officials come from and then go back to the financial sector. Fed officials tend to believe that the institution should have a large measure of independence from democratic control, even though in law it is under the ostensible control of Congress.

Initially, QE contributed to a pretty significant increase in inequality. It raised asset prices, which are owned primarily by the wealthy, while having relatively small if any positive impacts on bank lending, employment, wages or economic growth, so ordinary people haven't had much help. By the third round of QE in 2012-2014, the effects had likely muted quite a bit. There were probably not big impacts on asset prices from QE and the positive effects on employment growth might have strengthened somewhat.

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.