Raising interest rates might lead to some initial reductions in wealth by lowering asset prices, but it could also take a bite out of your paycheck and dampen your prospects of finding a job. It's a bit of damned if you do and damned if you don't.

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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.

Most progressive critics don't want to destroy the power of the Fed to regulate the macroeconomy and finance. They want to regain control over it so that it better serves the interests of the whole population.

The Fed cannot reduce inequality on its own; far from it. This requires a concerted effort by the government, broadly speaking, to support a variety of efforts. These include things like raising the federal minimum wage, eliminating unfair restrictions on union organizing, increased fiscal spending on needed infrastructure with a condition that these jobs will be decent paying jobs. Of course, this is just the tip of the iceberg, and far from the question of the role of the Federal Reserve.

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.