I don’t see how the Fed could have any real impact on inequality long term. They can’t push unemployment below NAIRU in the long run.

It’s certainly true the Fed overestimated NAIRU in recent years, but that’s not because the Fed hates poor people. It’s because NAIRU is really, really difficult to estimate a priori.

So would it be better for the Fed to run the economy tighter? I don’t see that. Overshooting NAIRU will cause inflation, which will have to be met by swift rate hikes to bring inflation back to target, which will naturally cause unemployment. You’re not helping low income people by taking away the jobs they just got. This isn’t even mentioning risk of over-tightening from overshooting NAIRU.

The best thing the Fed can do for low income people is to maintain the current expansionary period as best as they can with as much stability as possible. Inequality concerns need to be addressed first, second, and third by fiscal policy.