I don't think either Biden or the Fed raising interest rates will stop inflation. Why?

 Because the causes are so completely unexpected in the long or short run.

We are presently worldwide in a perfect storm of inflation caused by primarily Covid worldwide (which has an effect similar to World War II on the world in many ways) and Putin invading Ukraine which drives up gas and diesel prices worldwide exponentially. This perfect storm isn't likely to abate anytime soon either.

So, because of this, neither Biden or the Fed is likely to be able to stop inflation, especially in regard to gas and diesel prices which is what hauls all the food people eat most places on earth. So, food will tend to keep rising in costs as oil prices stay high over time.

So, the Fed likely will reduce housing being able to be sold by people wanting mortgages to the point where ONLY people with cash will buy which will tend to corner the market by the rich to begin with buying low at good prices and selling later when mortgage are more reasonable in price at some point in the near or far future.

But, once again I think that Biden likely has little to no control over inflation and neither would any president have any control over this kind of inflation.

The person most responsible for the world wide recession likely coming now would be Putin because of the war in Ukraine he started without any discernible provocation. (at least from a western viewpoint).