There is a lot of literature about the conduct of monetary policy at the zero bound, that is, when the policy rate is zero and can’t be lowered. Bernanke is the author of a lot of this literature; it’s one of his academic specialties and why he is uniquely qualified to be chairman at a time when the Fed is operating at the zero bound.
Bernanke has taught us that the monetary authority is not helpless at the zero bound, because the crucial policy tool is not the nominal short-term rate but rather the real short-term rate. The real rate is the nominal rate minus expected inflation. The higher the level of expected inflation, the lower the real rate will be at a zero nominal rate. As an extreme example: If we knew that Bernanke was a madman plotting to destroy the United States via hyperinflation, we would probably want to move our money out of M2 and into something more tangible, like a business or a machine or property. We would know that the real interest rate was about to become highly negative, and thus the cost of holding M2 was about to become very high.
Thus, the policy objective of the Fed today is not to merely increase the monetary base, but rather to make forward statements about the growth of the monetary base that are sufficiently shocking that our inflation expectation will rise. There are many things the Fed could say, such as “we plan to grow the monetary base by one trillion this year and one trillion next year no matter what”. Or they could say “we plan to double the dollar price of gold (or the euro)”. Or they could say, “we will target 5% inflation until unemployment falls below 6.5% on a sustained basis”. But they have said none of those things. They have said almost the opposite.
Remember, the policy objective is to raise inflation expectations in order to make the real funds rate sufficiently negative to change economic behavior; to make liquidity very expensive, and to make risk very cheap; to induce actors to invest in productive capacity instead of M2. Bernanke laid this all out for the Japanese in his inflation speech in Tokyo ten years ago this month.