The idea has not held up. As I write the rate on 6-month T-Bills is 0.06%. That is pretty close to zero, right?
And yet everyone is debating what will happen with the rate of price inflation. No one is claiming it is indeterminate, as the simplest liquidity trap models suggest. Nor, with rising rates of price inflation, can it be argued that inflation inertia is dominant. Instead, it is obvious that the Fed has let the current inflation happen. It is true that the inflationary pressures stem from (roughly) coordinated acts of monetary and fiscal policy, rather than monetary policy alone. But no one is doubting that the Fed is in charge of forthcoming rates of inflation.
(And if the T-Bill rate is ever so slightly above zero, rather than at or below zero, that too seems to stem from higher expected rates of price inflation in the first place.)
I agree with those individuals who suggest that the currently higher rates of price inflation will not be with us 4-5 years from now, and that is because the Fed does not want that to happen.
Paul Krugman recently wrote (NYT):
Seriously, both recent data and recent statements from the Federal Reserve have, well, deflated the case for a sustained outbreak of inflation. For that case has always depended on asserting that the Fed is either intellectually or morally deficient (or both). That is, to panic over inflation, you had to believe either that the Fed’s model of how inflation works is all wrong or that the Fed would lack the political courage to cool off the economy if it were to become dangerously overheated.
In other words, the Fed to a considerable degree can indeed control the rate of price inflation, and with nominal T-Bill rates very close to zero. Thus the liquidity trap doctrine is dead, discarded once it no longer provides an argument for an ever-more expansive fiscal policy.