The institutional fact that makes a liquidity trap an irrelevant academic construct is the unlimited ability of the central bank to create money. One can make this point in an irrefutable manner by noting that the logical conclusion to unlimited open-market purchases is that the central bank would end up with all the assets in the economy including interest-bearing government debt, and the public would hold nothing but non-interest-bearing money.
I say again that a genuine liquidity trap (and Hetzel shares my narrow definition) is a unicorn--something we have never seen and never will see.
The Fed was very successful at bailing out large financial institutions. It was a failure at maintaining nominal GDP growth. You would think that this would make the Fed highly vulnerable politically. However, the political right protects the Fed by raising false alarms about inflation, thereby arguing for monetary policy to be tighter, not looser. And the political left protects the Fed by insisting that things would have been much worse without the bank bailouts and by insisting that we are in a liquidity trap.
As you know, I do not buy into textbook macro. But textbook macro has a nonzero probability of being correct, and if it is then the Fed ought to set an aggressive target for the level of nominal GDP and do whatever it takes to hit that target.
I favor this as a Pascal's Wager policy. On inflation, my fear is not monetary policy but fiscal policy. As I have said before, hyperinflation is a fiscal phenomenon. See if you can show me a country where the money supply doubled in a year while the budget was balanced or in surplus.
Finally, I want to point out that while the right-wingers who worried about high inflation in the U.S. in recent years over-estimated inflation, if you had bet on the Phillips Curve you would also have underestimated inflation. (My guess is that if you look carefully, you will see that the Keynesians who got their inflation forecast right did so while getting their unemployment rate forecast badly wrong, which says that their Phillips Curves were off.) A crude linear approximation of the Phillips Curve would be that inflation equals 7.5 percent minus the unemployment rate, which would have predicted negative inflation for the past few years. Instead, inflation has been positive. One can counter that the Phillips Curve is very nonlinear (so that each additional percentage point of unemployment now produces very little disinflation), or that inflation is mis-measured, or somesuch. But I would raise the possibility that the recession is about breakdowns in PSST, so that textbook macro is wrong. In that case, there won't be much payback from following the Pascal's Wager policy.