Suppose that the Federal Funds rate falls to zero. Does that mean that we are in the infamous liquidity trap, in which the Fed is powerless to use open market operations to affect the economy?
I think not, and I'm pretty sure that only Paul Krugman or someone too awed by Krugman to think for himself would suggest otherwise.
The Fed Funds rate competes with the rate on short-term Treasuries. The rate on short-term Treasuries these days is being determined by their value as collateral. Every financial institution is saying "asset-backed securities bad collateral, Treasuries good collateral." So the demand for Treasuries is through the roof, and when the price of a bond is high, its interest rate is low. So you get ridiculously low short-term interest rates on Treasuries, and also on Fed Funds.
If this safe-collateral mania keeps up, zero might not be the lower bound. Somebody might be so desperate to put up a Treasury security as collateral that the would be willing to pay interest to the Treasury for the privilege. That would mean a negative interest rate.
Now, I don't really believe that's very likely. The main reason I don't believe in the liquidity trap is that I recognize that there are multiple interest rates. If it gets to the point where the Fed cannot trade money for Treasuries, then it can trade money for Freddie Mac debt, which is still trading at a high risk premium over Treasuries.
So if anybody tries telling you that we are in a liquidity trap, tell him to shut his trap.
I don't think it's as complicated as Greg Mankiw makes it sound.
Also, I think that the spread between inflation-indexed Treasuries and regular Treasuries right now reflects the collateral squeeze more than it reflects expected deflation.