Now, at this point any Taylor rule fitted to past Fed behavior says that the Fed funds rate should be something like minus 5 or 6 right now, but you can’t do that, so we’re stuck with an interest rate that’s too high given low inflation and very high unemployment.I wish people would stop making the argument this way. If your model is a New Keynesian one, as seems to be the case here, and you are thinking about policy in terms of a Taylor rule, you better take account of the fact that there is a zero lower bound on the nominal interest rate. If the rule is telling you that the fed funds rate should be minus 5 or 6, you have the wrong rule.
Roughly, the rest of Krugman's argument hangs on this:
The crucial thing to understand about this position is that it’s not self-correcting. On the contrary, as inflation falls over time and possibly goes to actual deflation, we sink deeper into the trap.Now he's just making it up. "As inflation falls over time..." Why? How? Then he qualifies it ("...possibly goes to actual deflation"). Is that high probability or low probability? Can you put a point estimate on that, with a confidence interval? Why do you get trapped? If Krugman knows, he should lay this out for the rest of us so we can evaluate it.
A crucial element in this is what happens to the quantities, in particular the ones on the Fed's balance sheet, as this process unfolds. New Keynesians wanted to ditch monetary quantities from their models, in part because this made things simple, and so they could focus on what they thought was important, principally the welfare losses from sticky price frictions. Contributing to that was the failure of Old Monetarism, principally due to instabilities (over virtually any horizon) in "money demand" functions.
However, the financial crisis caught many people with their pants down, unfortunately. The New Keynesians are trying to rectify that by getting monetary quantities and financial factors back in their models. Of course the Real Business Cycle people had their pants down too - it's as dangerous to put all your eggs in the TFP basket as it is to put them all in the sticky price basket.
Here, I construct what I think is a plausible future scenario for future Fed policy, and I can't convince myself that sustained deflation can happen. If you think it is likely, you need to explain (carefully) why financial institutions, and everyday Joes and Marthas, will continue to hold $2.3 trillion in outside money which is appreciating in real terms, and not somehow use the stuff in transactions, thus causing inflation. And the answer can't be "Japan."