Krugman has some criticism of Mankiw's note on the liquidity trap.
I'm not sure Krugman is thinking about this entirely right. It seems like the really relevant question is whether the coefficients are estimated in a period that is (1.) stable, (2.) we think the Fed behaved correctly, and (3.) we'd like them to behave that way again.
Why does Krugman's estimate make it look like we've got longer to go? Well for a lot of the years he adds to the analysis (i.e. - the early 2000s) the Fed probably had rates that were low relative to Mankiw's rates. Krugman perhaps thinks this is justified - he's said before that rates weren't too low. But of course if you develop a "where the Fed should be if they could be there" rule from a decade where policy was particularly loose, you're going to get a number that says they're farther from where they should be than you otherwise would.
So it's not that Mankiw is wrong to use his coefficients - it turns on what periods you think are best for modeling the answer to the question "where should Fed policy be now if it could be there?" If you think the 1990s are better than the 2000s for that, Mankiw has your answer. If you think the 2000s are just as good, Krugman has your answer.
His point is certainly right that none of this says anything about what's going to happen in the future. But I still like the direction its heading.
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