Paul Krugman has a new post that explains why he is pessimistic about monetary stimulus at the zero bound. He briefly describes his 1998 paper on the zero bound problem. This paper shows that if base money and bonds are perfect substitutes at the zero bound, and if monetary stimulus is expected to be temporary (i.e. not to affect future money supplies) then conventional open market purchases are ineffective at the zero bound.
From a technical perspective, there is nothing wrong with Krugman's model. The real problem is the way he uses the model. A model by itself cannot tell us much about the impact of monetary policy on the economy, because we don't know if it describes reality, or leaves out important aspects of the real world.
A better way to proceed is to first observe that QE does impact market prices (such as foreign exchange rates) in a way that is at odds with the predictions of Krugman's model, and then construct a new model to explain why. That's actually pretty easy to do, for instance one simple way is to assume that QE affects the future expected money supply. And that's hardly an ad hoc assumption; indeed it is the standard assumption that's been used in monetarist economics for decades. They don't always say so explicitly, but quantity theoretic claims about the impact of money on prices always assumed that monetary injections were permanent. But those implicit monetarist assumptions were just as ad hoc as Krugman's assumption that monetary stimulus is temporary.
We need to look to real world data to figure out how markets perceive a given policy action. Krugman's mistake is to work from his model to conclusions about real world cause and effect. Instead he should be adjusting his model to figure out why QE announcements in the US, Japan, and the eurozone cause currencies to depreciate.
PS. I do agree with Krugman on one important point. When I read Krugman's critics, it seems like some of them do not understand his argument. They really should read his 1998 paper. There's nothing wrong with the paper itself, and indeed after writing the paper Krugman starting criticizing the Japanese for fiscal stimulus, encouraging them to rely more on monetary stimulus. More specifically, he encouraged the BOJ to make its monetary stimulus permanent. Later he reached different conclusions. The model didn't change, just the way he interpreted the model.
PPS. Ambrose Evans-Pritchard points to another important piece of evidence against Krugman's claims. The US, UK, and eurozone all did roughly equal amounts of austerity in the past 4 years, and yet the US and UK created jobs at a much faster rate, due to much more expansionary monetary policies.