Warning - this is technical, so really just for macroeconomists.
The idea that we could get stuck in a steady state with nominal interest rates at zero and negative inflation has been dismissed by some because it has been associated with the policy proposal to raise nominal interest rates to avoid that outcome. Here I want to explore an alternative interpretation that disconnects the theory from the policy.
First, a recap on the theory. Take a really simple model, where the real interest rate is positive and constant. The central bank sets the nominal rate according to a Taylor rule that obeys the Taylor principle. The rule is calibrated such that there is a steady state at which nominal interest rates are positive and inflation is at target. Furthermore under rational expectations/perfect foresight, if agents know the inflation target, the real rate and the rule, we immediately go to that steady state. In more complex and realistic models it may take time to get to this ‘intended’ steady state, but it is ‘locally’ or ‘saddlepath’ stable.
However there is another steady state, because nominal interest rates cannot go below zero. For given real interest rates, this Zero Lower Bound (ZLB) steady state must involve negative inflation. This steady state is ‘indeterminate’, which means that we can describe dynamic perfect foresight paths that start at some arbitrary level of inflation below the central bank’s target, but end up at the ZLB steady state. To see this diagrammatically, look at this earlier post, or (plus algebra) this from David Andolfatto, or pages 123 to 135 in Woodford’s Interest and Prices. 
Stephanie Schmitt-Grohe and Martın Uribe have a paper which embeds this logic in a more elaborate model of involuntary unemployment based on nominal wage rigidity. They suggest that it tells a better story about the US recession than the New Keynesian idea involving a downward shift in the natural real interest rate. It is a story of a jobless recovery: growth resumes at the ZLB steady state, but involuntary unemployment is also positive at that steady state, because inflation is negative and nominal wages are downward rigid.
The paper interprets the ZLB steady state as one where agents have the wrong expectations about the central bank target. Call this the ‘mistaken beliefs’ story. With that story, raising rates could reveal or signal the authority’s true inflation target. In Stephanie and Martin’s paper, because raising nominal rates leads to an immediate change in beliefs and therefore a rise in expected inflation, we see an immediate jump to output growth above trend, which allows unemployment to fall. Many will just think this idea is incredible, but as Paul Krugman keeps emphasising, ZLB economics often turns things upside down.
In an earlier post I suggested that this story could possibly be plausible for (pre Abe?) Japan or the Euro area, because their inflation targets are one-sided: they seem content if inflation is below target, so in principle it might be possible to believe they might be content to end up at the ZLB steady state. In addition there is no QE in the Eurozone, and was only briefly in Japan. I suggested, I hope correctly, that the situation is different in the US, and it clearly is in principle in the UK. For that reason alone, I thought the mistaken beliefs story unlikely for these two countries.
However, after seeing Stephanie present her paper last week and thinking more about it, I wondered whether we could give the ZLB steady state a different interpretation? Suppose agents believe that is where inflation is heading because they do not think monetary (or any other) policy is capable of achieving the inflation target. Given current attitudes to fiscal policy, and a pessimistic view of the power of QE, this interpretation does not seem so farfetched for the US or UK. Economists sometimes worry about a deflationary spiral, where inflation just keeps falling into a bottomless pit. But maybe the ZLB steady state is like a ledge that can stop this descent. 
Under this interpretation, the policy of raising interest rates could be a disaster. There is no boost from any increase in expected inflation, because beliefs do not change. We lose the negative inflation equilibrium, but what seems likely in that situation is that we just get a negative deflationary spiral. The ledge preventing descent into the deflationary pit crumbles away.  If this interpretation is tenable, then it means that the possibility of becoming stuck in a ZLB steady state is not necessarily linked to the policy proposal of raising rates to get out of it.
My own view of the evidence is that the ‘balance sheet recession/natural rate too low’ story is still the more convincing, and that we are currently seeing in the US and UK a very slow return to the inflation target equilibrium. However that story is not without its problems: with a simple New Keynesian Phillips curve, a gradual reduction in the output gap should be associated with inflation gradually rising towards target, which is not what we are seeing at the moment. So I am not so confident that I can dismiss the ZLB steady state story out of hand. The message I draw from that possibility is that inflation targets need to be two sided and clear, and that policy (monetary and fiscal) at the ZLB should do everything it can to try and achieve that target. Assuming that below target inflation must eventually rise because nominal rates are zero could turn out to be a big mistake. 
 At the intended steady state, where inflation is at target, the target fixes the end-point of any dynamic process, and this (rather than history) then determines the initial level of inflation. At the ZLB steady state, there are multiple dynamic paths that lead there, so something else (‘confidence’) fixes the initial point. It cannot be history, because the model is forward looking and history does not matter. This may be a little too arbitrary or extreme for some tastes.
It is also controversial whether an inflation target is sufficient to fix an end-point for any dynamic inflation process, rather than allowing dynamic processes that explode. As I note in my earlier post, John Cochrane says: “Transversality conditions can rule out real explosions, but not nominal explosions.” I have less of a problem than he does with this.
 A third interpretation might be that agents revise down their beliefs as inflation falls. The problem there is that this involves learning, which may make the stability of the ZLB steady state problematic. Jess Benhabib, George Evans, and Seppo Honkapohja have modelled learning when there are the same two steady states, and what they find is that the ZLB steady state is unstable: inflation keeps on falling. (It is a deflationary spiral.) My intuitive explanation for their result is that learning is equivalent to introducing backward looking expectations dynamics, and typically an indeterminate equilibrium with rational expectations dynamics (which the ZLB steady state is) becomes unstable with backward looking dynamics. Equally a ‘saddlepoint’ perfect foresight equilibrium (which the intended steady state is) becomes stable when expectations are backward looking, so they find that the inflation target steady state is stable under learning.
 Following on from footnote , you might ask why agents in this case will not select the only steady state left, and therefore raise their expectations. Why can I imagine agents assuming a deflationary spiral, but I want to rule out inflationary spirals? The answer is because the ZLB provides asymmetry. If it looks like an inflationary spiral is developing, the central bank can depart from its Taylor rule and raise rates substantially. That should change beliefs. They cannot do the same for a deflationary spiral.
 In an early draft of this post I had a different introduction, based on Narayana Kocherlakota’s recent dissent. Some may recall that Kocherlakota originally put forward the mistaken beliefs ZLB steady state idea, but then seemingly recanted. So my idea was that perhaps what had changed was not his view about the theory, but his interpretation of it. However having read some more about his current views, I don’t think this stands up, but it was such a neat idea I cannot resist mentioning it as a footnote.