We spend a lot of time thinking about how to get out of a liquidity trap. Maybe we can think more clearly about that question if we instead ask the exact opposite question.
But let's be a little more precise about our question:
How can you get an economy into a liquidity trap in such a way that someone else couldn't get it back out of that same liquidity trap just by reversing whatever it is you were doing? Because it's not really a trap if someone else can get the economy out of it.
I can get a car stuck. That's easy. Any fool can do that. But getting a car stuck so badly that another driver couldn't take over and reverse the car back out is a little bit harder. You have to do something that's irreversible to make it really stuck.
If monetary policy were loose enough, you would never get into a liquidity trap in the first place. The Zero Lower Bound on nominal interest rates won't be a constraint, for any conceivable shock, if you are targeting 100% inflation. Hitting the ZLB means you were running too tight a monetary policy, given the driving conditions, in the first place.
If one night I snuck in past security, locked the doors behind me, and took over the Bank of Canada, and if I were full of bad intent, I could very easily get the Canadian economy stuck at the ZLB. I would just tighten monetary policy, and announce loudly that I was tightening monetary policy, and force NGDP growth to be so negative that the equilibrium nominal interest rate would need to be negative. No problem.
But what happens when they finally break the locks, escort me out, and Steve Poloz and his old team take over again, and everybody sees that Steve is back in charge of monetary policy?
What could I possibly do, short of physically smashing the printing presses, that would prevent Steve from simply reversing what I had done? Where's the irreversibility?
The fact that I would have destroyed a lot of physical and human capital is a form of irreversibility. But it's not a form of irreversibility that would make it harder or impossible for Steve to get the economy out of the liquidity trap. If anything it would make it easier for Steve, because standard models of investment say that investment demand is a negative function of the existing capital stock, so a war that destroys part of the capital stock causes a rebuilding boom and increases the natural rate of interest when the war ends.
I can only think of one plausible candidate that might work: inflation inertia. If there is inflation inertia, monetary policy still ultimately controls inflation, but the inflation rate has a lot of momentum, so that it's hard to get it to speed up or slow down quickly. If there is sufficient inflation inertia, I might be able to get the Canadian economy stuck in a liquidity trap so badly it would be very hard for anyone else to get it out again.
Suppose I targeted minus 10% inflation, and I eventually hit my target, before they managed to break the locks. If there is inflation inertia, the inflation rate won't immediately go back to 2% when Steve takes over. Just like a car, no matter how powerful the engine, won't accelerate from 0 to 100km/hr in 0 seconds. This means there may be some strictly positive time period during which the ZLB will be a binding constraint on short-term nominal interest rates even after Steve takes over again and everyone knows Steve is back in charge for good. If that is the case, does there exist an equilibrium time-path in which inflation eventually returns to Steve's 2% target? If not, then I have succeeded in getting the Canadian economy irreversibly stuck in a liquidity trap.
The answer isn't obvious. If saving and investment depend only on the short-term real interest rate, and if actual inflation depends only on lagged inflation and current output and short-term expected inflation, then there may not exist an equilibrium time-path in which inflation eventually gets back to Steve's 2% target. Because Steve's forward guidance can influence long-term real interest rates and long-term expected inflation, but these don't matter by assumption. So the short term real interest rate will be above the natural rate for some period, which means output will be below the natural rate for the same period, which means that actual and expected inflation would fall still further during that period, which prolongs the return to the 2% target, and so on. Which means I might be able to get the economy irreversibly stuck.
But is there inflation inertia? The answer to that question isn't obvious either.
There is no inflation inertia in the Calvo Phillips Curve assumed in standard New Keynesian models. If output is at the natural rate, and if expected inflation is at 2%, actual inflation will also be at 2%, regardless of what it was in the past. So if the standard New Keynesian model is true, Steve can reverse what I did and get inflation back to 2% with no lag. But nobody actually believes the Calvo Phillips Curve; we only assume it because it makes it possible to do the math.
Empirically the evidence seems to be mixed, at least to my eyes. During relatively normal times there looks like a lot of inflation inertia. It's just too easy to forecast inflation, especially core inflation, from lagged inflation. But in abnormal times, when there is a clear change in monetary regime that changes expectations, inflation seems to change very quickly. We saw that when the Bank of Canada announced the original inflation targeting agreement. We saw it even more clearly in Sargent's "The ends of four big inflations" (pdf). Dragging me out of the Bank of Canada and putting Steve Poloz back in charge would be a very big and obvious change in monetary regime.
[Update: See Marcus Nunes for another example where apparent inflation inertia suddenly disappeared when the monetary regime changed.]
Dunno. It might be possible to get an economy irreversibly stuck in a liquidity trap. But it's a lot harder than you might think.