Paul Krugman, responding to Simon Wren-Lewis, wants a model to better articulate Ken Rogoff's fears of debt and deficits (pdf). Fair enough request. I can't give Paul a fully worked-out formal model, but I think I can give him a sketch of what such a model would look like.
(Update: If Paul likes, he could maybe simply change his own model by drawing two IS curves instead of just one. There's a "low" IS curve, when people expect the economy to stay at the ZLB equilibrium in future; and a "high" IS curve, when people expect the economy to stay at the normal equilibrium in future. And a higher stock of government bonds shifts both IS curves to the right. Update 2: Hmmm. I rather like that way of looking at it. Because desired saving and investment will be qualitatively different when the central bank is doing sensible monetary policy in the normal equilibrium than when the central bank either cannot or will not do sensible monetary policy and the economy is in the ZLB equilibrium.)
It's a model with two equilibria: a normal equilibrium; and a ZLB equilibrium. A sunspot (any intrinsically irrelevant event that causes a self-fulfilling change in expectations) can flip the economy from one equilibrium to the other.
That seems plausible to me. If people expect low aggregate demand in the near future, current aggregate demand (consumption and investment demand) will be low too. (Any New Keynesian model with an Euler-IS curve has that property.)
Set to one side the question of whether the ZLB really is a binding constraint on monetary policy that prevents the central bank credibly announcing a time-path for future monetary policy that enables the economy to escape the ZLB.
Assume the demand for government bonds (relative to GDP) is "high" in the ZLB equilibrium, and "low" in the normal equilibrium.
That too seems plausible to me. If there's a recession, private investment opportunities won't be as attractive, because people fear the recession may continue, so there won't be sufficient future demand for the extra output created by the investment. Government bonds look good in comparison, even at low or negative real interest rates.
In the normal equilibrium, the quantity of government bonds demanded depends on normal things like the real interest rate on those bonds and the expected probability of default (whether through unforeseen inflation or through simple non-payment of obligations). So in the normal equilibrium, a higher stock of debt, other things equal, means a higher equilibrium interest rate on that debt. And a higher interest rate implies a higher primary surplus needed to service that debt and prevent the debt/GDP ratio rising. And running a primary surplus is something governments don't like to do, and so the higher the primary surplus the higher the risk of default. And the higher the risk of default, the higher the rate of interest would need to be to persuade people to hold the debt. Which creates a positive feedback loop, because it means a higher primary surplus...which might create a crisis, if the positive feedback effect is strong enough.
This is a model where a higher level of government debt has real effects in the normal equilibrium. It is a model where Ricardian Equivalence is false. An overlapping-generations model would have that property.
Now let's close the loop. In the ZLB equilibrium, the demand for government bonds is high, which means the demand for money will be high too, which means the demand for goods will be low, which means the economy is stuck at the ZLB. In the normal equilibrium, the demand for bonds will be low, which means the demand for money will be low too, which means the demand for goods will be high, which means the economy will be in a normal equilibrium away from the ZLB. In other words, the fact that the demand for bonds will be high in the ZLB equilibrium and low in the normal equilibrium is precisely what creates those two equilibria.
Suppose the economy is initially in the ZLB equilibrium. Suppose the government is running a deficit, so the level of debt is rising. Suppose no sunspot comes along. The demand for debt is high in the ZLB equilibrium, but it's not infinite. Eventually, when the level of debt gets high enough, the ZLB equilibrium disappears, leaving only the normal equilibrium. But the transition to the normal equilibrium is not smooth and continuous. The demand for debt suddenly jumps down, and interest rates jump up. (And no, the central bank can't push them back down again, because the normal equilibrium is a normal equilibrium, where the central bank can't lower interest rates while keeping inflation on target at the same time.)
The bigger the debt when the economy does return to the normal equilibrium, the bigger the jump in interest rates when it does return to the normal equilibrium. Will the jump in interest rates be big enough to cause a solvency crisis? I don't know. It depends.
Whether a solvency crisis, and the enforced fiscal tightening, would cause a deficiency of aggregate demand and a recession, is another question. Presumably it wouldn't, if monetary policy could offset any fiscal tightening. Which presumably it could, in a normal equilibrium. But the fiscal tightening and solvency crisis could still be very ugly. Deficiencies of aggregate demand matter, but they aren't the only things that matter.
Of course, if people foresee that the debt will soon get high enough to eliminate the ZLB equilibrium and force a return to the normal equilibrium, the economy might jump back to normal before it is forced to jump. And if so, it jumps at a lower level of debt than if people hadn't foreseen it, so the jump in interest rates would be smaller. Which would be a good thing all round.
What to do?
Keeping the deficit and debt low, and just waiting for a sunspot to return the economy to normal, is not obviously the wrong policy. Nor is it obviously the right policy. It probably depends on the frequency of sunspots, and on lots of things.
Personally I would prefer creating a sunspot, rather than waiting for one to turn up spontaneously. That's what central banks are for. But now I'm going off-topic.
Is some sort of model like this at the back of Ken Rogoff's mind? I don't know.