[This post is unfinished. I was writing it yesterday, thinking it would work out, then I realised there was a problem. I slept on it, but can't see any obvious resolution. But sometimes we learn from seeing that things don't work out the way we thought they would. So I'm posting it anyway. I will discuss the problem at the end.]
Alternative title: "A model for Steve Randy Waldman (who had better like it, because it's roughly based on what he's been saying)".
Let me give you the intuition first:
It is well understood by New Keynesian macroeconomists (or it ought to be) that the natural rate of output in a NK model is a decreasing function of firms' profit-maximising markup of price over marginal cost, and that markup is in turn a decreasing function of the elasticity of substitution between varieties in the Dixit-Stiglitz utility function.
It is also well understood by finance people (I think) that if the managers of a firm face a serious risk of bankruptcy, and get the same utility whether the firm goes bust by a small amount or a big amount, they tend to act as if they had Panglossian expectations. They make their choices as if they were assuming the best, because if the best doesn't happen they are bust anyway and their choices don't matter. (I think I stole this from Willem Buiter, but can't remember precisely.) If firms set price before observing a relative demand shock, firms with Panglossian expectations will set a higher price than firms with rational expectations, because they will act as if they knew their firm would face a big positive relative demand shock.
Putting those last two paragraphs together: that means the more Panglossian are firms' expectations, the higher the markup of price over the rational expectation of marginal cost, and the lower the natural rate of output. And the bigger the real value of the stock of debt, the more Panglossian expectations will be.
If firms inherit a fixed nominal stock of debt, the lower the price level, the bigger the real stock of debt, and the more Panglossian are expectations. We can't now talk about the "natural" rate of output (because it's not independent of the equilibrium price level, so money is non-neutral), but we have a model in which the Aggregate Supply curve is upward-sloping. A leftward shift in the AD curve causes a fall in both P and Y. But prices are not assumed "sticky" with respect to aggregate shocks (they are only assumed "sticky" with respect to microeconomic shocks to relative demand).
It is possible that the AS curve will be horizontal for a low enough price level. (That's Steve's punchline).
OK, that was the intuition. Now for the semi-formal stuff.