without nominal rigidities, why doesn't the PSST model specifically predict that prices will adjust to restore full employment?
Suppose that a bunch of mortgage underwriters get laid off. There are two possible full employment equilibria.
(a) They can be instantly employed as dishwashers at 20 cents an hour.
(b)They can be employed as health insurance claims processors at a salary close to what they were making as mortgage underwriters.
The reason that we don't observe (a) is that wages are not perfectly flexible, if for no other reason than minimum wage laws. Point conceded to Bryan.
But the PSST story is focused on why we do not observe (b). The answer is that it takes time for entrepreneurs to figure out that there is a need for more health insurance claims processors, for the mortgage underwriters to seek and obtain retraining, etc.
Part of the reason that wages are sticky is that unemployed expect that the "right" equilibrium looks like (b) rather than (a). But more wage flexibility does not get you to (b). Instead it gets you to (a). That is why I do not think of wage flexibility as being a solution to problems of finding PSST.
To put this another way, suppose that policy makers, observing the correlation between nominal GDP and employment, try to exploit this correlation by raising nominal GDP. If there is enough money illusion, they will move the economy to (a). But I think instead all that happens is that the economy takes its own sweet time moving to (b), and in the mean time nominal wages and prices are higher than they would have been had the government done nothing.
Just as Milton Friedman predicted that the Phillips Curve would break down of policy makers tried to exploit it, I predict that the correlation between nominal GDP and employment will break down if policy makers try to exploit it. They will get mostly higher prices for their troubles. I may be wrong, and things are so bad that I would be willing to try the experiment for a while, but I predict that it will not turn out well.