Arnold tells us:

The PSST story is equally consistent with a correlation between
employment and nominal GDP. It just interprets the causality as running
the other way. If a bunch of workers are laid off, for whatever
reason, nominal GDP will go down, unless productivity and/or inflation
rise in order to compensate.

But Arnold, without nominal rigidities, why doesn’t the PSST model specifically predict that prices will adjust to restore full employment?  And if you allow nominal rigidities, what does PSST add to the standard Sumnerian story?  I don’t mean to be difficult, I just don’t understand how PSST makes sense without nominal rigidity.