The ratio of nominal GDP to employment is NGDP/L, where L is the level of employment. This can be decomposed into:
NGDP/L = (NGDP/RGDP) x (RGDP/L) = the GDP deflator x productivity
. . .
The way I look at it, this means that the relationship between nominal GDP and employment has almost no theoretical import. In particular, it does not constitute evidence in favor of the AS-AD paradigm. The AS-AD story, as Scott Sumner tells it (and pretty much any mainstream macro would say the same thing), is that changes in nominal GDP cause changes in employment, rather than the other way around.
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.
Defining aggregate demand as nominal GDP finesses such difficult issues as defining the money supply or justifying specific parameters of a macroeconomic model. But there is a priced to be paid. And that price is vacuousness.
Ok so the anchor in all of this getting us to a nob that everyone can agree the Fed controls.
So, the key question is do we believe that the Fed can indeed control NGDP? Or, put another way, can the Fed control the total amount of nominal spending in the economy.
If the answer is yes, the we can use that same relation to decompose Fed action into its consequences. If the decomposition shows – as is Scott and many other’s point – that employment moves, not just inflation or productivity then this is saying that the Fed controls employment.
So the crux of this is whether or not you believe that the Fed can set NGDP. And, if it can we have an important implication.