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

As long as inflation and productivity growth are close to trend, or as long as the product of the two is close to trend, the relationship between nominal GDP and employment will be close to trend.

This leads me to expect to find that when nominal GDP growth is low, employment growth is also low. You would only not get that if there were a big surge in inflation and/or a big surge in 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.