Civilian labor force participation and inflation

Carola Binder discussed Brad DeLong's discussion of Charles Evans statement that the US has "essentially returned to full employment". I'm not going to add much to the discussion of full employment. However, Binder shows us a graph of the civilian labor force (CLF) participation rate for prime age workers (25-54). It's a pretty pristine example of a dynamic equilibrium subjected to shocks:

Actually, I accidentally (LOESS) smoothed the data too much when in order to look at the derivative, but it resulted in a happy accident. The dynamic equilibrium model almost perfectly matches the smoothed data:

Another way to put this: the model is an almost perfect smoothing of the data. That's pretty astonishing.

Binder also says:

"It is not totally obvious why prime-age employment-to-population should drive inflation distinctly from unemployment--that is, why Delong's λ should not be zero, as in the standard Phillips Curve."

However this seems to have the situation entirely backwards. There might well be a second order effect relating unemployment and inflation:

But the dominant (and indeed, across several countries, principal) component of inflation over the post-war period seems to be driven by demographic factors involving labor force participation (women entering the workforce).

...

Update: Here is Fed Chair Janet Yellen on women in the workforce.