Dynamic equilibrium in occupational classes

David Andolfatto has a post up about trends in employment. One of the things he notes is the "cyclic asymmetry" of the unemployment rate that is pretty well described by the dynamic equilibrium model [1] (also see the underlying matching model). The sequence of shocks leading to lower and lower male participation was also noted in [1]. However, David did put up some data about the fraction of "routine manual" labor that is also well described by the dynamic equilibrium model:

In the second graph, the equilibrium growth rate is (consistent with) zero however I translated and scaled the shocks to show them superimposed on the same graph. Some observations:

• Routine manual labor shows a similar pattern to male participation rate in [1], however since it is not growing (male participation rate grows between shocks), it just gets hit with shocks and never rises.
• Female routine manual labor shows roughly the same pattern as male, just from a lower base. The shocks in 2001 and 2008 were a little bigger and a little smaller than the shocks to the male routine manual labor fraction, respectively.

The other occupational classes (non-routine manual, routine cognitive, non-routine cognitive) also display dynamic equilibrium but also show more influence of the non-equilibrium process of women entering the workforce (see also here) that didn't reach equilibrium until the 1990s. A couple of differences:

• Non-routine cognitive is growing for both men and women (non-zero growth rate, unlike the zero growth rate above).
• Non-routine manual is growing but at a fairly slow rate for men that was outpaced by women until after the Great Recession.
• Routine cognitive shows the strongest signal of women entering the workforce in the 80s (e.g. office admin jobs, recalling the cultural touchstones of the time), eventually matching the zero growth equilibrium for men in the 2000s.

Here is what that that last dynamic equilibrium description looks like (you can see that the slope falls until it reaches about the same slope as for men in the 2000s):