I think sufficient evidence has accumulated to say that there was likely a positive shock to prime age labor force participation rate (LFPR) in 2016 associated with the shock lowering the unemployment rate (U) in 2014. I posited the existence of this shock based on the observed relationship between LFPR and the unemployment rate despite the limited evidence in the LFPR data itself. Much like how the similar shock structure of JOLTS hires, wage growth, and the unemployment rate imply a relationship that could be used for forecasting, the downward shift in unemployment in 2014 forecast such an upward shift in labor force participation some time later.
As we can see by comparing the models with and without the shock, it's definitely an improvement  (click to enlarge):
The relationship between LFPR and U implies a Beveridge-like curve — however it would be one that is completely obscured by the long duration of shocks to LFPR (it reacts slowly, while U reacts quickly with greater magnitude). The recent data remains consistent with the predicted relationship:
 Of course, the data is still consistent with a somewhat higher value for the dynamic information equilibrium slope:
The next few months should allow us to distinguish between these models (as data will being to fall below the forecast relatively soon if the actual slope is lower).