Trend vs. cycle in the employment-population ratio

Two stylized facts about U.S. labor markets are that (1) while the unemployment rate has fallen substantially since the Great Recession, the employment-population ratio (E/P) has not nearly recovered to its pre-recession level, suggesting to many observers continuing labor-market slack, perhaps due to discouraged workers and other labor-force dropouts; and (2) E/P has been trending down for some time, partly due to demographic factors (e.g., retiring baby boomers) and possibly also due to institutional factors, such as changes in disability insurance work incentives.

The issue matters, because E/P is often thought to be a more reliable metric for labor-market "slack" than the conventional unemployment rate, and if so the apparently weak recovery of E/P could suggest continuing weakness in labor demand and thereby strengthen the case for continuing relatively expansionary monetary policy. So... where is E/P relative to its long-run trend or "full-employment" level?

This interesting post from the NY Fed claims that a demographically-adjusted E/P has fallen far enough that "roughly 90 percent of the labor gap that opened up following the recession has been closed." The authors' adjusted series is supposed to remove the business cycle effect and leave just the changes due to demographic shifts, reflecting the changing age structure of the population and life-cycle employment rates for a series of cohorts. Here is the money chart:

Very interesting, indeed, but there are a couple of slightly strange things going on here. First, the authors had to use a normalization to set the level of the trend E/P. That is, they can only calculate the shape of the blue curve, not how high or low it is. Their approach was to assume that the average gap between the actual and adjusted E/P was zero over the entire period, so the red curve has to spend something like half the time above the blue curve, by assumption. If you thought the economy was around "full employment" during those episodes of peak actual E/P in the late 1990s and mid-2000s, a more logical normalization might be to shift the blue cure up so that it sat on or near the top of those peaks. But their assumption seems a reasonable alternative. I would be reluctant to conclude that the convergence of their curves implies a return to full employment... perhaps more neutrally, we could call it a return to E/P "normalcy."

What troubles me more, however, are the dramatic changes in slope of the blue trend, around 1994 and again around 2008 or 2009. The latter is particularly puzzling. If it reflects a cohort shift in E/P at each stage of the life-cycle, then how can we be sure this is not a consequence of the severe recession? If that's not the explanation, then what accounts for the sudden acceleration in the decline of adjusted E/P?

It does seem very likely that the trend in E/P has been downward over the past 15-20 years, and in that case the actual E/P has been closing in on a moving target and may be closer to "full employment" than the red line by itself might suggest. Just how much closer is a difficult question to answer.