Unpeel the onion on @ernietedeschi's very thoughtful tweet thread on measuring slack through the unemployment rate vs. employment population rate first and if you still have any energy read this one too.
FIRST POINT: it is worth being aware/clear that PA EPOP is improving faster than UR lately. Everyone following these issues knows the level fact (EPOP not recovered while UR is), worth knowing the change one too.
You can see that in this graph which shows predicted changes in EPOP based on changed in UR. Most of the time changes in UR and changes in EPOP are effectively the same. In 2010-13 EPOP generally underperformed while in 2016-17 it has overperformed. 
In other words, slack is closing FASTER in the last two years than is apparent from the fall in the UR because labor force participation rates are rising faster than would be expected given the fall in UR.
SECOND POINT. Wages for WORKERS (e.g., AHE, Atlanta Fed) are underperforming wages for JOBS (e.g., ECI). This matters because everyone is wondering why wages for workers are not rising faster. Changing the question to ECI does not provide a full answer to this question.
The @ernietedeschi and @ModeledBehavior regressions are focused on explaining ECI wage & salary growth. ECI fixes industry-occupation weights to effectively present wage growth for an unchanging job structure. This may make sense analytically for their model.
But in the late 1990s average hourly earnings growth was much higher than you would have predicted with ECI, in recent years it has been lower than you would predict with ECI. Slack can't be the explanation because it was already used to predict ECI.
For @nick_bunker's sake showing the same for the Atlanta wage tracker (which controls for demographic shifts). The story is similar but weaker: wages outperformed ECI in the late 1990s, underperformed in 2017.
So, even if the EPOP/ECI models are right we still have a puzzle of wage growth for workers underperforming.
THIRD POINT: I am still skeptical of the overall model because it makes what I believe to be the unwarranted assumption that prime age EPOP is stationary, at least since about 2000.
The issue is that EPOP is only a good measure of slack if it doesn't have large trend movements for structural reasons unrelated to slack (e.g., women entering workforce, mass incarceration). But it does have large trend moves and these did not end in 2000.
Here is a graph of prime age male EPOP since 1948. Looks anything but stationary. Which year had more slack, 1982 or 2017? The URs were 9.7% and 4.4%. PAM non-employment rates were 13.5% and 14.6%.
I worry when I see people making inferences about slack over longer periods of time by using metrics that would clearly fail the test of assessing whether the economy was deeper in recession in 1982 or 2017. A trend of even 1pp/decade hugely complicates inferences over time.
If EPOP does have larger structural trends over time then UR then it is a poor explanatory variable, the R2 is misleading & we would worry out of sample (although, as @ernietedeschi and @ModeledBehavior behavior point out it has done quite well out of same so far).
CONCLUSION OF THREAD: Notwithstanding the above, the EPOP story is compelling and worth continuing to track out of sample, the rapid EPOP improvements are encouraging but the underperformance of AHE/Atlanta Fed is not.
Apologies to all of twitter for imposing these threads on you. All of twitter except @ernietedeschi @ModeledBehavior @nick_bunker @marthagimbel @econjared @Noahpinion @greg_ip @JayCShambaugh
