What are the potential gains from letting the economy run hot?

That's the question on every economist's mind right now after Federal Reserve Chair Janet Yellen managed, in a footnote of her recent speech, to elevate a fundamental question about the influence of aggregate demand on potential supply.

In the press conference following the bank's September meeting, Yellen referred to the recent flatness of the unemployment rate (which DoubleLine Capital's Jeffrey Gundlach seized upon as a "necessary, but not sufficient, sign of a coming recession") as a "very welcome development" — something that implied job numbers that remain robust are drawing new workers into the fold.

In a note to clients on Monday, Goldman Sachs Group Inc. Economist David Mericle noted one of the benefits of an improving economy buttressed by accommodative monetary policy: the labor-force participation rate among people between the ages of 25 and 54 (often the called "prime age" segment of the population) has risen by 0.9 percentage points to 81.5 percent over the past year.

But a look at why prime-age participation picked up yielded curious results.

"While all categories of non-participation have fallen, the most obviously cyclical category — workers who say they want a job — has actually contributed the least," he wrote. "Instead, the bulk of the rebound has come from surprising places: the declining share of 25-54 year-olds who previously said either that they were disabled or that they do not want a job."

Now, the tentative hypothesis might be that these categories which are seemingly not so cyclical — like the people who have disabilities or say they don't want a job — are actually quite responsive to changes in economic conditions. Or, as Mericle dubbed them, they potentially represent "doubly-disguised unemployment."

In fact, that's what Fed Chair Janet Yellen was referring to when she discussed the potential benefits of letting the economy run hot — chiefly, reversing hysteresis (the tendency for deep recessions to have a permanently scarring effect on a portion of the unemployed, prompting them to withdraw from the labor force for the long-term).

But just because these developments occurred amid a cyclical improvement in the labor market doesn't mean they were fueled by cyclical factors. When Mericle used state-level data to judge the extent and granularity of this cyclicality — that is, whether there was a relationship between the change in the population shares of those two groups and the recent trend and level of the unemployment rate, he found the following:

The correlation between changes in the disabled share and changes in the unemployment rate is only modest, while changes in the don’t want a job share and changes in the unemployment rate are uncorrelated. When we instead compare to the level of the unemployment rate, the recent decline in the disabled share looks somewhat more cyclical, while the decline in the don’t want a job share still appears acyclical…the lack of correlation between labor market improvement and the share who do not want a job suggests that it is not obvious that the recent rebound has been a primarily cyclical story.

This isn't the first time a peek under the hood of jobs market data doesn't fully jibe with the Fed Chair's narrative on participation. There's also a dearth of evidence suggesting that "a substantial number of people are being attracted into the labor market," as Yellen said in September. Flows into the labor force have dropped off significantly — driven by a plateau in the number of people who get a job each month who hadn't been counted as looking for one, along with the continued downward trend in the number of people who enter the labor force to search for a job.

However, Goldman still believes in the thrust of Yellen's narrative, that an improving labor market can prompt some people on the sidelines to return to the work force — but doubts the scope for progress on this front is immense.

"We continue to see only limited room for a substantial further increase in the labor force participation rate," concludes Mericle. "As a result, we expect the unemployment rate to resume its earlier decline before long and reach 4.5 percent by the end of 2017."