(Reuters) - The latest U.S. payrolls report did little to settle the debate about where the job market is headed, with ample fodder for both "soft-landing" believers and doubters over whether the Federal Reserve can tame inflation without sending millions of workers onto the jobless rolls.

True, the "blowout" gain of 272,000 jobs in May exceeded every single estimate among 77 economists polled by Reuters ahead of the release of the report on Friday, and the breadth of hiring was the widest in 16 months.

But also true is that the increase in the unemployment rate to 4% snapped a run of more than two full years below that benchmark. Moreover, that rise happened for the "wrong" reasons: People left the workforce on balance, while more reported as unemployed and far fewer as having a job.

Here are some of the numbers that have economists jawboning.

BREADTH

The employment gain last month was almost exactly in line with the 12-month trailing average of nearly 276,000 jobs and exceeded the average of 188,000 over the 10 years prior to the COVID-19 pandemic by 84,000.

On top of that, hiring was broad. In fact, it was the most widespread among all 250 industries tracked by the Bureau of Labor Statistics since January 2023. For the 72 manufacturing industries tracked by the BLS diffusion index, hiring was the broadest since October 2022, signaling perhaps a turnaround for a sector where employment growth has lagged for roughly a year and a half.

ALL BACK

All the major industry groups are now back above their pre-pandemic employment levels, with a revision to the numbers in April lifting the lone laggard - leisure and hospitality - back above its high-water mark from before the onset of the health crisis in early 2020. That group also suffered the largest losses during the pandemic.

THE 4% CLUB PARTIES ON

The unemployment rate rose to the highest level since January 2022, snapping a streak of 27 straight months below 4%, the longest sub-4% run since the 1960s and a bragging point for Democratic President Joe Biden's administration.

But 4% is still a historically low level of joblessness and just six of the 14 presidents in the post-World War Two era have governed during such a stretch, including the two most recent, Biden and his predecessor, Republican Donald Trump. It's a figure to watch as the two rivals face off again in the Nov. 5 presidential election.

PRIME TIME

While the overall number of people in the workforce shrank by 250,000 in May and the labor force participation rate fell, a key demographic held its ground: prime-aged workers between 25 and 54 years old. The participation rate for this group - the largest slice of the U.S. workforce - rose to a record 83.6%.

Women have led the charge. Not only is the prime-aged female participation rate of 78.1% a record high, it's just 11.1 percentage points below the rate for prime-aged males - the smallest gap ever. The rate for men edged up but, at 89.2%, is below where it was before the pandemic and is well below the over-90% range that prevailed prior to the 2007-2009 financial crisis.

NEWCOMERS

The immigration wave is still leaving its imprint on the U.S. job market, as foreign-born workers continue to account for the largest share of job gains and workforce growth. That could change in the months ahead, however, with the Biden administration clamping down on crossings at the southern border.

FALTERING FLOWS

Beneath the data on changes in the overall level of the workforce are figures on the flows driving those changes. Every month the workforce status of millions of people changes among the three broad categories: Employed (with a job); unemployed (no job but actively seeking one); and not-in-labor-force (no job and not looking for one).

For example, did a person graduate from high school or college and land a job (not-in-labor-force to employed), get fired from a job and start looking for a new one (employed to unemployed), start a job search after months or years on the sidelines (not-in-labor-force to unemployed), land a job after a period of actively seeking a job (unemployed to employed), or retire from a job or quit to take care of a child or relative (employed to not-in-labor-force)?

Through much of the last two years, more people on balance have flowed into the workforce, either as job recipients or job seekers, than have flowed out of it. That has begun to change, and over the last six months more people on average have flowed out of the workforce altogether than have flowed in. And the share of those quickly landing a job as new members of the labor force is declining.

TALE OF TWO SURVEYS

While the establishment survey of the latest employment report showed payroll job gains of 272,000, the household survey side showed employment dropped precipitously, by more than 400,000. The two frequently do not agree on size or even direction of monthly changes, but over time do track each other.

The household measure of employment has been flat for roughly a year - with declines seen in five of the last eight months - while the establishment survey has shown more than a quarter of a million new jobs a month on average. Economists say that at some point one or the other must give. Which will it be?