WASHINGTON, July 2 (Reuters) - A weaker-than-expected jobs report could renew debate at the U.S. Federal Reserve about how to read the labor market at a time when the number of people available to work may also be in decline due to an aging population and tough immigration laws.

Despite firms reporting only 57,000 new jobs in June and downward revisions to strong job creation in April and May, the unemployment rate fell slightly to 4.2% from 4.3%, and the number of people reporting themselves as unemployed dropped by 213,000.

Yet the number of people reporting they had jobs also fell by around half a million, with the drop in the unemployment rate largely due to an exodus of people from the labor market altogether. The workforce fell in June by around 700,000, and since President Donald Trump returned to office has declined about 1.3 million. About 1.5 million fewer people were working in June than in January 2025 at the start of Trump's second term.

Such "bad" declines in the unemployment rate are tough for the central bank to diagnose, with the headline jobless rate indicating tighter job market conditions, but the decline in the labor force a discouraging sign for future growth.

"The unemployment rate's decline to 4.2% is a case of good news for the wrong reasons: it was driven by people leaving the labor force, not by more hiring. This points to a labor market that's stubbornly refusing to reaccelerate, despite recent optimism," said Daniel Zhao, chief economist of job site Glassdoor.

Even with high inflation a priority for the Fed, San Francisco Fed President Mary Daly said on Thursday before the release of the jobs data that there was "a scenario where the growth just doesn't continue to sustain itself...or...investment slows because people are worried they haven't seen the gains yet."

Uncertainty about which risks will need attention - too much inflation or weaker growth - is a reason to wait on any decision about interest rates, Daly said, despite financial markets betting the Fed will raise borrowing costs soon. That conviction slipped after the new jobs data were released on Thursday.

Concern about the state of the U.S. labor market had been easing in recent months after job growth rebounded in the spring and prompted some Fed officials who were preparing for rate cuts to agree rate increases may be necessary.

If history proves an accurate guide, June's weaker-than-expected first look could well be revised sharply lower in the reports for July and August. June is one of the most consistently volatile months for revisions, and last year, two months after reporting a hefty gain for June, the Bureau of Labor Statistics had shaved it by 160,000 to a net loss of jobs. April's and May's job creation estimates were already cut by a combined 74,000, and if the typical June revisions come into play in the next couple of months, the conversation about the job market could become more urgent.

Other developments in the job market may also move back to the fore of Fed discussion, posing the possibility that optimism about rising productivity may be tempered by a decline in the number of people willing to work or able to find a job.

Fed debate focused last year on the impact of new immigration rules, a discussion sidelined as job growth jumped and on the arrival of new Chairman Kevin Warsh, who has not focused on the issue so far.

Yet it could figure importantly into the U.S. growth outlook, and whether the pace of job creation month to month is considered adequate. Former Fed Chair Jerome Powell, now a Fed governor, said the job market was in a "curious kind of balance" if anemic job growth was enough to keep the jobless rate steady, and one that left Fed officials uncomfortable about the state of the economy.

It is not a phrase Warsh has adopted, but the trend raises important issues for him and policymakers in general about a U.S. economic future with potentially fewer but potentially more productive workers. The implications for overall economic growth depend on both the number of people working and their average output.

Warsh, who has been bullish in general about the implications of artificial intelligence for the U.S., noted in comments to a European economic panel on Wednesday that a recent jump in U.S. productivity was coming at a time when the average number of hours worked had flatlined, a further potential constraint on output.

Warsh remains overall optimistic on the net impact, even if the timing in particular remains uncertain.

"Potential growth looks like it's trended up," with productivity on the rise, Warsh said, but "labor market hours worked are relatively flat."

"Nothing is in the bank at this time of consequence, but if the last four quarters are an indication, which is really largely before the advent of the new surge in what artificial intelligence can do, there's reason to be optimistic. Does that optimism convey into policy in the next six or nine months? Still too soon to say."

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