(Reuters) - Behind the gradual and relatively small rise in the U.S. unemployment rate in recent years are a couple of less-closely followed labor market indicators that are flashing yellow for recession risk, according to research published on Monday by the Federal Reserve Bank of San Francisco. 

The analysis suggests a measure of hidden weakness in what has widely been seen as a solid labor market that is now coming under pressure from the Trump administration's massive tariffs, which have raised the twin risks of higher inflation and higher unemployment. 

In the lead-up to many past recessions, it has been typical for people who are out of work to take longer and longer to find a job, and to spend an increasing amount of time among the ranks of the unemployed, the authors of the regional Fed bank's latest Economic Letter found. 

"In the past, such patterns frequently occurred during the onset of recessions, suggesting that these developments could be signs of rising recession risk," the Letter's four co-authors wrote. 

The rise in the unemployment rate over the last couple of years has been slow, to 4.2% last month from a low of 3.5% in the second quarter of 2023. Many Fed policymakers have noted the relatively still-low unemployment rate as an indication of labor market strength.

But a measure of the share of the unemployed finding jobs each month has been declining since mid-2023, a trend that mirrors that which preceded many previous recessions, the authors of Monday's Letter show.

At the same time, since mid-2022, the median length of time spent unemployed has risen from about 8 weeks to more than 10 weeks. That compares to the peak of 10 weeks during the 2007-2009 financial crisis. 

"Although the size of the recent increase in unemployment remains relatively small compared with past onsets, the recent data trends warrant close monitoring for potential signs of rising recession risk," the Letter's authors wrote. 

(Reporting by Ann Saphir and Howard Schneider; Editing by Andrea Ricci)