The American job market shows signs of entering a new stage that will bolster households as employers fight to retain and attract workers by paying them more.

Wages for private-sector employees climbed 0.7 percent in the first quarter and were up 2.8 percent in the 12 months through March, the biggest gain in more than six years, the Labor Department reported Thursday.

The agency also said the number of claims for jobless benefits declined last week to the lowest level since 2000.

Six years after the recession ended, unemployment may now be low enough to start prompting companies to compete against each other for staff. Bigger paychecks, a missing piece of the expansion, would make it more likely that the slowdown in economic growth last quarter will be fleeting, bearing out Federal Reserve policy makers’ assessment.

“You can feel somewhat more constructive on consumer spending in the next quarter or so given that wages have picked up and given that claims are so low,” said Michelle Meyer, deputy head of U.S. economics at Bank of America Corp. in New York. “There’s still further ammunition for consumers to spend.”

The Labor Department’s total employment cost index, which includes wages and benefits, also climbed 0.7 percent in the first quarter from the prior three months.

It was up 2.6 percent from the same time in 2014, the biggest year-to-year advance since the end of 2008. In the first quarter of 2014, the 12-month gain was 1.8 percent, and the 0.8 point pickup since then marks the biggest acceleration since records began in 2001.

“This is mostly a story about a healthy pickup in wage pressure that almost certainly reflects the tightening in the labor market,” Omair Sharif, a rates sales strategist at Societe Generale Americas Securities LLC in New York, said in a research note.

Because the ECI tracks the same job over time, it removes shifts in the mix of workers across industries. That measure showed a 2.1 percent increase in March from a year earlier, close to the 2 percent average since the start of the expansion.

Increased employer costs would be a sign that businesses might be starting to feel the effects of a dwindling pool of workers, who are able to demand bigger paychecks.

The number of unfilled positions at U.S. employers climbed to 5.13 million in February, the most since January 2001, Labor Department data showed earlier this month.

There are about 1.7 unemployed Americans per opening, matching the lowest level since November 2007.

That’s one reason firings have abated. The number of first- time filings for unemployment insurance benefits fell by 34,000 to 262,000 in the week ended April 25, the lowest since April 15, 2000, the Labor Department also reported Thursday.

The figure was smaller than the lowest projection in a Bloomberg survey of economists.

“It gives you confidence that employers aren’t looking at their workforce and saying, ‘Gee, I’m stuck with too many workers for the kind of demand I’m facing,’ ” said Guy Berger, an economist at RBS Securities Inc. at Stamford, Connecticut. “It’s a good sign, no doubt about it.”

The unemployment rate held at 5.5 percent in March, its lowest since May 2008, the Labor Department reported earlier this month.

That puts it close to the 5 percent to 5.2 percent range that Fed policy makers have defined as full employment.

Another report Thursday showed consumer spending climbed in March, capping a lackluster first-quarter performance on a positive note. Purchases rose 0.4 percent, the biggest increase since November, after a 0.2 percent February gain that was larger than previously estimated, according to Commerce Department figures.

Focus is on spending

Economists are counting on household spending to do the heavy lifting in reviving growth after slumps in business investment and exports caused the economy to stagger at the start of 2015.

An improving job market and nascent acceleration in wage increases are among reasons such a rebound is probably in the works.

“What we went through over the first quarter was simply a soft patch related to the weather and port strikes,” said Tom Porcelli, chief U.S. economist at RBC Capital Markets LLC in New York.

“Ending the quarter on a pretty strong note like spending did is indicative of an economy that seems poised to rebound.”

The report represents the monthly breakdown of data published Wednesday that showed consumption climbed at a better- than-expected 1.9 percent in the first quarter. Still, that was less than half the pace of the prior three months, when spending rose at the fastest rate since 2006.

The U.S. economy barely grew from January to March, with gross domestic product rising at a 0.2 percent annual rate. GDP advanced 2.2 percent in the prior quarter, Commerce Department data show.

Wither the Fed?

The Fed, which is considering raising interest rates for the first time since 2006, said the slowdown during the winter months in part reflects “transitory factors,” according to a statement Wednesday following a two-day meeting.

“The Fed should find some solace in the fact that labor costs are advancing,” Neil Dutta, head of U.S. economics at Renaissance Macro Research LLC in New York, said in a research note. “Given the continued improvement in the labor market, we would expect wage pressures to continue building, pushing the labor share of income higher.”

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