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The vast U.S. services sector showed a solid rebound in May, the Institute for Supply Management said Wednesday, but the Labor Department reported that first-quarter productivity rose more than originally thought, a bad sign for the weak jobs market.

The institute said its index of non-manufacturing activity rose to 54.5 from 50.7 in April, a larger-than-expected increase that showed better times at businesses, ranging from mortgage banking to entertainment. Services make up about 80 percent of the economy.

The jump was the biggest since May 2002, and it is the 15th time in the last 17 months that the sector has grown. A reading above 50 signals expansion; one below 50 signals contraction.

“It’s a fairly benign report,” said William Cheney, chief economist at John Hancock Financial Services. “We are seeing growth but not enough to create jobs or inflation.”

Transportation, utilities, construction, banking and mining showed the highest rates of growth, the institute said.

New orders rose to 54.7 from 50.6 in April, the largest gain since February 2002. Order backlogs jumped to 51 from 46. The employment index edged up to 48.7 from 48.2.

“There are tentative signs that positive momentum is starting to build,” said Steven Wood, chief economist at Insight Economics LLC in Walnut Creek, Calif. “However, businesses remain very cautious about hiring and rebuilding inventories.”

In another sign that companies might not be in any rush to hire new workers, the Labor Department said productivity grew at a 1.9 percent rate in the first quarter, higher than the 1.6 percent previously reported. The revised rate was the highest since the third quarter of 2002, when productivity jumped at a rate of 5.5 percent.

RBS Greenwich Capital chief economist Jade Zelnik said the determination of companies to shore up profit margins has contributed to the jobless recovery.

“Much stronger economic growth will be needed to support both healthy productivity gains and job creation,” she said.

Although economists like to see productivity go up, they would prefer that gains not come at the expense of jobs.

“Right now, it is a headache for the recovery, because companies don’t need more workers,” said Clifford Waldman, economist at Manufacturers Alliance/MAPI, a research group.

The gain in productivity also was costly for employees. Their hours worked dipped 0.1 percent in the first quarter, compared with an increase of 0.9 percent in the fourth quarter.