WASHINGTON – The American job market improved modestly in October, and economists looking deeper into the numbers found real reasons for optimism – or at least what counts for optimism in this agonizingly slow economic recovery.

The nation added 80,000 jobs. That was fewer than the 100,000 that economists expected, but it was the 13th consecutive month of job gains. Fears of a new recession that loomed over the economy this summer have all but receded.

The unemployment rate nudged down, to 9 percent from 9.1 in September. “Those are pretty good signs,” said Michael Hanson, senior economist at Bank of America Merrill Lynch. “We’re hanging in there.”

No one looking at Friday’s report from the Labor Department saw an end anytime soon to the high unemployment that has plagued the nation for three years. The jobless rate has been 9 percent or higher for all but two months since June 2009.

Still, economists pointed out bright spots in the report:

• One government survey that tracks the job market by canvassing households found a gain of 277,000 jobs in October and an average of more than 300,000 jobs a month since August.

A separate survey of employers is used to determine the overall jobs number, but the household survey is the only one that includes farms and the self-employed. It also may be better at picking up improvements in small business.

• Average hourly wages rose 5 cents a week, to $23.19. More pay for workers means they have more spending power in the economy. Many businesses are waiting for customer demand to pick up before they hire in big numbers again.

• August and September turned out to be much better months for job creation than first thought. The nation added 104,000 jobs in August and 158,000 in September, a total of 102,000 more than earlier estimates.

“Overall, while this report is not good enough, several key numbers are now moving in the right direction,” Ian Shepherdson, an economist at High Frequency told clients.