Washington ? The American job market improved modestly in October, and economists looking deeper into the numbers found 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 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 a quick end 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.

The government uses a survey of mostly large companies and government agencies to determine how many jobs were added or lost each month. It uses a separate survey of households to determine the unemployment rate.

The household survey picked up a much bigger job gain — 277,000 in October, and an average of 335,000 per month for the last three months. The household survey picks up hiring by companies of all sizes, including small businesses.

The household survey is more volatile and less comprehensive than the other survey, and is not followed as closely by economists. Still, job growth in the household survey has not been this strong for three months since the end of 2006.

People counting themselves self-employed increased by 200,000 in October, accounting for most of the increase, but it is difficult for economists to explain the three-month trend.

Economists pointed out other bright spots in the unemployment report:

l 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.

l 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. The August figure was first reported as zero.

l The number of people considered long-term unemployed, meaning they have been looking for work for at least six months, fell by 366,000, to 5.9 million. That is the fewest since April.

“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 Economics, a data analysis company, told clients.

He said the prospects for the next few months “seem to be improving.”

The job gain was the smallest in four months. And because the population is always growing, it takes many more jobs — about 125,000 a month — to keep up with population growth, more to bring down the unemployment rate.

The job market turned consistently negative in February 2008. The nation lost jobs for 25 months in a row — almost 8.8 million in all. Since then, the economy has only recovered 2.3 million jobs. The adult nonmilitary population has grown 7.5 million.

The Federal Reserve earlier this week lowered its economic forecast for the rest of this year, and said unemployment is not expected to fall significantly through the end of next year. It should still be at 8 percent even through 2013, the Fed said.