WASHINGTON — Federal Reserve policy makers say that while the American job market shows signs of improving, they are still concerned with the “elevated” level of unemployment. One reason may be because employers can’t find qualified help, according to economists like Dean Maki.

The number of positions waiting to be filled this year has climbed to levels last seen in 2008, when the jobless rate was around 6 percent. The housing bust and ensuing financial crisis put people out of work whose skills may not correspond with those needed by the health-care providers and engineering firms where jobs go wanting.

“What’s going on here is a mismatch of the skills of the unemployed and at least some of the positions that are becoming available,” Maki, chief U.S. economist at Barclays Capital in New York, said in an interview. “This seems to be slowing the pace of filling those job openings.”

The issue has come to the forefront in Maine, particularly through meetings Gov. Paul LePage has held around the state with employers. Employers have consistently said they have open positions – looking for everything from skilled machinists to computer programers — that go unfilled, due to a lack of qualified applicants.

Nationwide, a dearth of skilled applicants may prevent the unemployment rate from declining further and could crimp consumer spending, which accounts for about 70 percent of the economy. Companies also may remain reluctant to expand their workforces as the threat from Europe’s debt crisis and political gridlock in the U.S. weighs on the economic outlook.

Over the three months ended in October, the average number of positions waiting to be filled climbed to 3.26 million, the most in three years, according to Labor Department data released Tuesday in Washington. The jobless rate, which averaged 5.8 percent that year, was at 9 percent in October. It fell to 8.6 percent last month, in part reflecting a drop in the size of the labor force, the agency’s data showed earlier this month.

Compared with the 13.9 million Americans who were unemployed in October, that means that that there were about 4 people vying for every opening, up from about 1.8 when the recession began in December 2007, the report showed.

During the years leading up to the 18-month U.S. recession, millions of Americans sought out jobs in industries that are now struggling, according to economist Julia Coronado.

“A lot of people went into real estate, construction and finance and acquired a lot of skills that are now not as useful to the current economy,” Coronado, chief economist for North America at BNP Paribas in New York, said in an interview. “You just have a skills mismatch in this economy.”

Sixteen percent of small-business owners said they had openings that were difficult to fill in November, up 2 percentage points from the prior month, according to results of a survey issued yesterday by the National Federation of Independent Business. While the share is usually between 20 percent and 30 percent during economic expansions, last month’s reading was the highest since September 2008.

“There’s no doubt that employers need more hiring flexibility, but at the same time they continue to struggle to find talent with mission-critical skills,” said Jonas Prising, president of the Americas for Milwaukee-based Manpower Inc., the world’s second-largest provider of temporary workers. “The lack of demand for products and services and the ongoing skills mismatch profoundly impact hiring decisions.”

Manpower’s 2011 Talent Shortage Survey, issued in May, showed 52 percent of companies polled said they found it more difficult to find qualified help. That was up from 14 percent in 2010 and the highest percentage in the survey’s six-year history.

In addition to the displacement caused by the recession, the relationship between job openings and unemployment may have shifted because of the extension of jobless benefits or the detrimental effects of long-term unemployment, according to Zach Pandl, a senior economist at Goldman Sachs in New York. The change means the equilibrium level of joblessness, or the rate equated with steady inflation, has probably climbed to 6 percent from 5 percent before the economic slump, Pandl wrote in a Dec. 8 research report.

“The economy has been expanding moderately, notwithstanding some apparent slowing in global growth,” the Federal Open Market Committee said in a statement at the conclusion of its meeting Tuesday in Washington. “While indicators point to some improvement in overall labor market conditions, the unemployment rate remains elevated.”

Concern over the economic outlook may also be affecting employment. The threat that the euro region may slide into recession, causing a global slowdown that would also limit U.S. growth, may be encouraging companies to hold back.

For example, the performance of the Chicago Board Options Exchange Volatility Index, also known as the VIX, which measures the cost of using options as insurance against declines in the S&P 500, also foreshadows payroll gains, Maki, a former Fed economist, said.

“When the VIX index is elevated, it means job growth is going to be more subdued,” he said. The gauge climbed as high as 48 in August and closed yesterday at 25.4. It averaged 16 in the five years leading up to the recession that started in December 2007.