Two years into his new career writing code for phone apps, Leo Landau works for companies as far away as Australia while never leaving his apartment in Eugene, Ore. By year's end he expects to earn $10,000 more than inspecting buildings for asbestos, a job he lost in 2008.

Digital freelancers such as Landau represent a growing portion of American workers. An Accenture study included estimates of 20 percent of the US work force while the Freelancers Union, a New York-based advocacy group, puts the number at 42 million.

Some of these independents are attracted to the flexible lifestyle, others because they can't get a job locally that matches their skills. They are replacing traditional work — being employed by a company — with a mix of projects completed over the Internet.

The recession that ended in June 2009 helped boost freelancing as a way for the newly unemployed to support themselves, and the practice has gained traction since. Internet exchanges allow companies to reduce labor costs by enlisting freelancers, who give up a reliable salary for discretion over how they work.

"All major recessions change the lens on how we approach work," said Andrew Liakopoulos, a principal in Chicago at Deloitte Consulting and co-author of a report this year called "The Open Talent Economy." People "don't necessarily have to be fully employed, with a number and a badge." Behind this shift, Liakopoulos said, is the technological ability for companies to divide their needs into projects and farm them out to a talent pool regardless of geography. As companies move toward accessing labor, rather than acquiring it, they'll be able to respond more nimbly to macroeconomic shocks, he said.

The freelancers often are highly skilled and choose that style of work because it offers them flexibility and variety, Liakopoulos said.

"People used to have a stable 40-hour workweek," said Sara Horowitz, who founded the Freelancers Union. "What we're seeing now is an economy where people are going from job to job, putting together a series of gigs and calling that a career."

These workers may be excluded from official employment statistics as the measures haven't adapted to cover new, more fluid arrangements, she said. "I think the unemployment numbers are wrong," Horowitz said. "They're just not reflecting the reality of how many Americans are working."

The jobless rate was 7.3 percent in August, the lowest since December 2008, and labor-force participation was the lowest in 35 years, down to 63.2 percent.

Census Bureau workers ask in monthly surveys if people worked "for pay or profit" in the previous week. Freelancers might answer no if they were between gigs or weren't paid during the survey period. They would be counted as having left the workforce if they respond that they're not looking for a conventional job. Steven Hipple, an economist with the Bureau of Labor Statistics, said the agency stopped tracking contingent workers in 2005 because of funding constraints.

"They're supposed to be classified as self-employed, but it's possible that some of these people could be missed," Hipple said in a Sept. 30 interview, the day before the government's partial shutdown began. "It's unfortunate that we don't have more recent estimates."

Private studies have tried to quantify how many Americans are turning to freelancing for a career. An estimated 20 percent to 33 percent of the US work force consists of independent workers, according to a 2013 study by Accenture, the world's second-largest technology-consulting company.

• ASSOCIATED PRESS