Despite what the group's name suggests, the "Fed Up" campaign doesn't want to get rid of the Federal Reserve. Or even weaken it.

Instead, according to group leaders who organized protests outside the central bank's annual conference in Jackson Hole, Wyo., this year and last, Fed Up wants a stronger central bank.

The initiative, started by Center for Popular Democracy, says that could be achieved by including elected members, having governmentreview and oversight and eliminating commercial bank ownership of the Fed's 12 regional branches.

"These reforms would ensure that the Fed is a publicly accountable institution that takes a wide array of economic perspectives into account," Fed Up argued in a white paper produced in tandem with the Economic Policy Institute and released Aug. 22.

Protesters at the Jackson Hole conference last week made similar arguments in person when they were granted a meeting with Federal Reserve officials, using the opportunity to urge the central bank not to increase interest rates before employment growth has both broadened and deepened.

"To suggest that we are near full employment overlooks a lot of the labor market slack that persists," Fed Up campaign manager Jordan Haedtler said in a phone interview.

He cited lower-than-expected wage growth as well as high numbers of part-time workers who want full-time jobs and discouraged laborers who have left the workforce altogether.

While the most commonly cited unemployment measure, which includes adults who have sought jobs in the past four weeks, has fallen to 4.9% from a peak of 10% in the wake of the last recession, broader gauges are higher. The rate including discouraged workers and jobholders wanting to move into full-time posts was 9.7% in July, down from a peak of 17.1%.

"The Fed really should test the bounds of full employment and see how low unemployment can get, how much we can reduce these racial disparities and how much we can improve wage growth before raising interest rates," Haedtler said. "The inflation threat that they are constantly concerned of just doesn't seem to be anywhere in sight."

While Fed Chair Janet Yellen didn't signal a change in monetary policy in her speech at Jackson Hole on Friday, she noted employment growth has made an interest-rate hike more feasible. That would be another step toward normalizing short-term rates that the central bank has held below 1% since 2008.

A 25 basis-point hike last December moved the range from a low end of zero for the first time in seven years and the Fed signaled as many as four hikes this year before backing away from that target amid global market volatility. Regular rate hikes are important for banks such as JPMorgan Chase (JPM) - Get Report, Wells Fargo (WFC) - Get Report and Bank of America (BAC) - Get Report , which typically boost revenue by passing on increases more quickly to borrowers than to depositors.

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"In light of the continued solid performance of the labor market and our outlook for economic activity and inflation, I believe the case for an increase in the federal funds rate has strengthened in recent months," Yellen said. 

Fed Up, however, argues that high underemployment shows the case is still not strong enough.

Indeed, the number of part-time workers seeking full-time positions is "higher than what we would expect in a normal economy," Ryan Sweet, Moody's Analytics director of real-time economics, said in a phone interview.

It may not return to pre-recession levels, however, because of changes in labor-market structure such as the Affordable Care Act. Employers with less than 50 full-time employees don't have to comply with the federal law, designed to expand the availability of health-care coverage, so many have increased part-time payrolls to avoid just that.

There are other weaknesses in the labor market as well, Sweet added. Under typical circumstances, wage growth should be between 3% to 3.5%, but current growth in the U.S. from year to year is about 2.6%, according to his analysis.

The labor force participation rate of 62.8%, meanwhile, is the lowest since the late 1970s, though Sweet noted that that reflects an aging population as well as people with disabilities or in school.

Despite its challenges, the "U.S. labor market is enjoying the longest string of monthly job gains in the nation's history," adding 15 million jobs over the past six years, he said.

The Fed doesn't necessarily need to wait for 2% inflation -- which along with maximum employment is a key element in the bank's interest-rate calculus -- before acting, he said.

"Monetary policy at the Fed needs to be forward looking," Sweet said. "The bottom line is we're getting close to full employment. We're not there yet, but if the job market continues to improve at the pace we've seen over the last couple of years, we'll be there very soon."

While opinions on the timing of the rate hikes vary, the need for broader reforms at the central bank doesn't, the Fed Up campaign says.

Currently, 10 of the 12 regional Federal Reserve presidents are white males and nearly 83% of the banks' directors are white, according to the paper released before the Jackson Hole conference. Less than 5% of the Fed directors "represent organizations governed by community members and employees," Haedtler and others wrote in the document

"When you have disproportionately white men from corporate and financial backgrounds in the room advising these policymakers on what labor market conditions are, that skews the perspective," and "not just away from how low-wage workers or people of color are experiencing the economic recovery," Haedtler said.

"When people say that the Fed has a bias towards its inflation mandate, I think part of the reason that that's the case is that you have multimillionaires, primarily CEOs of major corporations and commercial bankers, occupying the vast majority of those 108 regional bank board-of-director seats," Haedtler said.

Those directors choose the regional bank presidents, who make up a significant bloc of the central bank's monetary policy committee.

That panel, which sets the benchmark short-term rate, includes five regional bank presidents as well as all seven members of the bank's board of governors.

Fed Up proposes to make its representation more democratic by eliminating commercial bank ownership of the regional branches, then having directors nominated instead by elected officials while the bank's board of governors makes the ultimate selection. The more diverse regional board would then retain the power to hire its president.

Simultaneously, instead of terms for policymakers that vary from 14 years for Fed governors to renewable four-year stints for the Fed chair, the group proposes staggered non-renewable seven-year terms for all.

"Our proposal just happens to preserve the original bank structure and also strengthen it by requiring that a broader array of local organizations, nonprofits, academic institutions, and regional elected officials are included in this election process," Haedtler said.