NEW YORK, NY - JULY 22:  (Photo by Spencer Platt/Getty Images)

Democratic candidates in the presidential race are extolling the virtues of a higher minimum wage, and not just for workers at the bottom of the pay scale. Party front-runner Hillary Clinton included a higher (but unspecified) minimum wage in her package of economic proposals, all aimed at raising the “real incomes of everyday Americans.” Her rivals Bernie Sanders and Martin O’Malley have endorsed a $15-an-hour minimum nationwide, as part of broad strategies to lift workers from poverty and expand the middle class.

If you're a worker earning the minimum, it's easy to see how a higher minimum wage would boost your pay (provided your employer doesn't eliminate your job to save costs). But how might raising the wage push other, higher-paid workers toward the middle class? You would need what some researchers call a "ripple effect," where employers respond to a minimum-wage hike by raising wages for more experienced employees, too, in order to keep them ahead of their entry-level colleagues.

In theory, that "ripple effect" could be large enough to bump some workers from the high end of poverty and into the lower reaches of the middle class.

In recent years, though, there's not much evidence of that happening. An analysis by the economic research group EMSI shows no correlation between metro areas who raised their minimum wages between 2010 and 2014 and the cities that added the most "living-wage" jobs, which begin at the low end of what many economists consider middle class.

EMSI also found little correlation between the pace of job growth in an area and whether the area increased its minimum wage. This suggests that, in recent years at least, minimum-wage hikes haven't been the job killers that some economists fear.

“For cities with a minimum-wage increase, we found that the change in minimum wage could have an effect on percentage job growth — but definitely does not have an effect on the share of living wage jobs,” said EMSI spokesman Josh Wright. “This is likely because most occupations that pay at or above the living wage aren't affected by any changes to minimum wage laws."

In other words, raising the wage for fast food workers doesn’t make it more likely that plumbing companies — which already pay a little more — will boost their salaries, too.

Both those conclusions will be tested in the years to come, though, because a wave of cities have recently passed much more aggressive minimum-wage increases. The hikes of the last several years were relatively small, compared to, say, Los Angeles's move to a $15-an-hour minimum. Much larger increases at the bottom could lead to a stronger ripple effect that pushes more workers up into the middle class. They could also force more employers to cut jobs overall, to save costs.

Comparing cities in Florida and Minnesota illustrates how middle-class job growth and minimum wage increases haven't gone hand in hand over recent years. 

Between 2010 and 2014, Florida raised its minimum wage by 68 cents, to $7.93. In most of the state's metropolitan areas, including Orlando, Pensacola, Tallahassee and Sarasota, only between 18 and 25 percent of new jobs paid the local living wage for two adults and one child, which is to say a salary that would put the household in the lower middle class.

That’s partly because while Florida added jobs during the economic recovery, the growth came disproportionately in the hospitality industry, which tends to pay near the bottom of the wage scale.

“I don’t think there’s a magic wand in terms of getting people to a living wage,” says Sean Snaith, head of the Institute for Economic Competitiveness at the University of Central Florida. “I think the increase in the minimum wage in Florida has not triggered some larger scale rise in wages across the board.”

Compare that to Minneapolis-St. Paul, Minn., where the minimum wage stayed the same as the federal minimum from 2010-2014. (Minnesota has since decided to raise it). There, a full 60.9 percent of new jobs paid the living wage for the area. Part of that may have to do with the large number of healthy and growing company headquarters in the area, which generate relatively well-paid corporate office jobs.

That’s an extreme contrast, but the point is this: In recent years, whether or not an area creates more living wage jobs has more to do with its underlying economic makeup than where it sets its minimum wage.

Even the research that looks at the spillover effect of minimum wage in other periods finds that it only meaningfully impacts the bottom 10 to 25 percent of the workforce, with diminishing influence as you move up the pay scale. That’s because employers usually react to minimum wage hikes by giving a smaller raise to those making just above the minimum, and an even smaller raise to the people right above that, etc. — just enough to maintain a differential. That effectively compresses workers at the bottom end of the wage distribution, but it doesn’t move many people into what could be considered “middle class” pay.

“There’s a decreasing increase so that you can maintain equity across the different wage levels,” says Charles Fay, a compensation expert at Rutgers’ School of Management and Labor Relations.

People with more experience need to make more than people who just got hired, he says, to avoid upsetting employees — which appears to have been the consequence of Wal-Mart’s wage hike, for example.

Liberal activists are hoping, after successful campaigns to pass $15 an hour minimum wages in liberal cities like Seattle and San Francisco, that more dramatic hikes at the bottom will push more workers into the middle.

Of course, the magnitude of the impact could run both ways. While employers might boost everybody up the payscale to keep the wage ladder intact, it’s also possible that they’ll hold a larger number of employees to the new minimum wage in order to keep a handle on labor costs -- or just reduce employment overall.

“With larger minimum wage increases affecting more workers, we might expect employers to be more constrained,” says David Neumark, a professor at the University of California-Irvine whose research has poured the most water on the idea that the minimum wage will raise incomes without adverse employment effects. "Thinking that the minimum wage is a path to growing the middle class is, in my view, completely unfounded."

Nevertheless, Democratic candidates have big incentives to push for minimum wage hikes this campaign.  Doing so is as popular as any economic proposal they might offer, with at least 60 percent support across the board. As the evidence rolls in from the bold experiments currently underway, that support could shift in either direction — but probably not before voters elect the next president.