Workers protest outside a McDonald's restaurant in Miami, Florida. The protesters are demanding action from state legislators and presidential candidates to raise the minimum wage to $15 an hour. Joe Raedle/Getty Images The fight for a higher minimum wage is picking up steam, gaining support from political candidates and affecting policy in cities across the country.

The idea goes that raising the floor on what people earn should help the poorest workers make ends meet.

It may not be that simple.

The Federal Reserve Bank of Cleveland published a Q&A with senior researcher Murat Tasci on the subject.

"Sum and substance: Raising the minimum wage won’t necessarily reduce poverty," they concluded.

An argument for raising the minimum wage has been that it has not kept up with income growth and the growth of the wage has not kept up with the dollar's purchasing power.

This isn't totally true, said Tasci.

"Since the US federal minimum wage is set nominally, over time it tends to decline in terms of its purchasing power. Changes since the 1980s coincide with a decline in the real hourly minimum wage to around $6 per/hour (normalized to 2015 levels)," he said. "This time around, though, in real terms the minimum wage doesn’t seem to be exceptionally low relative to its high levels in the late 1970s."

An argument against raising the wage floor is the potential loss of jobs since companies will want to pay less overall for workers.

While Tasci said that raising the minimum may have unintended consequences on employment, he reiterated that the effects so far have been small and may be different on a national scale.

"While the estimated effects are small, much of the evidence suggests that the negative effects on employment in response to raising the minimum wage fall disproportionately on lower-skilled workers," said Tasci.

"Many of the current proposals would be for larger changes, potentially making the employment effects estimates unreliable."

He said that any negative effects would fall mainly on small businesses, who have a limited ability to absorb cost shocks and low-skill workers, by quickening the pace of technological replacement.

In terms of the effects on the income of low-income families, Tasci said that a bump would have little impact.

"Really, many of the people likely to benefit from an increase are teenage members of wealthier households," he said.

"As a poverty-reduction tool, minimum wage is a very blunt one, and research suggests that its negative employment effects are amplified for exactly the groups needing targeted poverty measures."

Tasci also points out that only 3.9% of hourly workers were paid the minimum wage in 2014, against 15.1% in 1970. 21.4% of those earning the minimum wage are age 16-19, and

Tasci does not, however, go into the impact of a minimum wage increase on those making just over the floor, or on the earnings for the rest of hourly workers.

He does favor a more targeted approach for combating poverty, such as the Earned Income Tax Credit.

"But it might make more sense to devise a targeted poverty-reduction measure for the low-income households directly, such as with the Earned Income Tax Credit," he said. "As long as the parent’s total income meets certain thresholds, his or her tax burden will be substantially alleviated, effectively raising the household’s income."

So instead of using a ax, a federal minimum wage increase, he favors a scalpel approach.