As a campaign to raise the minimum wage as high as $15 has achieved victories in such places as Seattle, Los Angeles and New York, it has bumped up against a harsh reality: Plenty of scofflaw businesses don't pay the legal minimum now and probably won't pay the new, higher wages either.

Some economists, labor activists and regulators predict that without stronger enforcement, the number of workers getting cheated out of a legal wage is bound to increase in places where wages rise.

Estimates on the size of the problem vary, but the Bureau of Labor Statistics said that in 2014, roughly 1.7 million U.S. workers — two thirds of whom were women — were illegally paid less than the federal minimum of $7.25 per hour.

Other studies put the number higher. A report by the Department of Labor in December estimated that in New York and California alone, there are 560,000 violations of the law every week, representing $33 million in lost income.

Those figures represent workers like Celina Alvarez, who came to the U.S. from Michoacan, Mexico, four years ago and took a series of poorly paying jobs as a cook after settling in New York City.

At the first two restaurants, Alvarez worked 12 hours per day, six days a week for a flat weekly wage of $350. That comes out to about $4.86 per hour. There were no tips and no overtime pay. Some weeks, Alvarez said, she and other women in the restaurant didn't get paid at all. Managers didn't care if they quit. They'd just hire someone else.

"We were dispensable to them," she said.

The U.S. Labor Department investigates those types of violations and is already doing a brisk business in enforcement cases. During the last federal fiscal year, it said it recovered $270 million in back wages for 270,000 workers.

But the agency's roughly 1,000 investigators, who police 7.3 million businesses employing 135 million workers, don't enforce state and local wage laws, for the most part. That means that cities and states that hike their minimum wage above the federal rate of $7.25 are on their own.

That's causing some concern that, without a robust enforcement mechanism, many workers could wind up being left behind.

"A lot of states are facing that challenge now," said David Weil, administrator of the U.S. Labor Department's Wage and Hour Division. "It is very important to pass those minimum wage increases ... Then, how do we make sure workers really receive them?"

Twenty nine states now have a minimum wage higher than the federal rate, but anti-poverty activists have been campaigning hard for municipal lawmakers to bypass both Congress and their state legislatures and set wages much higher.

Seattle, Los Angeles, and San Francisco and its Bay Area brethren, Oakland and Berkeley, have all begun phasing in a minimum wage that will hit $15 per hour within the next few years. Labor groups in California are trying to get a measure on the ballot increasing the rate to $15 statewide.

A regulatory board in New York took the unorthodox step last month of hiking the minimum to $15 for fast food workers.

Other, less expensive cities have been shooting slightly lower. Chicago and Kansas City, Missouri, are both raising the rate to $13. Albuquerque, New Mexico, and, Portland, Maine, are both raising rates to just under $11. Most of these raises are being phased in gradually over several years.

Those measures have been strenuously opposed by many corporations and entrepreneurs, who say that many businesses with thin profit margins will be forced out of business or fire workers to stay afloat.

Tia Koonse, a researcher at the UCLA Labor Center, said there is no question that some employers doing things legally now might be tempted to start breaking rules.

"If there is not a credible threat of a compliance check, then what happens?" she said.

Some municipalities that have raised wages have talked about following the example of San Francisco, which created its own labor standards enforcement division.

The head of that unit, Donna Levitt, said the number of complaints about wage violations did not go up when the minimum wage stepped up to $12.25 in May. But she said that doesn't necessarily reflect what is really happening.

"There are a lot of reasons that people are fearful of coming forward and asserting their rights, even if they know the minimum wage has increased," Levitt said.

Celina Alvarez, 51, said that when she first came to New York, she knew that she was being paid less than the legal minimum, but felt she had no option but to take whatever work was offered. She's uneducated and doesn't speak English, and a job paying the New York state hourly minimum of $8.75 seemed impossible to find.

"Nobody pays that salary," she said. Most workers like her, she added, are unlikely to complain. "They are scared of losing their jobs."

Manuel Santiago, a Mexican laborer in New York City, said when he had a wage dispute a few years ago at a deli that was paying him $300 per week, for 78 hours of work, the boss threatened to call immigration officials and have him deported.

Instead, Santiago filed a labor law complaint and eventually recovered all the money he was owed, plus penalties.

Cheated workers also have the option of filing a civil lawsuit. Michael Faillace, an attorney who helps underpaid workers file lawsuits to recover back wages, said there were more than enough potential clients to go around.

"Pick any street in Brooklyn and any street in Queens. Go into any restaurant. And there are no documented workers. None of the delivery guys are documented. Probably none of the kitchen staff are documented. And they are all getting less than minimum wage."

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Associated Press writer Claudia Torrens contributed to this report.