Dalia Catalán’s daughter is 13 years old, but Catalán hasn’t seen her since leaving their home in Guatemala four years ago, when she and her husband came to Washington seeking work.

Catalán, her husband and a two-year-old son, Carlos, live in a cramped basement apartment in Fort Totten. In a dimly lit bedroom, she pulls a picture of Dalia Belen off the dresser. In it the girl, then eight, smiles confidently.

Catalán, 30, has tucked away money bit by bit to build to the $7,000 she estimates it will cost to bring her daughter to join the family in the United States.

She’s got about half of that saved, and with the $1 jump in the D.C. minimum wage that kicked in July 1 — to $10.50 an hour — the pile is growing $40 a week faster. At this faster rate, the teen could arrive in time to complete a high school education — which Catalán believes will set her daughter on a better path.

"I want her to study, and I want him to study. That’s my goal,” said Catalán in Spanish, through a translator, while wrangling Carlos. "As a mother, it’s everything for your kids. We don’t want our kids to go through what we went through.”

A ballot initiative slated for next year’s election could help Catalán even more, if D.C. voters agree to raise the minimum wage to $15 an hour.

The minimum raise is already on the rise in the District, where the floor went from $8.25 an hour in 2014 to $10.50 this year. It’s set to rise to $11.50 in 2016. Each $1 an hour climb adds $160 a month. While the small bumps of years past haven’t immediately transformed lives, earning three dollars more an hour could help someone afford rent in a neighborhood with better schools, or save for a car that could provide access to a better job.

That is, of course, if people can hold on to their minimum-wage jobs.

To date, there isn’t much evidence that the modest wage increases that have taken effect in recent decades have significantly reduced business’ willingness to hire. A wave of research in recent years has been fairly convincing in this regard — most notably a 2010 study led by Arindrajit Dube of the University of Massachusetts that analyzed the employment response to wage differences across adjacent counties.

But there’s little precedent for doubling the federal minimum wage — big wage hikes in cities like Seattle haven’t been in place long enough to deliver solid data — and no one’s quite sure how the economy will adjust. Some economists, like David Neumark of the University of California-Irvine, believe that they will kill jobs for wage earners, and that there are more productive ways to boost the incomes of America’s poorest.

There’s more agreement, however, on the question of how the substantial minimum wage increases that have passed lately will affect workers who do receive them and are able to work full-time.

“It’s making a big change,” said Alan Akers, a job counselor with the nonprofit Jubilee Jobs, where he works with people just trying to crack into the job market. “I don’t think anybody in D.C. can have a good quality of life at $18,000 a year. You can’t pay rent in D.C. with that amount of money.” Fifteen dollars an hour comes out to a little over $30,000 a year, which he thinks is basically livable.

And it’s not just the nation’s capital. After decades of incremental increases, cities, states and counties are raising their wage floors by leaps and bounds. San Francisco, Seattle and Los Angeles have decided to go all the way to $15 an hour. New York State is moving to get to $15 in stages for fast-food workers, and more initiatives are being teed up across the country.

While it’s easy to imagine what workers might do with an extra few thousand dollars in their pockets, it’s a lot harder to forecast how employers might respond. In D.C., most already pay more the minimum, for all but the most junior employees. Luc Brami, a principal of Gelberg Signs, said the company typically pays minimum wage only when it wants to give at-risk young people a chance.

“It limits our ability to take on the really hard to hire,” Brami said, adding that the company has not had to cut back yet. And though he’s not a fan of the $15 proposal, if phased in over five years — as is being done in other cities — he figures it wouldn’t have much of an impact. “I wouldn’t love it, because it’s meddling,” Brami said. “But I would think that our wages would get there eventually anyway.”

An economic analysis by the Urban Institute last summer projected that raising the minimum wage in Washington to $11.50 by 2016 would have a minimal negative impact on employment, and raise wages for 41,000 people, one in five of whom fall under the federal poverty line.

However, the study also said the increase could prompt employers to cut hours, or move recipients to an earnings bracket so high they are no longer eligible for subsidies like housing vouchers or the District’s Temporary Aid to Needy Families program — resulting in an actual net loss of income.

Indeed the D.C. Chamber of Commerce said it recently surveyed city employees and found most would be reluctant to add workers if the minimum wage were to increase to $15 an hour. More than half said they would have to reduce working hours.

It’s too early for official data on the outcomes of the wage increases; the D.C. government says it hasn’t begun to study the effects on residents’ welfare. But Samantha Davis, a senior advocacy specialist with the homeless services nonprofit So Others Might Eat, says it appears employers may not be bluffing.

"The biggest thing we’re finding out is that employers are cutting hours,” Davis said. “So it’s very hard at this point to see any positive change, because employers are reacting this way.”

Other trade-offs may be more subtle. Ari Schwartz, an organizer with the advocacy group D.C. Jobs With Justice, said he’s noticed employers raising people to the new minimum wage instead of giving scheduled pay increases that they planned to give anyway.

Even without the increases, hourly work can be fickle. Catalán found this out when she asked for a schedule change as a contracted cleaner at Target in Columbia Heights — she wanted to work days instead of the graveyard shift. The cleaning company gave her a daytime shift, but only four hours, and at a faraway location. Catalan tried that for a few weeks, but with the Metro fares and time spent getting there, it cost more than it was worth.

For a brief period, her husband also had reduced hours at his plumbing job, which put the family under a lot of strain. Earlier this year, Catalán found a job with another company that cleans the Fairmont Hotel, in Georgetown. Her schedule is somewhat unpredictable — she learns a few days ahead of time whether she’ll be working from 6:30 a.m. to 3:00 p.m. or 2:30 p.m. to 11:00 p.m. — but at least it’s full time. And it’s certainly better than the clothing factory where she worked in Guatemala.

“For now, things are okay, but I wouldn’t call it comfortable,” said Catalán, back in her bedroom where a large American flag hangs on the wall.

Between them, she and her husband earn about $1,700 a month. About $600 pays rent for the tiny apartment that they share with another couple, and $400 goes to a babysitter who cares for Carlos while his parents are at work. They send $150 a month home to Catalán's parents. That leaves only a few hundred left over for food, clothes — and saving to bring their daughter to join them.

That’s why a raise to $15 — almost to the living wage for a working family like theirs — would mean so much. “It would make a really big difference for us,” Catalán says.