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It’s been slightly more than half a year since Mayor Vince Gray signed a bill to raise D.C.’s minimum wage, and more than a month since it took effect, bringing the lowest allowable hourly wage to $9.50 before it gradually rises to $11.50 in July 2016 and then changes with inflation. But the effect the legislation is having and will have remains unclear. Certainly, July 1 didn’t bring a spike in unemployment or new fortunes to the District’s working masses. But what will happen when the full wage hike is in place?

According to a report out today from the Urban Institute, the impact may be smaller than some residents anticipate.

Back when Gray signed the bill, the D.C. Fiscal Policy Institute’s Elissa Silverman, who advocated for a higher minimum wage and is now running for a D.C. Council seat, gave me a back-of-the-envelope calculation indicating that slightly more than 40,000 D.C. residents are likely to get a bump in wages due to the law by July 2016. That’s not an insignificant number; it represents about 12 percent of working Washingtonians.

The Urban Institute arrives at a nearly identical figure, finding that 41,000 people living and working in the District will be affected by the $11.50 minimum wage. But the study concludes that for many of those people, the financial impact will be minimal. Taking into account the increased taxes these people will pay and the decrease in government benefits they’ll receive, the median worker affected by the wage hike will gain only about $1,000 annually.

The reason, says the report’s lead author, Gregory Acs, is that the competitive employment market, driven in part by the high cost of living in the District, has already raised many D.C. wages above the minimum—-if not quite beyond $11.50, then close enough that the new law doesn’t make a huge difference.

“The District is basically a high-wage urban area,” he says. “If you look at the experience of other high-wage urban areas that raised their minimum wage, like San Francisco, you see that the range in which the wage increased ended up not having profound effects, largely because by the time you get around to raising the minimum wage, the market has already gotten around to raising the wage.”

The industry where most workers will be affected is food services, the study finds, constituting 16 percent of affected workers. Health and social services (14 percent) and retail (11 percent) follow.

While the majority of affected workers are black and nearly a quarter are Hispanic, the study emphasizes that the affected workers don’t conform to stereotypes that people might hold. Only 11 percent of beneficiaries are single parents (the overwhelming majority have no children); 28 percent receive food stamps, or SNAP; and just 13 percent live in public and subsidized housing. Nineteen percent fall below the poverty line. Just over half are women.

The effect that the wage hike will have on workers varies substantially by their family situation. A single, childless resident working 40 hours a week, making the minimum $8.25 an hour prior to the July increase, and receiving SNAP and the Earned Income Tax Credit would experience a 25 percent increase in income—-from $15,736 to $19,694—-after accounting for increased taxes and decreased benefits. By contrast, a single parent of two working under the same conditions would gain only 4 percent in income, although starting and ending at a much higher level ($30,240 and $31,568, respectively) due to higher SNAP payments and tax credits for workers with children.

The study also tested three scenarios: one in which the wage hike has no effect on unemployment; one in which each 10 percent increase in hourly wages brings a 1 percent decrease in the average worker’s employment; and one in which the decreased employment affects just workers under 25. The scenarios produced small differences in average income changes. “There’s probably a disemployment effect, and it’s probably small,” says Acs, basing his conclusion off ample research by others. He says the study’s assumptions under the disemployment scenarios fall about in the middle of the possible range, but that “even if you double our effect, you still get less than 1,000 folks displaced.”

For 13 percent of families with a worker who’d otherwise be making under $11.50 in 2016, the effect of the wage hike is big, producing more than $2,500 in additional income. But for most D.C. families affected by the new law, while the higher wage is certainly welcome, it might not be the game-changer it was sometimes portrayed as during the heated political battle leading up to the bill’s signing.

Chart from the report