Unfortunately, it’s far from clear that these results tell us very much about immigration in the U.S. context. In the first place, even after the influx, foreign born folks make up a much smaller percentage of Denmark’s labor force—just 6.1 percent—than in the U.S., where the latest data from the Bureau of Labor statistics show that foreign born workers are 16.1 percent of the labor force.

It’s easy to see how this can make a difference. It may well be that in a population of mostly natives there will be plenty of natives forced to perform occupations below their capabilities. As economist Tyler Cowen has written, “In a society of Einsteins, Einsteins take out the garbage, scrub floors, and wash dishes.” In those cases, the arrival of low-skilled immigrants frees up natives to take jobs better attuned to their potential.

At some point, however, this runs aground the stubborn reality of human limitations. We’re not in Lake Wobegon, where every child is above average. Not every native low-skilled worker can be forced to move into more complex occupations. They will, instead, be forced into direct competition with the newly arrived workers. Wages will fall, unemployment will rise. The invisible hand will press their living standards downward instead of lifting them up.

(Read: Immigration reform and low-skilled workers)

It’s important to remember that Denmark is special. It is, according to the United Nations, the happiest place on earth. Its entire economic paradigm is very different from what we have in the United States.

“There, you have a place where you are taxed to the mean. A cultural norm reminds everybody that they are no better than everybody else, so you’re not going to choose your career path based on status. You’re in a place where a garbage man makes as much as a lawyer. So what you have are 4 million people who excel at things like furniture design and architecture,” writer Dan Buettner told NPR in an interview a few years ago.

It’s easy to see how a country where lawyers and garbagemen have similar incomes might have a lot of people in low-skilled jobs capable of doing much more. In a country like the United States, where income inequality is much more pronounced, it is far less likely that we have many workers in low-skilled occupations that are capable of taking on high-skill jobs.

(Read: Immigration reform may hurt U.S. workers)

Another reason for caution here is that the immigrants to Denmark came for very different reasons than most immigrants to the U.S. Denmark’s immigrants are refugees from war and its aftermath. Immigration to the U.S. is very different. The primary driver of immigration is the pursuit of economic opportunity. Which is to say, Denmark’s immigrants were often people who were forced out of their country while America’s tend to be people drawn into ours. The motivations for immigration very likely effect the types of people who immigrate, the types of jobs they pursue, their behavior after immigration, and the impact they have on native worker incomes.

In short, the lesson of Denmark’s immigration experiment may be just that immigration helps native workers—in Denmark. There’s very little to learn from it for the U.S.