What Denmark doesn't tell us about low-skill immigration

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In the middle of the nineties, the brutal wars in what had been known for decades as Yugoslavia produced hundreds of thousands of refugees—and triggered a natural economic experiment in Denmark.

A decade earlier, Denmark had put in place laws that created a generous refugee program. But until the outbreak of the Yugoslav wars, Denmark remained almost exclusively the land of Danes. The foreign-born population was miniscule—somewhere around one or two percent of the population.

That started to change in 1995, when a large number of refugees from the Yugoslav wars entered the country. They were followed by Somali refugees. Then, after 9/11, by refugees from Afghanistan and Iraq. Even after the initial waves of refugees were settled, immigration from those countries was maintained at high levels because of family reunification policies.

A simple supply-and-demand model would suggest that an influx of low-skilled labor would depress the wages of natives, particularly those in low-skilled occupations. The beneficiaries of higher immigration, it's often argued, are elites who benefit from a larger, cheaper labor pool. Curiously, that doesn't seem to be what happened in Denmark.

A new working paper studying the effect of this wave of immigration finds that the newcomers did not depress native wages. In fact, the influx did not increase unemployment and led to higher wages among the less-educated natives. Higher-educated natives also saw an increase in wages but that effect was only temporary. Only low-skilled workers in the public sector suffered a fall in wages due to immigration.

So what happened to the law and supply and demand? The authors of the study, Mette Foged of the University of Copenhagen and Giovanni Peri of U.C. Davis, write that native workers were pushed into more complex—and higher paying—occupations by the competition from the new immigrants.

"Hourly wages of less educated natives were on average positively affected by immigration, the effect increases as the low skilled gradually move towards more complex occupations and a fraction receive formal training to increase their complementarity with the manual jobs performed by non-EU immigrants," Foged and Peri write.

Naturally, this is being greeted as great news by supporters of more open immigration in the United States. If immigration improves the lot of native workers—especially low skilled natives—it would seem to be a win-win scenario.

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.

—By CNBC's John Carney. Follow me on Twitter @Carney