Danophilia is alive and well in America. Bernie Sanders and other liberals have lauded Denmark’s social democratic dream state, with its free college tuition, nearly universal pre-K, and plentiful child care. While Republicans and Democrats both praise the virtues of what economists call “intergenerational mobility”—the chance for a poor young child to become at least a middle-class adult—America doesn’t lead the world in the pursuit of the American Dream. The standard social mobility statistic measures how much each generation's income is determined by its parents' income. By that measure, northern Europe and Scandinavia have the highest social mobility in the advanced world, and Denmark tops the list.

But this Danish Dream is a “Scandinavian Fantasy,” according to a new paper by Rasmus Landersø at the Rockwool Foundation Research Unit in Copenhagen and James J. Heckman at the University of Chicago. Low-income Danish kids are not much more likely to earn a middle-class wage than their American counterparts. What’s more, the children of non-college graduates in Denmark are about as unlikely to attend college as their American counterparts.

If that’s true, how does Denmark rank number-one among all rich countries in social mobility? It’s all about what happens after wages: The country’s high taxes on the rich and income transfers to the poor “compress” economic inequality within each generation: When the rungs on the economic ladder are closer together, it’s easier to move a little bit up (or down) over the course of a generation.

“The Scandinavian Fantasy” is a rich, complex paper that is already making waves in the newly popular subject of intergenerational mobility. It makes three major points.

The first big idea is that Denmark is not a nation of Horatio Algersens. Its high social mobility is not the result of an economy that is uniquely good at helping poor children earn middle-class salaries. Instead, it is a country much like the U.S., where the children of poor parents who don’t go to college are also unlikely to attend college or earn a high wage. Social mobility in Denmark and the U.S. seem to be remarkably similar when looking exclusively at wages—that is, before including taxes and transfers.

It is only after accounting for Denmark’s high taxes on the rich and large transfers to the poor that its social mobility looks so much better than the U.S.’s. America’s (relatively conservative) economic philosophy is that, with low taxes and little regulation, the market is an open savannah where the most talent will win out. But Denmark’s economic philosophy seems to be that the market is an unfortunate socioeconomic lottery system, and so the country compensates the poor with generous transfers paid by high taxes on the rich.

The second big idea in the paper is that Denmark’s large investment in public education pays off in higher cognitive skills among low-income children, but not in higher-education mobility—i.e., the odds that a child of a non-college grad will go on to finish college.

Overall, Denmark spends much more than the U.S. on all levels of education. In particular, a much higher share of its poor young children is enrolled in daycare and preschool than the United States. This large public investment in kids seems to increase cognitive skills among poor Danish children compared to their American peers. In international math and reading scores, for example, the poorest quartile in Denmark far outperforms their counterparts in the U.S.

But despite this far greater investment in young children and public colleges, Danish children of high-school graduates are still extremely unlikely to go onto college. Put slightly differently, a tiny share of Denmark’s college graduate population comes from homes where neither parent finished high school. The children of college-grads almost always go to college; the children of non-grads often don’t—even in Denmark.

The third big idea is that Denmark’s welfare policies might reduce its citizens’ incentives to go to college. In the early 1990s, when Denmark raised the minimum age of eligibility for social assistance, college enrollment among Danish twentysomethings fell below its trajectory. Based on this finding, the researchers conclude that welfare policies may reduce college enrollment. Denmark makes it more comfortable to be poor and less lucrative to be rich, so many young people decide to end their education after high school.

This final idea may be the most controversial. After all, it’s not clear how to frame this finding. Democrats can say: Despite conservative arguments that a welfare state could destroy poor young people’s ambition, Denmark’s educational mobility is no worse than the U.S. But Republicans can say: Despite liberal arguments that Denmark is so much better than the U.S. at social mobility, its poor kids are no more likely to go to college. “There is something here for the Republicans and for the Democrats,” Heckman told me.

The most significant implication of this paper is not a happy one: Equality of opportunity is a fantasy. It does not exist in the U.S., it does not exist in Denmark, and it probably doesn’t exist anywhere. The children of rich college graduates are far more likely to grow up to become rich college graduates, even in the world's social-democratic fantasyland. That is because, everywhere, parents matter.

And it’s probably a good thing that parents matter. For the government to make equality of opportunity its singular and absolute policy goal would probably mean breaking up neighborhoods, forcing arranged marriages, enrolling all children in a unified curriculum, and having them all taught by a mass-produced robot; that would eliminate neighborhood effects, assortative mating, peer effects, curricular differences, and the problem of unequal teaching quality. It is unclear that there is a constituency for this policy, even among the most radical of Bernie bros.

But just as Denmark’s policy may have its own unintended consequences, the American philosophy of opportunity has its own dark side. For example, high income inequality in the U.S. makes a college degree more valuable in America than in similar countries. This may encourage more poor Americans to enroll in college.

For many, college pays off. But the recent rise in college attainment in the U.S. has come at a terrible cost for some. Student debt has exploded, particularly at for-profit colleges serving older, poorer students, the majority of whom drop out with student loans that aren’t dischargeable in bankruptcy. So the social siren of American inequality—join the rich! go to college!—lures many first-generation students to put tens of thousands of dollars toward a degree that they never get. If they default on their student loans, they won’t be able to get a loan to buy a house. Which means the housing market is constrained by student debt defaults. Which means other industries that rely on a healthy housing market—furniture, cars, plants, kitchen appliances, apparel—are also affected.

Denmark doesn’t have all the answers, and apparently its leaders know it—that’s why they have such a strong public assistance system in the first place. But the U.S. mythology of social mobility is also self-defeating, in ways that are exceptionally American.