At a speech in December to celebrate the 10th anniversary of the left-leaning Center for American Progress, President Barack Obama declared, "The combined trends of increased inequality and decreasing mobility pose a fundamental threat to the American Dream." He added, "And greater inequality is associated with less mobility between generations." Never let it be said that our president doesn't learn to trim his rhetoric. Earlier this month, a new study by researchers at Harvard University and University of California, Berkeley concluded that, in fact, income mobility in the United States has not decreased. Consequently, in his State of the Union address on Wednesday, President Obama more circumspectly stated, "Inequality has deepened. Upward mobility has stalled."

However, the Harvard and Berkeley researchers also argued that it is harder for Americans to change their relative level of income than it is for people living in other rich developed countries, specifically mentioning Denmark. In his December speech, the president declared "that it is harder today for a child born here in America to improve her station in life than it is for children in most of our wealthy allies—countries like Canada or Germany or France. They have greater mobility than we do, not less."

People living in Denmark, Germany, and France have a relatively easier time passing through various income quintiles than do Americans largely because of greater income equality in their countries. Basically it is easier to change quintiles because the differences in the amount of income between the quintiles are much smaller than in the United States. Using Eurostat data, let's take a look at that paragon of income mobility, Denmark.

In 2011, the cut-off point for household income for the bottom income quintile in Denmark was $25,000 compared to $20,000 in the United States. The cut-off points for the next quintile up were $32,000 and $38,000 respectively. The middle quintile cut-offs were $40,000 versus $62,000. The fourth quintiles were $50,000 in Denmark and $102,000 in the U.S. The cut-offs for the 95th percentile were $72,000 and $186,000. And the cut-offs for the top one percent were $115,000 and $368,000.

Below is a table using 2011 Eurostat post-tax income data converted from current Euros to current dollars. I could find no U.S. income data that provided post-tax quintile thresholds so I have included 2011 pre-tax quintile thresholds on the top row and 2010 average post-tax income data in the second row. The starred figures are average post-tax U.S. incomes for households between the 96th and 99th percentiles and the top one percent respectively. Comparing these data give a rough idea of how U.S. income quintiles compare with those of other wealthy countries.

Quintiles 1st 2nd 3rd 4th 95% 99% U.S. cutoffs before tax $20,000 $38,000 $62,000 $102,000 $186,000 $368,000 U.S. average after tax 2010 $24,000 $41,000 $58,000 $81,000 $215,000* $1,013,000* Denmark $25,000 $32,000 $40,000 $50,000 $72,000 $115,000 Germany $17,000 $23,000 $29,000 $50,000 $57,000 $86,000 France $19,000 $24,000 $31,000 $41,000 $68,000 $123,000 Sweden $21,000 $28,000 $34,000 $42,000 $58,000 $82,000

Also bear in mind that in 2011, the U.S. pre-tax median household income was $50,000. The post-tax median household income for Danes was $36,000, for Germans was $26,000; French $27,000, and the Swedish median income was $31,000.

One way to think of the comparison between the U.S. and Denmark is that, in absolute terms, it takes only an increase in income of $47,000 for a Danish household to rise from the bottom quintile to that country's top five percent. A comparable rise in the United States would mean that a household's income has increased by $166,000 to cross the pre-tax threshold or $190,000 to achieve the average post-tax income of Americans who are between the 96th and 99th percentile of incomes. In some sense, it's easier to appear "mobile" when you have a lot less distance to travel.

Another way to think about comparing the U.S. and Denmark is that with an increase of $47,000 an American household would rise from the bottom quintile to the middle quintile of the U.S. income distribution. In other words, a solidly middle class American income is comparable to an income that would put a Danish household in its country's top five percent of households.

The Harvard and Berkeley researchers observed, "Scandinavian economies have much greater relative intergenerational mobility than the United States." But they added that that "does not necessarily mean that children from low-income families in Denmark do better than those in the U.S. in absolute terms."

That is true. One oft-cited statistic is that 16 percent of Danes born into households in the bottom quintile rise to the top quintile in their country—an income journey of $25,000 dollars. Whereas only eight percent of similarly poor Americans make to the top quintile in the U.S., an income journey of $82,000.

However, a study by economists at the U.S. Treasury Department published in the May, 2013 American Economic Review reported that 27 percent of American teenagers who were living in households with incomes in the bottom quintile in 1987 were now in households with incomes above $62,000 (fourth and fifth quintiles) by 2007. In other words, in terms of absolute income gains, poor Americans were almost twice as likely as poor Danes to make incomes found in the top Danish income quintile. The rungs of the income ladder are further apart in the U.S., but successfully climbing each one takes an American a lot farther than a Dane or a German ascending his country's income rungs.

So why are the rungs on the income distribution ladders in other rich countries so much closer together? One word: redistribution. For example, the marginal income tax rate in Denmark tops out at 60 percent at $55,000.

Inequality is often measured by the Gini coefficient in which a score of 0 indicates perfect income equality and a score of 1 means that one household gets all the income. In December, the Pew Research Center published data showing how the pre-and-post redistribution Gini coefficients of various rich countries stacked up. Below is a table with selected values.

Gini Coefficient Pre-redistribution Post-redistribution U.S. 0.499 0.380 Denmark 0.429 0.252 Germany 0.492 0.286 France 0.505 0.303 Sweden 0.441 0.269

Taking from the rich to give to the poor clearly shrinks the distance between income rungs. In his State of the Union address, President Obama declared, "Opportunity is who we are." Yes, but it's hard to see how shortening the income ladder provides more opportunity for income mobility. It just makes everyone equally less well off.