Are the rich getting richer? Yes. Are the poor getting poorer? No. In fact, over the past 35 years most Americans got richer. Has income inequality increased in the United States? Yes. Does it matter? Well, President Barack Obama thinks so. In a December speech at the Center for American Progress, the president declared that "a dangerous and growing inequality and lack of upward mobility" is "the defining challenge of our time." Is that true? No.

In December 2013, a Congressional Budget Office (CBO) study looked at historical tax burdens borne by Americans at all income levels. Among other things, the CBO examined after-tax income trends for each quintile of American households since 1979, including not just wages but benefits and transfer payments. Using the CBO data, the Brookings Institution economist Gary Burtless has shown that from 1979 to 2010, the last year for which data are available, the bottom fifth's after-tax income in constant dollars rose by 49 percent. The incomes of households in the second lowest, middle, and fourth quintiles increased by 37 percent, 36 percent, and 45 percent, respectively. The poor and the middle class got richer.

Burtless then divides the households situated in the top fifth of incomes into four groups: those in 90th percentile and below, those in the 91st through 95th percentiles, those in the 96th through 99th percentiles, and the top 1 percent. From 1979 to 2010, incomes for those fortunate households increased by 54 percent, 67 percent, 79 percent, and 202 percent, respectively. The rich got richer too, and they got richer faster.

Because of these differential increases in income, the share of pre-tax national income going to the top quintile has increased from 43 percent in 1979 to just over 50 percent in 2010. The share of income accruing to the top 1 percent increased from 9 to 15 percent.

So inequality in the U.S. has increased. But if most Americans' incomes are rising, does it matter if some are getting a larger share?

Inequality is often expressed in the Gini coefficient, a number that ranges between zero (indicating complete equality) and one (indicating that all income goes to one person). The higher the number, the more concentrated the country's income. If the rich get richer and the poor get poorer, the Gini coefficient goes up. If everyone gets richer but the rich get more, the Gini coefficient still goes up.

The Harvard economist Martin Feldstein explained in 1999 why over-relying on this measure is a mistake. "The common procedure of regarding a higher Gini coefficient as a deterioration of the national condition," Feldstein wrote, "is equivalent to treating the marginal social utility of high incomes as negative, i.e., that something bad has occurred when the well-to-do become better off."

Those worried about rising income inequality also often make the mistake of assuming that each income quintile contains the same households. They don't. Between 2009 and 2011, for example, 31.6 percent of Americans fell below the official poverty threshold for at least two months, but only 3.5 percent stayed below it over the entire period.

In his December speech, the president suggested that rising inequality is limiting income mobility, leaving poor Americans increasingly stuck and struggling on the lower rungs. The data do not support this claim.

In 2009, two economists from the Office of Tax Analysis in the U.S. Treasury compared income mobility in two periods, 1987 to 1996 and 1996 to 2005. The results, published in the National Tax Journal, revealed that "over half of taxpayers moved to a different income quintile and that roughly half of taxpayers who began in the bottom income quintile moved up to a higher income group by the end of each period."

On the other hand, the researchers found that the incomes of taxpayers in the top 1 percent of the income distribution in 1996 were more likely to drop to a lower income group by 2005, although only 12 percent of those households fell out of the top quintile. Nevertheless, more than half of the households in the top 1 percent in 2005 were not there in 1996.

The researchers concluded that 57.5 percent of individuals changed income quintiles between 1996 and 2005, compared to 58.3 percent between 1987 and 1996. In other words, income mobility has barely changed.

The Treasury researchers updated their analysis of income mobility trends in a May 2013 study for the American Economic Review, finding that about 75 percent of taxpayers between 35 and 40 years of age in the second, middle and fourth income quintiles in 1987 had moved to a different quintile by 2007. For example, 24 percent of those who had been in the middle quintile in 1987 were still there in 2007, but 23 percent had moved up a quintile and 18 percent had moved down one. On the other hand, 42 percent of those who had started out in the bottom quintile remained there 20 years later, while 46 percent in the top quintile stayed on top.

But how did the children of households in the bottom and top quintiles fare? The researchers report that 27 percent of the 35-to-40-year-olds whose parents were in the bottom quintile in 1987 were also there in 2007, while 10 percent had made it into the top quintile. On the other hand, 39 percent of the kids whose parents were in top quintile in 1987 were still there in 2007; 9 percent had fallen to the bottom. In other words, kids, especially those whose parents were on the lower rungs, were more liable to change status than their parents. "We leave it to the reader to look at the results and decide whether they think the observed mobility and turnover at the top are sufficient and good," the Treasury researchers conclude.

In January, scholars from Harvard and University of California, Berkeley bolstered the Treasury economists' conclusions. Parsing data from the 1950s and 1970s, the researchers, who are involved with The Equality of Opportunity Project, reported that "measures of social mobility have remained stable over the second half of the twentieth century in the United States." The researchers also found that income inequality has indeed increased in the United States, which means that "the rungs on the income ladder have grown further apart." Nevertheless, "children's chances of climbing from lower to higher rungs have not changed."

What factors retard upward income mobility? Among other things, being located in the southeastern United States, greater residential segregation by race and ethnicity, poor public schools, residing in areas with lower social capital, and living in neighborhoods with higher percentages of single-parent families.

The real defining economic challenge of our time isn't to end inequality. It's persistent joblessness and weak economic growth perpetuated by feckless Obama administration policies.