One of the best-selling books of 2014 is Capital in the Twenty-First Century by French economist Thomas Piketty, a 696-page doorstop tome on economic history. Why is a data-heavy treatise from the “dismal science” so appealing? Because it is about income inequality and immobility, which in a December 2013 speech President Barack Obama called “the defining challenge of our time,” concluding that it poses “a fundamental threat to the American dream.” But does it? Maybe not.

The rich are getting richer, as Brookings Institution economist Gary Burtless found by analyzing tax data from the Congressional Budget Office for after-tax income trends from 1979 through 2010 (including government assistance). The top-fifth income earners in the U.S. increased their share of the national income from 43 percent in 1979 to 48 percent in 2010, and the top 1 percent increased their share of the pie from 8 percent in 1979 to 13 percent in 2010. But note what has not happened: the rest have not gotten poorer. They've gotten richer: the income of the other quintiles increased by 49, 37, 36 and 45 percent, respectively.

The pie metaphor is deceptive because a pie is of a fixed size such that if your slice is larger, then someone else's is smaller. But economies grow, and the pie gets larger such that you and I can both get a larger slice compared with the slices we got from last year's pie, even if your slice increase is relatively larger than mine. A report released by the Federal Reserve in early 2014, for example, noted that the overall wealth of Americans hit the highest level ever, with the net worth of U.S. households rising 14 percent in 2013, which is an increase of almost $10 trillion to an almost unimaginable $80.7 trillion, the most ever recorded by the Fed. Of course, on a planet with finite resources such an expansion cannot continue indefinitely, but historically capital and wealth production shifts as industries change from, say, farming and agriculture to coal and steel to information and services.

What about income mobility, which President Obama also identified as a problem? Writing in the National Tax Journal, economists Gerald Auten and Geoffrey Gee analyzed individual income tax returns between 1987–1996 and 1996–2005 and found that for individuals age 25 and up, “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” and that “those with the very highest incomes in the base year were more likely [than those in other quintiles] to drop to a lower income group.” In fact, they found that “60 percent of those in the top 1 percent in the beginning year of each period had dropped to a lower centile by the 10th year. Fewer than one fourth of the individuals in the top 1/100th percent in 1996 remained in that group in 2005.” In a follow-up study that included income data through 2010, the economists found that “approximately half of taxpayers in the first and fifth quintile remained in the same quintile 20 years later. About one-fourth of those in the bottom moved up one quintile, while 4.6 percent moved to the top quintile.”

One reason for the controversy is that people overestimate differences between the rich and poor. In a 2013 study published in Psychological Science entitled “Better Off Than We Know,” St. Louis University psychologist John R. Chambers and his colleagues found that most people estimate that the richest 20 percent make 31 times more than the poorest 20 percent (it is 15.5 times), and they believe that the average annual income of the richest 20 percent of Americans is $2 million, whereas in fact it is $169,000, a perceptual difference of nearly 12 times. “Almost all of our study participants,” the authors concluded, “grossly underestimated Americans' average household incomes and overestimated the level of income inequality.”

So both income inequality and social mobility, though not as ideal as we would like them to be in the land of equal opportunity, are not as large and immobile as most of us perceive them.