People in the middle of the middle are richer than those in the middle, says Pew. Mmm.

Joe Smith rides on a swing with his daughter Rowan as his wife Andrea plays with her children Norah and Chase  at a playground in Winthrop Harbor, Illinois, May 9, 2014. Three of their children have been diagnosed with atypical Hemolytic Uremic Syndrome, and one is a carrier which was diagnosed using genome sequencing. Once strictly the domain of research labs, gene-sequencing tests increasingly are being used to help understand the genetic causes of rare disease, putting insurance companies in the position of deciding whether to pay the $5,000 to $17,000 for the tests. Genetics experts say that sequencing more than doubles the chances that families get a diagnosis, and saves spending on multiple tests of single genes. Even if no treatment is found, the tests can also end hugely expensive medical odysseys as parents frantically search for the cause of their child's furtive illness. Picture taken May 9, 2014. To match Insight HEALTH-SEQUENCING/    REUTERS/Jim Young (UNITED STATES - Tags: SCIENCE TECHNOLOGY HEALTH SOCIETY BUSINESS) - GM1EA6J1MA301

As if on cue, just a day after we published our definition of the middle class, Pew issued their latest report on the changing state and shape of the U.S. social classes, “The American middle class is stable in size, but losing ground financially to upper-income families”. Let the wonk wars begin!

Pew defines the middle class as a range around the median income (in their case, from two thirds to twice the median). Senior Researcher Rakesh Kochhar shows using CPS data that, on this definition, the middle class has shrunk from 61 percent of the population in 1971 to 52 percent in 2016, though has not changed in size very much in recent years.

As regular readers will know, we have rejected this approach in favor of a fixed percentile range of the middle three income quintiles. Partly this is because when the middle class grows or shrinks as a percentage of the population, it is hard to interpret income shares over time. A median-pegged definition reflects changes in the shape of the income distribution, changes that may be seen as good or bad, depending on your point of view.

Kochhar then compares the incomes of the three class groups – low, middle, upper – by reporting the median for each group (adjusted for household size, and in 2016 dollars for a three-person household). Here is Kochhar’s summary:

“The median income of middle-class households increased from $74,015 in 2010 to $78,442 in 2016, by 6 percent. Upper-income households (where 19 percent of American adults live) fared better than the middle class, as their median income increased from $172,152 to $187,872, a gain of 9 percent over this period. Lower-income households (29 percent of adults) experienced an income gain of 5 percent, about the same as the middle class.”

This is not easy to wrap your head round. The economic position of each of the three different groups is here being measured by their median income; but the groups themselves are defined in relation to the overall median.

One result of this approach is that the median income of the “middle class” is not the same as the median income of the whole society. In the chart below, we show median income, and median “middle class” income, according to Pew. There is a sizable gap, of more than $10,000 in 2016, and of almost $17,000 in the midst of recession, in 2010:

So: middle class incomes defined as the median dropped quite precipitously in the recession, but middle class incomes defined as the median of the “middle class” dipped only modestly. Each may be correct (though like many, we are increasingly worried about CPS data), but each tells a different story.

By contrast, our own preferred definition of the middle class is symmetrical around the median, including the 30 percent below and the 30 percent above. This means that the median middle class income is, by definition, always the same as the median U.S. household income.

This is not to say that the Pew approach is wrong, and ours right: or indeed to make this claim of any of the other myriad definitions. Each definition does a different job: we just need to be clear what that job is, and why this is the best definition to complete it.

But it is to say – and we promise to shut up about this soon – that definitions really matter when it comes to describing the condition and prospects for the middle class. As we wrote earlier, it is clear that the condition of the American middle class is a cause for deep concern and for a concerted collective response. Back in 1972, Richard Sennett and Jonathan Cobb warned of the “hidden injuries of class.” Today’s class wounds are no longer hidden. Populist political leaders are channeling middle class angst, only to promote policies that will reinforce, rather than redress, class division. Our political and policy challenge is to improve the quality of life of America’s middle class, and to increase the number of people rising to join its ranks. But in order to provide concrete help to the middle class, we have to know who we are talking about.