It turns out that the middle class isn’t stagnant after all.

You know the conventional wisdom. The richest 1 percent of Americans have siphoned off all the income gains of recent decades. Everyone else is treading water. The claim has been repeated so often that it’s taken on the aura of truth.

The reality is different: Living standards for most income groups have improved, especially for the upper-middle class, which has more than doubled in size.

We know this from a new study by economist Stephen Rose of the Urban Institute, a think tank. Rose subdivided the population into five economic classes. The poor and the near-poor had annual incomes from $0 to $29,999; the lower-middle class, from $30,000 to $49,999; the middle class, from $50,000 to $99,999; the upper-middle class from $100,000 to $349,999; and the rich, $350,000 and up. He then examined how each group had fared between 1979 and 2014.

Here’s what he found. There was a gradual and broad-based shift of Americans from poorer to richer status. Productivity gains have translated into higher living standards more than is generally believed.

The most spectacular change involved the explosion of the upper-middle class. It grew from 12.9 percent of Americans in 1979 to 29.4 percent in 2014 — from one in eight U.S. households to more than one in four. The rich went from 0.1 percent of households to 1.8 percent in 2014. If these two groups are combined, nearly one-third of Americans have incomes exceeding $100,000. All these thresholds apply to three-person households; income levels are adjusted for differences in household size.

Meanwhile, the poorer segments of the population declined. The poor and near-poor dropped from 24.3 percent of the population in 1979 to 19.8 percent in 2014. The lower-middle class fell from 23.9 percent to 17.1 percent, and the middle class decreased from 38.8 percent to 32 percent.

All in all, it’s an important story. “The growth in the rich and upper-middle class and the declining proportion of the population in the middle and lower classes indicate widespread economic growth between 1979 and 2014,” writes Rose.

Still, the story is largely ignored in favor of the notion that only the top 1 percent is advancing. The murkier truth is that the top 1 percent are simply getting richer much faster than everyone else.

And it’s buttressed by a paper from economist John Komlos of the University of Munich. Komlos estimates that the incomes of the richest 1 percent have been growing about 3.9 percent annually compared with 1 percent or less for most of the population.

Just what has caused top incomes to skyrocket is unclear. But we do know that the ranks of the top 1 percent include: highly paid CEOs and corporate managers; investment bankers, advisers and hedge fund operators — aka, “Wall Street”; successful private business owners; sports stars and media celebrities; well-paid doctors and lawyers.

We do know that growth of inequality has been powerful. Komlos figures the income of the top 1 percent is 51 times the income of the poorest fifth of Americans, up from 21 times in 1979. Wow! But we also know the economy still generates higher living standards for most households, though the process is slow and often unappreciated.

People are getting ahead but don’t feel they’re getting ahead. The explanation is simple enough. The significant gains cited by Rose occurred over a 35-year period. Though they are sizable now, the increases in any one year may have been so small that people don’t register a “positive change in standard of living,” as Komlos puts it.

Confusing matters further is the distinction between absolute and relative income. Absolute income refers to households’ spending money; relative income compares household income to some benchmark — say, median household income. Rose focused on absolute income. Some economists prefer relative income, which often shows the middle class shrinking, because some incomes aren’t keeping pace with the benchmark even if purchasing power increases.

We’ll hear a lot about inequality in this presidential campaign. We need to strip away as much rhetoric as possible. Our central goal should be getting the bottom up, which is more important than pulling the top down. It’s also tougher.

Robert Samuelson is a columnist with The Washington Post Writers Group.