There’s a commonly held view expressed by many that America’s large middle class is disappearing, much like the typewriter, rotary phone, and, dare I say, VCR. In their place is left the poor and rich, with little social glue in-between.

One problem with determining whether this is true is simply defining middle class. Although scholars, journalists, commentators, and politicians all talk about the middle class, there’s actually no official definition of the group. So if we can’t define middle class, how do we know if it’s changing?

One way around this issue is to look at what’s happened to households of different income levels over the decades. Recently some new Census data were released that allowed such an examination for 1967 to 2005.

The Census data are valuable because they allow apples-to-apples comparisons. I think you’d agree that in examining income changes over time, it’s incorrect to treat, for example, a $35,000 salary in 1967 as being equal to a $35,000 salary in 2005. Obviously, price increases between 1967 and 2005 make the purchasing power of $35,000 in 2005 much less than the purchasing power of $35,000 in 1967. Fortunately, the Census folks recognize this and have made the appropriate adjustments to permit direct income comparisons.

The Census data are divided into nine income categories, from low to high, where the incomes in each category have the same purchasing power over time. In looking at the percentage of households in each category in 1967, and then again in 2005, the Census analysts found some major shifts in the distribution of income, but perhaps not in the way you might expect.

There was a lower percentage of households in each of the three lowest income categories (household incomes up to $15,000 in today’s purchasing power). The percentage of households in these three groups dropped from 21 percent to 15 percent between 1967 and 2005.

There was also a lower percentage of households in each of the three middle-income categories (household incomes between $15,000 and $50,000 in today’s purchasing power), with the collective percentage falling from 51 percent to 39 percent. These three income groups constitute one definition of the middle class, so by this calculation, the middle class did shrink.

The biggest surprise, at least to this economist, is what happened to households in the higher-income categories. The percentage of households in each of the upper three income groups (household incomes above $50,000 in today’s purchasing power) increased. Some did substantially. The percentage of households earning between $75,000 and $100,000 doubled in the 38 years, and the percentage of households earning over $100,000 quadrupled. Together, the share of total households with incomes above $50,000 jumped from 28 percent in 1967 to 46 percent in 2005.

Statisticians would call what’s happened to household incomes an “upward shift in the income distribution.” More households have moved up the income ladder, and those at the top end (upper three income categories) now outnumber those at the lower end (lowest three income groups) by 3-1.

Yet there are also fewer households in the middle, and with this has come an increase in income inequality. With fewer middle-class households, the gap between the upper-income and lower-income groups has increased. Other Census data show upper-income households have experienced much bigger income gains than lower income households in recent decades. The reasons for this are varied, but a big one is the larger impact that education has today on earning power, and higher-income workers tend to have the most education.

So, three conclusions can be drawn from this number crunching. Yes, the middle class has gotten relatively smaller, if middle class is defined as those in the middle of the income distribution. But this is because more households have moved up the income ladder in the last 40 years than have moved down. And, although there is a smaller percentage of households in the lower-income groups, the difference in incomes between them and those at the upper-income levels has widened.

Dr. Michael L. Walden is a William Neal Reynolds distinguished professor at North Carolina State University and an adjunct scholar of the John Locke Foundation.