Let me do something New York Times NYT -0.13% columnist Paul Krugman isn't exactly famous for doing, at least not graciously: acknowledge a mistake.

In my Dec. 31 column on income inequality, I used a data set from the U.S. Census Bureau to make the case that incomes in the U.S. have been growing across the board, even if the incomes of the wealthy have grown faster than those of others further down the income scale. But I wrote those lines looking at a set of numbers that had not been adjusted for inflation.

Professor Krugman, in a post on his New York Times blog, takes me to task for this. Had I done so looking at the inflation-adjusted table, it would have shown the incomes of the bottom 20% essentially stagnating since 1979 (and long before then, too), though it also would have shown incomes for the top 20% rising far less dramatically.

That was an error, roughly of the kind the Nobel Laureate economist made last August when he confused an x for a 1/x. As is his charming wont, Mr. Krugman accuses me not of making an honest mistake, but of "pulling a fast one."

My mistake is all the more unfortunate because the basic point I was making is right: Americans are getting richer across the entire income spectrum, even if they are getting richer at very different rates. That much is confirmed by data from the Congressional Budget Office. The CBO finds that between 1979 and 2007 income for poor households grew by 18%, for the middle classes by nearly 40%, and for the top 81-99% by 65%. It's the top 1% who have made out very handsomely, with a jump of 275% over nearly three decades.

The difference between the Census Bureau and CBO data comes down to the complicated (and ultimately subjective) way in which "income" is defined. The Census Bureau data relies on a definition of income that is pre-tax but post-transfer cash income. But it also excludes the non-cash benefits that go to many of the poor, such as food stamps, Medicaid, CHIP (children's Medicaid) and housing subsidies. (and now more free or subsidized medical care and medications)

By contrast, the CBO numbers measure after-tax, after-transfer income. It also includes non-cash transfers. Those benefits may not be fungible, but they do have value. And they vindicate my core point: "The richer have outpaced the poorer in growing their incomes, just as runners will outpace joggers who will, in turn, outpace walkers." What mattered, I said, was that "the walking man walks."

My column also noted that President Obama erred when he said the top 10% take half of aggregate income; in fact, it's the top 20% who take half the income, according to Census Bureau data. Mr. Krugman takes issue with this, too, saying the Census Bureau figures are pretty much worthless when it comes to quantifying the aggregate incomes of the very rich. Much better, he says, is data from a controversial study by two left-wing French economists, Emmanuel Saez and Thomas Piketty, which is in line with President Obama's contention.

Talk about a fast one. As Greg Mankiw, chairman of the Harvard Economics department, notes, Saez-Piketty has its own set of very large problems: "The data are on tax units rather than households, they do not include many government transfer payments, they are pre-tax rather than post-tax, they do not adjust for changes in household size, and they do not include nontaxable compensation such as employer-provided health insurance."

Ultimately, debates about income inequality are never going to be settled because both "income" and "inequality" are very hard to measure. Is the best measure of inequality wage inequality, income inequality, or consumption inequality? If a poor family today can now afford a car, an air conditioner, a computer and other goods unaffordable or unavailable to the poor of 35 years ago, can they really be said to have stagnated economically? How do changes in the tax code affect the ways in which income can be reported, sheltered and measured? What is the true money value of health insurance?

And so on and on. The argument I made in my column is that inequality should only matter to Americans if, Russia-like, the rich are getting richer at the expense of the poor. Neither the Census Bureau nor the CBO figures show that.

None of this is to excuse the fact that I goofed in my use of data. My apologies. As for Mr. Krugman, he should bear in mind something the public editor of the New York Times once said about him: "Paul Krugman has the disturbing habit of shaping, slicing and selectively citing numbers in a fashion to please his acolytes but leaves him open to substantive assaults."