The first in a recent series of New York Times articles about “class in America” claimed “the after-tax income of the Top 1 percent of American households jumped 139 percent, to more than $700,000, from 1979 to 2001, according to the Congressional Budget Office” (stopping at 2001 because the figure for 2002 fell to $631,700).

A recent article in the same paper used a black box “computer model” to slice the pie even thinner, down to the top 145,000 taxpayers. Author David Cay Johnston concluded, “The average income for the top 0.1 percent was $3 million in 2002. … That number is 2? times the $1.2 million, adjusted for inflation, that group reported in 1980.”

I criticized the first New York Times article in a May 18 Wall Street Journal piece, partly because the ephemeral incomes of a few entertainers, athletes and investors had nothing to do with the series’ theme of upward mobility among the general population. More to the point, I cryptically suggested it is inappropriate to use income tax statistics to measure long-term changes in income inequality. That needs more explaining.

Unlike Census statistics, the tax statistics include capital gains — but only those gains that are realized and taxable. This is particularly deceptive when comparing recent years with 1979–80, because Individual Retirement Accounts began in 1981, and 401(k) and Keogh plans came later.

Unlike 1979, most capital gains now accumulate invisibly in tax-deferred plans for retirement and college. Since 1997, couples may repeatedly realize capital gains of up to $500,000 from selling their homes, yet those gains are likewise missing from “income” as measured by the New York Times.

Because most people now accumulate most capital gains and dividends in ways undetectable on tax returns, tax data wrongly suggest only the very rich (whose investments exceed the caps on 401(k) and Keogh contributions) still appear to be realizing many gains. This creates a statistical illusion only those at the top appeared to benefit much from the 1982–2000 boom in stocks and bonds.

A related problem motivated the New York Times’ allusion to growth in “after-tax income of the Top 1 percent, as estimated by the Congressional Budget Office (CBO). The reason after-tax income appeared to rise faster than pretax income was not because of reductions in personal tax rates on salaries and capital gains — which brought in more money from the rich rather than less. It was because of big reductions in effective corporate tax rates after 1981. The CBO had to assign those corporate tax cuts somewhere, so they did so on the basis of who had the most “interest, dividends, rents and capital gains” in tax returns.

Recent tax data exclude trillions of dollars average families hold in tax-deferred retirement and education savings plans, however, not to mention nearly all capital gains on homes. Ownership of stocks and homes is now far more widely dispersed among families with modest incomes than in 1979.

Unable to detect these investment returns from Internal Revenue Service data, however, the CBO assumed the opposite — the Top 1 percent must be collecting a rising share of investment returns. They estimated the Top 1 accounted for 53? percent of investment returns in 2002, up from just 37.8 percent in 1979. As a result, they estimated the effective corporate tax rate attributed to the Top 1 percent of households fell from 13.8 percent in 1979 to 6.1 percent in 2002. This dubious gift of corporate tax cuts to the Top 1 percent inspired the Times to refer to that group’s alleged 139 percent growth in after-tax income through 2001 rather than the 98 percent increase in pretax income through 2002.

Even if income figures from tax returns were credible, it would still be extremely misleading to compare arithmetic (mean) averages among the Top 1 percent in 1979 with the averages among a quite different Top 1 percent in 2001 or 2002.

As I wrote in the Wall Street Journal: “It is statistically dubious to compare long-term growth of average income in any top income group with growth below. Only the top group has no income ceiling, and the lower income limit defining membership in that top group rises whenever incomes are rising.”

In all other income groups, large income increases result in more people moving into the next higher income group. When that happens to many people — because incomes generally are rising — it soon takes more money than before to qualify to be counted among the second, third and fourth quintiles (fifths) of the income distribution.

The rising income ceiling at the top of each quintile becomes a rising floor defining entry into the next highest quintile. Since the Top 1 percent has no ceiling, the mean average can easily be dominated by a tiny fraction at the top (as Mr. Johnston’s figures show), so this “average” is not typical of the group.

Over long periods, changes in the mean average of the Top 1 percent are largely explained by the fact all lower-income groups’ rising income ceilings must become the Top 1 percent’s rising floor. In 1979, households needed a “comprehensive income” of only $144,500 (in 2002 dollars) to be included in the CBO average income of the Top 1 percent, of $474,300 before taxes. In 2002, households needed a comprehensive income above $228,400 to be included in the average, which the CBO estimates at $938,100 in 2002.

Because it took almost twice as much income to be counted among the Top 1 percent in 2002 as in 1979, nobody should be surprised averages of all income above that doubled threshold likewise almost doubled. Suppose we averaged all incomes above $228,000 today, and then averaged all incomes above $474,300. Wouldn’t the second figure would be much larger than the first?

These are just a few reasons it is singularly inappropriate to use realized capital gains and other statistics from income tax returns to determine the arithmetic average of income among the Top 1 percent, much less to then compare such a flawed figure with some incomparable figure from 1979.

There are no good estimates of typical incomes among the Top 1 percent, but that is no excuse for repeatedly abusing innocent statistics.