A Wall Street Journal article by Arthur C. Brooks, president of the American Enterprise Institute, urges presidential candidate Mitt Romney to acknowledge two “simple facts” about income inequality. One is that “low-income Americans are struggling,” which is surely true by definition. The second is that “economic opportunity is declining.” The author scolds the Republican convention for being too cheerful about the facts, as though Romney never mentioned shrinking median income, or high poverty and unemployment.

That second “simple fact” (declining opportunity) is not simple and not a fact. When Mr. Brooks asserts that opportunity is declining, he means “mobility” supposedly declined before 2006 according to one source—a 12-page brief by Katharine Bradbury of the Boston Fed. But “mobility” is not at all the same as “opportunity,” because studies of this sort treat downward mobility the same as upward mobility. Bradbury is troubled by people making fewer big leaps from one fifth (quintile) to another, which Mr. Brooks likewise defines as declining opportunity; yet her data cannot distinguish ups from downs.

What is ostensibly being measured is the percentage of people in each fifth (quintile) of the income distribution who spend five or six years out of 10 in either the “same or adjacent” quintile. Bradbury compares three 10-year periods: 1976 to 1986, 1986 to 1996, and 1996 to 2006 and finds 27.4 percent remained in the poorest quintile during the earliest period and 25.9 percent in the most recent 10 years. Since that suggests increasing mobility for the poor, she switches to emphasizing how many remained in either the same “or adjacent” quintile. This permits Bradbury to argue that those in the poorest or richest quintiles “did not move very far.”

Switching to “adjacent” quintiles means anyone in the top or bottom quintile would have to leap all the way to the middle to be counted as having moved at all. Since those at the bottom or top can only move in one direction, Bradbury therefore finds (of course) that for “those in the poorest or richest quintile… mobility is quite low.” People in other quintiles can move either up or down, so their “mobility” appears higher by this peculiar definition, particularly during severe recessions.

It is unsurprising that there was greater movement (up and down) between adjacent income groups in 1976–86, since that period included nasty inflationary recessions in 1980–82, followed by four years of 4.8 percent economic growth. The 1986–96 period, by contrast, experienced a barely measurable slump in 1991, while 1996–2006 included the exhilarating tech boom of 1997–2000 and the perilous housing boom of 2004–2006. When the economy is rising steadily there is less risk of falling to a lower quintile, hence less movement (aka “mobility”). Since Brooks and Bradbury define income stability as “declining opportunity,” they would presumably define 1929–33 or 2008–2009 as periods of rising opportunity.

A more serious study of income mobility by Treasury economists Gerald Auten and Geoffery Gee in the June 2009 National Tax Journal found, “considerable income mobility in the U.S. economy over the 1987–1996 and 1996–2005 periods. Consistent with prior mobility studies, the data show that over half of taxpayers moved to a different income quintile and that roughly half of taxpayers who began in the bottom income quintile moved up to a higher income group by the end of each period. By contrast, those with the very highest incomes in the base year [the top 1 percent] were more likely to drop to a lower income group and the median real income of these taxpayers declined in each period. Economic growth resulted in rising incomes for most taxpayers over both time periods.” The largest percentage increases in real incomes were for those initially in the lowest income groups, while the most dramatic downward mobility was among those who had briefly occupied the top 1 percent. This evidence is consistent with my own work showing that rising income shares for the top 1 percent have been associated with falling poverty rates and vice-versa.