Mean vs. Median Income

I opened the discussion by presenting evidence suggesting little change since 1986-88 in the inequality in disposable income or consumption “among the U.S. population as a whole” (as opposed to, say, the 99.99th percentile doing better than the 99th percentile). One unique piece of that evidence — comparing growth of median income by quintile and decile from the Fed’s in-depth Survey of Consumer Finances — has attracted no comment. Instead, two commentators who might be expected to rely on Gini coefficients have resorted to comparing mean income or wages between top and bottom deciles, before taxes, and doing so for only two years.

Nobody, least of all Krueger and Perri, questioned my suggestion that consumption inequality has remained largely unchanged for many years, although Burtless did raise some concerns about data quality which I tried to resolve.

In the 2005 Consumer Expenditure Survey the bottom fifth accounted for 8.2% of total consumer spending, compared with 39% for the top fifth. But there were only 1.7 persons and 0.5 workers per “consumer unit” in the bottom fifth, compared with 3.2 persons and 2.1 workers in the top fifth. Consumption per capita or per worker is much more equal than the consumption shares indicate, and consumption shares are much more equal than income shares (particularly if taxes and transfer payments are excluded).

What about inequality of disposable income? The initial essay by Burtless said, “if you look at some of the most comprehensive definitions of income, it turns out that inequality increased less, possibly much less, after 1989 than indicated by the Census Bureau’s headline number.” Burkhauser likewise concluded that, “Since 1989 household income inequality has risen very little.” Aside from the one-year spike in 1993, in fact, he finds “remarkably little increase in income inequality” for the bottom 99% of the population since 1983. Bernanke mentioned disposable income but started with 1979 and used the wrong data. Thoma has not questioned any income distribution statistics offered by Burkhauser or me. So where is the disagreement?

Any remaining controversy about total income or labor income (“wages”) appears to have been narrowed to small fractions of the population (1-10%) rather than the population as a whole. If gains among the top 1-10% had a significant impact on middle- class shares of disposable income, however, that would have shown up as a rising Gini coefficient. That did not happen, as I showed graphically.

There is still considerable misunderstanding about the main reason that Henderson and I questioned the CBO’s misuse of income tax data to estimate disposable income of the top 1% (Piketty and Saez do not estimate disposable income). I will deal with those misunderstandings in a separate note, and with Thoma’s concerns about wealth inequality.

This comment begins with the 90/10 ratio – the ratio of average income or wages of the top 10% to the income or wages of bottom 10%. Such calculations exclude 80% of the population and usually exclude transfer payments and taxes, so they do not actually relate to the issue as I described it – namely, inequality of disposable income “among the U.S. population as a whole.” Since 90/10 ratios have nonetheless been presented as evidence that inequality of pretax income or wages has supposedly increased, the data demand a closer look.

Krueger and Perri write that 90/10 ratios “have the desirable properties that are not affected by changes in top-coding procedures.” Using the CES survey, they conclude that “the 90/10 ratio increases from around 5 in 1989 to around 6 in 2003.” After examining internal data from the Current Population Survey, however, Burkhauser, Feng and Jenkins discovered that 90/10 ratios based on public use files are seriously affected by top-coding. That is likely true of CES data too. Top-coding of 2004 CES public use files applies to wage income above $150,000, for example, and any higher wage is replaced with a mean average of all wages above that critical value.

There are other problems with using a consumption survey to estimate income. The small sample (7500) is made smaller and less random by the fact that some respondents refuse or neglect to report their income. Income is included in the data if respondents provide values for even one source, but many people have additional unreported income from more than one source (such as savings or transfer payments).

Burtless uses a 95/50 ratio for wages alone – that is, changes between two years in the wages of the top 5% of workers and median workers, whether full-time or part-time. He writes, “In 1988 – Reynolds’ preferred base year – a wage and salary worker who earned the median hourly wage received $13.20 an hour (measured in constant 2005 dollars). By 2005 the median worker’s wage increased to $14.29 an hour, an increase of 8.3%. Over the same span of years, a worker earning the 95th-percentile wage experienced a 20.3% gain in pay.”

I have no “preferred base year.” On the contrary, I strongly object to such two-year comparisons because they do not reveal what happened when. One reason, as I have repeated many times, is the break in the data in 1993 when the Current Population Survey (CPS) began to include higher incomes and the income share going to the top 5% suddenly spiked as a result. That same problem is likely to affect the “hourly wage cutoffs” that Burtless cites from the Economic Policy Institute (EPI), because those estimates are based on the “authors’ analysis of CPS wage data.” This is the same data Janet Yellen relied on in the speech Thoma cited.

The EPI’s 95/50 ratio was unchanged at 2.6 from 1985 through 1993, when it suddenly jumped to 2.8 in two years because, as the EPI explained elsewhere, “a change in survey methodology in 1993 led to a sharp rise in measured inequality.” The 95/50 ratio has fluctuated between 2.8 and 2.9 ever since. The Burtless comparison of 1988 and 2005 does not reveal that the ratio was flat before 1994 and after 1995.

Unlike Krueger and Perri’s 90/10 ratio for income, the EPI’s 90/10 ratio for wages shows no sustained increase since 1986. The EPI 90/10 ratio has fluctuated narrowly between 4.3 and 4.4 since 1986, with the familiar CPS spike from 1992 to 1994 and touching 4.5 twice since then. The increase since 1994 was partly because, as the EPI notes, “changes to the survey in 1994 led to lower reported earnings for low-paid workers.” In any case, the ratio was 4.4 in 1987 and 4.4 in 2004, so I too could play the two year game and say that proves there has been no increase in inequality since 1987.

Click on Burtless’s link to the EPI table and see for yourself that all of the years from 1987 to 2005 show no significant and sustained trend in the 90/10 ratio for wages. If Krueger and Perri’s CES data show an increase in the 90/10 ratio of income (not just wages), such different results may be because consumption by the bottom decile is mainly financed by uncounted transfer payments rather than wages.

The EPI estimates do not describe average wages of the top 5-10%, but only the “cutoffs” or minimum thresholds defining where the 90th or 95th percentile begins. They estimate that in 2005, for example, you had to make at least $41.70 to be in the top 5% of wage and salary workers. That figure is, as Burtless noted, is up 20.3% from 1988. But that cutoff or threshold was not pulled up from above (the EPI excludes wages above $100) — it was pushed up from below.

Third Way, a progressive think tank, notes that “From 1979 to 2005, the percentage of prime-age households earning over $100,000 in current dollars grew 12.7 percentage points, while those earning between $30,000 and $75,000 shrank 13.3 percentage points.” That huge increase in the percentage of “rich” households explains why it takes higher earnings than it used to in order to still be included in the mean average of top 5% incomes. With too many people crowding the EPI threshold from below, the threshold moved up. The bar was raised by a general increase in the percentage of workers earning high incomes. And because mean income above the higher threshold no longer encompasses lower earnings of $36-40 an hour that used to be included, a mean average of earnings above the higher threshold was bound to increase. I call this “threshold illusion” in my book, and explain it as follows:

A rising mean income among the top 5, 10 or 20 percent has been routinely misinterpreted as indicating that income gains were confined to only that top group. In reality, rising incomes among those with incomes below the rising threshold have caused the definition of top income groups to exclude incomes that had formerly been among the top group. The mean average of income in top income groups can be pulled up by a few unusually high incomes at the top. But the average can also be pushed up from below by rising numbers of people moving up — leaving what used to be considered a “middle class” income and “joining the ranks of the rich.”

In most of the income distribution data we have been discussing, such as Gini coefficients or the related income shares by decile or quintile, the income of top groups is described by a mean average. We just add up all the income above some threshold and then divide by the number of households, taxpayers or consumer units. Mean averages mislead in this case too, just as they do for total income.

New York magazine’s 2004 survey of Manhattan incomes identified a famous hedge fund manager who earned $1.02 billion. For that same year, the Census Bureau defined the top 5 percent of households as everyone earning more than $157,185. Blending together all incomes from $157,195 to $1,020,000,000 and then dividing that total by the number of households (113,146,000) produces a hodge-podge “average” of $264,387. But such a mean “average” tells us nothing about typical incomes of those 5.7 million households.

Any mean average of income for the top 1-10% is greatly distorted by a small number of outliers, unlike mean averages for all other fractiles which are bounded by an income ceiling. The table below shows that mean and median incomes are virtually identical for the bottom four quintiles. For the top 10%, however, mean income is 64-66% larger than median income. The last column, the source of Figure 7 in my January 11 presentation, shows that real median income of the top 10% increased by 20.7% from 1989 to 2004 – before taxes. Yet real median income of the bottom two quintiles also increased by 20-21%, although in-kind transfers are excluded.

Before-Tax Household Income (in 2004 dollars)

It is important to note that for the top 10% alone, the increase in real income from 1989 to 2004 was smaller for mean income (18.5%) than for median income (20.7%). If the growth of top 1 percent incomes had been nearly as great as suggested by Piketty and Saez or the CBO, then mean income of the top 10% would have grown much more rapidly than mean income, rather than the other way around.

Median income for all households was $43,200 in 2004 according to the SCF, and mean income was $70,700. Everyone would rightly argue that it would be extremely misleading for me to say the higher mean income describes an “average” household. I argue that is equally misleading to say that a mean average describes an “average household” within the top 10 percent. Why am I wrong?

Although I have followed academic convention by presenting mean income figures for the top 5 percent’s income share, and Gini coefficients based on mean income after taxes and transfers, I find such uses of mean averages inherently biased toward exaggerating the typical level of income among top income groups.

Even using conventional measures of mean income, however, no evidence has yet been presented to show any significant and sustained increase in inequality of disposable income among the U.S. population as a whole. That one-time 1993 spike in Census income keeps popping up, and the 1986 spike in capital gains realizations, but that is about all we have seen so far, aside from comments about my temperment or assumed policy agenda. Has anyone contemplated the possibilty that I might simply be right?

Also from this issue

Lead Essay

  • A headline in today’s Wall Street Journal reads “Fed Chief Warns of Widening Inequality.” Bernanke worries that inequality erodes tolerance of the “dynamism” that lays the golden eggs of “economic progress.” But is inequality widening at all? Cato Institute senior fellow Alan Reynolds has his doubts. Following up his own controversial Wall Street Journal op-ed, a Cato Institute policy forum, and a new Cato policy paper, Reynolds in this month’s lead essay digs yet deeper into the mysteries of the official numbers and comes up with … not much: “If there were any [good] data showing a significant and sustained increase in the inequality of disposable income, consumption, wages, or wealth since 1988,” Reynolds concludes, “I suspect someone would have shared it with us by now.”

Response Essays

  • Gary Burtless agrees that analysts of the American income distribution should “take seriously some of Reynolds’s criticisms of the data on income disparities.” “Reynolds points to some serious problems,” Burtless concedes, “and in many cases fair-minded experts will agree with him.” Nevertheless, Burtless dissents sharply from Reynolds’s larger claim that inequality apparently stopped increasing in the late 1980s. “Income inequality was higher at the end of the 1980s than it was in the beginning of that decade,” he states, “and it was higher in 2005 than it was in 1989.” According to Burtless, Reynolds can reach his unorthodox conclusion only by manipulating the evidence. “The problem is,” Burtless charges, “he is harshly critical of data series that do not support his views, while he is usually silent about equal or more serious problems with data sets that show little change in inequality.”

  • In his response to Alan Reynolds, Mark Thoma invites us to “step back” and survey the wider picture of data and expert opinion on income inequality. The verdict? Fed Chairman Ben Bernanke, and the consensus generally, has got this one right. “The preponderance of evidence and of professional opinion,” writes Thoma, “clearly indicates that inequality has been rising since [at least] 1988.” Like Burtless, Thoma finds little in Reynolds’ analysis to agree with, describing his main points as “either too inconsequential to change the inequality picture,” suffering from “an incomplete presentation of the evidence, or rebutted by other work.” Thoma then goes a step further, pointing to new evidence suggesting that income inequality might be even greater than currently estimated.

  • Invoking Kurosawa and Derrida, Richard Burkhauser dives into the contested complexities of the Current Population Survey data on household income. His conclusion: “Over the 1990s business cycle the entire distribution moved to the right with little or no change in income inequality. Since 1989 household income inequality has risen very little and much less than in the previous decade. This is very good news that matters.” Burkhauser admits that the CPS data are not well suited to tracking trends for the top 1 percent of earners. “But does this really matter?” he asks. “Our economy is not a zero sum game. My gain does not mean your loss or vice-versa. I know of no evidence that increases in the incomes of the top 1 percent of our population are the root cause of the challenges faced by those at the other end of the distribution.”

  • Dirk Krueger and Fabrizio Perri suggest that we shift our attention away from inequality in current incomes. “[I]f one is ultimately interested in the distribution of well-being across U.S. households,” they write, “the object of study ought to be the joint distribution of lifetime consumption and leisure across them.” Unfortunately, good data on lifetime consumption are not available. However, citing Milton Friedman and Franco Modigliani, Krueger and Perri contend that “if households can borrow and lend on financial markets, then there is a strong link between the lifetime resources of a household (sometimes also called its permanent income) and its current consumption.” And the trends in current consumption data show that “the increase in income inequality in the U.S. has been much more pronounced than the corresponding increase in consumption inequality.”