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Stretchy ends: The shape of income inequality


Income inequality was once a scholarly backwater. Henry Aaron, our Brookings colleague, once compared monitoring the unchanging statistics to “watching paint dry.” But inequality is now one of the most vivid public, political, and intellectual issues of the day. This is mostly because the facts have changed. In most nations, income gaps have widened, and the United States is no exception. The clamor of the “we are the 99%” Occupy movement has quieted. But the study of income distributions over time and between places has advanced considerably. Thomas Piketty’s Capital, Anthony Atkinson’s Inequality and Robert Reich’s Aftershock have helped to draw greater attention to the issue. The question of who gets what, economically speaking, is almost certain to feature strongly in the race for the Presidency between now and November 2016.

Inequality to inequalities

There are complex and contested relationships between inequalities of one kind and another—between, for instance, opportunity and outcome; earnings and income; income and wealth; wealth and political power; and so on. It is clear that inequalities overlap and reinforce each other. But it is less clear to what extent and with what implications. Even within the narrow space of income inequality there are a multitude of approaches and metrics, yielding different results. (Atkinson’s book is particularly strong on this complexity.) Income can be captured and defined in many different ways—there can be sharp differences between inequality of income derived from earnings and from a wider range of sources, to give just one example. Whether income is attributed to individuals, tax units, families, or households can also have non-trivial effects on results.

It is clear that inequalities overlap and reinforce each other. But it is less clear to what extent and with what implications.

There is also a question of which part of the income distribution matters most in terms of understanding inequality. Is the most important question how the bottom 99% is faring compared to the top 1%? Or how the middle class is doing (and how “middle class” is defined)? Are we most concerned with reducing the number of people in poverty, narrowing the gap between the rich and everybody else, or closing the gap between the rich and the poor? These are as much normative as empirical questions, and it is important for researchers to be candid about their motivation in selecting certain inequality measures over others.

There are some measures of inequality that summarize the whole distribution, of which the most well-known is the Gini coefficient. This has both the advantages and disadvantages of simplicity. In particular, the Gini does not provide information on where the action is: at the bottom, middle, or top of the distribution. Other approaches to measuring inequality can get closer, by comparing incomes at certain points in the distribution. Ratios can be calculated between incomes at various percentiles: 90/10, 50/10, and 90/50, for example. Such measures can provide a broad sense of the shape of inequality in terms of the “gap between rich and poor” (90/10), but also whether this inequality occurs primarily between the top and the middle (90/50), or the middle and the bottom (50/10).

Income distribution as a rubber band

But there is still a good deal missing. Say the 90/50 ratio is increasing over time. This could be happening because those in the 50th to 60th percentile are pulling apart or because those in the 80th to 90th percentile are pulling sharply upward. For illustrative purposes, it may help to think of the income distribution as a rubber band:

Rubber band representation - 50-90%

When you stretch a rubber band, the ends get further away from each other:

Rubber band representation - 50-90%

But that movement may be because of stretch at the upper end:

Rubber band representation - 80-90%

Or nearer the middle:

Rubber band representation - 50-60%

Using data from the Current Population Survey Annual Social and Economic Supplement for the years 1977-2014, we explore this question in more detail by breaking down the distribution into smaller component parts, or bits of the rubber band. Specifically, we calculate how much of the gap between incomes at the 6th and 96th percentiles can be accounted for by each of the six-percentile gaps along the way (i.e., 6/12, 12/18, 18/24, and so on, up to 92/96). We restrict our data to those between the 6th and the 96th percentile because the CPS has poor data beyond those limits; this means that we are unable to capture the extent to which inequality is driven by the extreme edges of the distribution—a common enough problem in studies of inequality. (For more details on our data and analysis, see the technical appendix at the end of this piece.)

We assess “stretchiness” across three variants of the income distribution, each one narrower than the last:

  1. Total family money income
  2. Family wages and earnings
  3. Family wages and earnings for families with at least one full-time earner

In each case, we adjust income for family size. It is important to note at the outset that our approach is insensitive to changes in the actual size of the income gap: we are simply looking at how much of that the gap is a result of “stretch” at different points in the distribution.

Money income: Income stretchiness at the top and bottom

Analyzing our full sample and broadest definition of income (family-size adjusted money income for all families), it is immediately clear that most of the stretch takes place at the top and bottom of the distribution. As Figure 1 shows, our highest and lowest slices (96/90 and 12/6) account between them for about 30 percent of the total stretch between the 6th and 96th percentiles:

Figure 1: family-size adjusted money income, all families over time

Since there is so little stretch in the middle, we next combine the nine slices between the 24th and 78th percentiles, in order to simplify the presentation of the data. While this middle section of the rubber band accounts for about 40 percent of the total stretch, the top (78th to 96th) and bottom (6th to 24th) chunks account for about 25 and 35 percent, respectively:

Figure 2: family-size adjusted money income

There does not appear to have been very much change in the stretch points in the distribution over time. At least since the mid-1970s, the majority of the stretch has been concentrated at the poles of the distribution. The only apparent shift is that since the 1990s, there seems to have been a reduction in the amount of stretch at the bottom of the distribution, and there was a little more stretch at the top, especially for the 96/90 gap during the 1990s (visible in Figure 1 especially). This is consistent with the body of research suggesting a ‘pulling-away’ of incomes towards the very top of the distribution in recent decades.


The income measure examined above is broad—including not only wage and salary income, but also capital income and cash transfers. But as well as overall inequality, many policymakers are also concerned with one particular source: the labor market. Next we restrict our income measure to wages and salaries, and again look for the stretch:

Figure 3: family-size adjusted wage and salary income, all families over time

Figure 4: family-size adjusted wage and salary income

Most of the stretch in the wage-only income distribution is, as for total money income, at the top and the bottom, although separation at the bottom of the distribution accounts for more of the gap. But the real difference is in the historical trend. In 1975, almost half of the total stretch in the 96/6 distribution was accounted for by the gap between the 24th and 6th percentiles. That share has steadily declined—in large part due to the decline in the 12/6 gap, with a corresponding increase in the stretch at the top of the distribution.

Full-time earners: Symmetrical stretching

There is a potential problem, however, with restricting our income measure to wages but still including all families. The preceding analysis included a large number of families containing people who are not working, either because they are out of the labor force or because they are unemployed. To the extent that these people are concentrated at the bottom, we may therefore be “artificially” over-stretching that part of the distribution (since they will report zero earnings). Other studies have dealt with this shortcoming by looking only at the wage income of fully employed males. We adopt a similar approach by limiting our scope to families with at least one member (whether male or female) working full-time for a wage or salary. Using this sample allows us to focus on families who are more strongly connected to the labor market. The picture that emerges is indeed quite different to the previous one:

Figure 5: family-size adjusted wage and salary income, earner families

Figure 6: family-size adjusted wage and salary income, earner families

While there is still more stretch at the top and bottom, the picture is less dramatic than in our earlier analyses. In particular, the stretch is no longer so concentrated in the bottom quarter of the distribution. Again, there is a slow shift over time with a slight increase in the stretchiness at the very top (96/90th gap), and a decrease in the stretchiness at the very bottom (12th/6th gap). One interpretation of these results is that compared to the 1970s, among full-time workers very low earners are doing better relative to low earners, while very high earners are slightly pulling away from merely high earners.


Our goal was not to investigate changes in inequality or the income distribution, but to examine changes in the distribution of inequality—in other words, how the rubber band of the distribution stretches at different points, at different times. As already noted, we are not able to reach the outer edges of the income distribution. We have also selected a particular set of outcomes and sampling approach. Our results should therefore be seen as illustrative, rather than definitive. Nonetheless, some patterns emerge.

First, there is little change over time in the middle of the income distribution. It is important not to confuse the issue of income inequality with the “state of the middle class” (if by that we mean those in the middle of the income scale). Our findings suggest that income gaps across the broad middle of the distribution—from about a quarter to three-quarters of the way up—account for about as much of top-bottom income inequality today as they did 40 years ago. The action is at the ends.

Second, while much of the political rhetoric is focused on inequality at the top, a large chunk of overall top-bottom inequality is due to gaps at the very bottom—the 24/6 gap or even the 12/6 gap. Policymakers seeking to combat inequality overall need therefore to focus on ways to lift the incomes of the very poorest, to get them closer to the middle class, rather than simply helping the middle class catch up with the rich. Inequality is a poverty story, too.

Technical note


We use 1977-2014 Current Population Survey Annual Social and Economic Supplement data, corresponding to income earned in 1976-2013, from IPUMS CPS. This includes the 1988b and 2001s iterations of the survey.


Our unit of analysis is the family. We include all families whose head (or spouse of head) is between the ages of 25 and 62.[1] Unrelated individuals living together (e.g., roommates) are treated as separate family units as are multiple families residing in the same household.


We use two different measures of family income: wage and salary and total money income. Total money income is derived from pre-tax income from wages, self-employment, capital income sources, and cash government transfers (e.g., Social Security, public assistance, etc.). Given inconsistencies in top-coding schemes across survey years, we use the revised income top-codes based on the rank proximity swapping method released by the Census Bureau for the years 1975-2010.[2] Subsequent surveys use this top-coding scheme by default. We exclude any family income observations which fall at or below zero.


For each family, we identify the age of the head of family, or in the case of married-couple families, the age of the older person in the head-spouse pair. We drop any family where the age of the head (or the spouse) is below 25 or above 62.

We rank families by year according to their size-adjusted income. We determine income ranks of individuals based on their income in the size-adjusted family income distribution, i.e., 5th percentile, 10th percentile, 15th percentile, etc. As a result, each income quantile contains equal numbers of individuals, not families.

We calculate logged income ratios for selected ranks within the size-adjusted family income distribution. Eliminating the tails, we measure how much of total inequality, as measured by the 96/6 gap, can be explained by gaps across different subsets of the income distribution.

“Earner” sample

For a portion of our analysis, we limit our sample to families which contain at least one civilian worker, male or female, who reported working at least 40 hours per week for wages or salary.[3]

[1] Sixty-two is the earliest age at which Americans can claim retired-worker benefits from Social Security.

[2] The files are available to download here:

[3] This is admittedly a “rough” definition of earners as it removes some people who are in the labor force, but aren’t classified as full time.

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