One of the most established measures of income inequality is the Gini coefficient that ranges from zero to one if only nonnegative incomes are taken into account. A Gini coefficient of zero represents perfect equality, i.e., everyone receives the same income. In contrast, a Gini coefficient of one implies perfect inequality with only one person receiving the total income in a population. Section 4.1 explains the decomposition of the Gini coefficient used in this study before Sects. 4.2 and 4.3 present the associated results for highly and less educated females and males with respect to the 2005–2018 ACS samples.

Lambert and Aronson (1993); Mookherjee and Shorrocks (1982), and Bhattacharya and Mahalanobis (1967) show that the Gini coefficient G of total income Y can be decomposed into

$$\begin G=G_+\sum p_a_G_+R. \end$$

(1)

The term \(G_\) denotes the between-groups Gini coefficient, in which every income in every subgroup is replaced by its respective subgroup mean. The variables \(p_\) and \(a_\) represent the population and income share of subgroup k, respectively. The Gini coefficient within subgroup k is denoted by \(G_\), and R is a residual that is equal to zero if the subgroup income ranges do not overlap. In this study, I split the population into two subgroups: subgroup \(k=1\) consists of individuals whose total income is equal to zero (\(Y=0\)) and subgroup \(k=2\) represents individuals with positive total income \((Y>0\)). These assumptions imply \(a_=0\), \(G_=0\), \(a_=1\), \(R=0\), and \(G_=1-p_\).Footnote 6 Hence, the associated decomposition of the overall Gini coefficient G is given by

$$\begin G= & G_-G_G_+G_,\\= & Z_}}+G_.\nonumber \end$$

(2)

This equation shows that the Gini coefficient G depends on the between-groups Gini coefficient \(G_\), the within-subgroup Gini coefficient \(G_\) among individuals with positive total income, and a (negative) composition effect due to interactions between \(G_\) and \(G_\). Moreover, compared with studies restricted to individuals with positive total income, the term \(Z_}}=G_-G_G_\) can be interpreted as the contribution of individuals with zero income (ZI) to overall inequality if this subgroup was additionally taken into account.

Furthermore, because total income is the sum of different income types, I follow Hungerford (2020) and decompose \(G_\) by different income sources using the method developed by Lerman and Yitzhaki (1985):

$$\begin G_= & \sum _Z_=\sum _S_G_R_, \end$$

(3)

in which the term \(Z_=S_G_R_\) represents the contribution of income source i to the overall Gini coefficient \(G_\). This approach is particularly interesting as it provides a more detailed picture of inequality between the respective age groups. The variables \(S_\) and \(G_\) denote the share in total income and the Gini coefficient of income component i, respectively. The term \(R_\) measures the ”Gini correlation” between income component i and total income. To keep the analysis tractable, I divide total income into the aforementioned six categories from Sect. 2 such that L = . Hence, the final total decomposition of the Gini coefficient G is given by

$$\begin G= & Z_}}+Z_}}+Z_}}+Z_}}+Z_}}+Z_}}+Z_}}. \end$$

(4)

For the 2005 ACS sample, the two panels in the first row of Fig. 1 present the age-group-specific Gini coefficients of total income of less (LE) and highly (HE) educated females (F), as well as the decompositions with respect to the income components ZI, WI, BI, SSBI, RI, AI, and OI. The x-axes denote the age groups. In these panels, the absolute contributions of each income component to inequality are displayed as stacked bar plots such that the age-group-specific vertical sums are equal to the respective Gini coefficients of total income, denoted by black dots at the midpoint of each age interval.

Decomposition of Gini coefficients of total income - Females (F) with high (HE) and low (LE) education

The left panel of the first row shows that the inequality of total income of highly educated females aged 26–35 was relatively low with a Gini coefficient of 0.44 and increased to 0.50 in the age group 36–45, mainly due to higher contributions of the wage income component WI to overall inequality, as displayed by the blue areas. Inequality then fell again and followed a weakly pronounced U-shaped pattern, with the Gini declining to 0.46 in the age group 46–55 and then rising again to 0.50 for females in the age groups 66–75. Thereafter, the Gini coefficient remained relatively constant among females aged 76–85. This pattern mainly resulted from a steady decline in WI, which was increasingly outpaced by larger contributions of the asset and retirement income components AI and RI with increasing age, according to the gray and dark green areas, respectively. Moreover, Social Security benefit incomes SSBI, which are displayed in orange, marginally decreased the overall inequality in the age group 56–65 due to a negative correlation with total income and contributed to a higher level of inequality among the older age groups. Furthermore, the contributions of business incomes BI and other incomes OI to overall inequality, see the yellow and light green areas, respectively, were relatively small across all age groups. In contrast, as the beige areas show, the zero income component ZI made more pronounced contributions to inequality in the first four age groups with females aged 26–65 because it accounted for a greater share of total inequality. On average, this share was equal to 11.77% in these age groups. Compared with highly educated females, the corresponding right panel shows that females with a low educational level faced higher levels of inequality in the first four age groups, whereas inequality was considerably lower in the last two age groups. Specifically, the Gini coefficient of less educated females at ages 26–35 was much higher, by as much as 18.28%, and amounted to 0.53, which only slightly decreased to 0.51 among females aged 46–55. Then, inequality increased to its maximum of 0.54 in the age group 56–65, before it steadily declined to 0.43 in the oldest age group 76–85. As the decompositions show, the contributions of ZI were much more pronounced in the first four age groups with less educated females at ages 26–65. On average, its relative contributions amounted to 16.90% and, therefore, explained a higher share of total income inequality in these age groups. Moreover, compared with highly educated females, the contributions of SSBI to overall inequality were much more pronounced in the two oldest age groups comprising females between ages 66–85. However, the income sources AI and RI particularly contributed much less to inequality in these age groups, which is why the Gini coefficients of total income declined.

The bottom four rows of Fig. 1 show how total income inequality evolved in each age group from 2005 to 2018. In these panels, the black dashed lines with dots represent the evolution of the normalized Gini coefficient (NGC) with 2005=100 as the base year. Moreover, the stacked bar plots display the associated absolute changes of each income component with respect to 2005, which were divided by the corresponding Gini coefficients of 2005 and multiplied by 100. Thus, these bar plots show the contributions of all income components to inequality growth in that the vertical sums are equal to the relative changes in the 2005 Gini coefficients. For the readers’ convenience, I centered these changes at the 100 line in each panel, so the sums coincide visually with the NGCs. Stacked bar plots above (below) this line, therefore, represent positive (negative) changes. The x-axes denote the time in years.

The panels in the second and the third row of Fig. 1 display the evolution of inequality among highly educated females. They show that, up to 2018, the NGCs of age groups 26–35 and 36–45 weakly declinded by 0.35 and 0.96%, respectively. In particular, the inequality among females at ages 26–35 first decreased during the Great Recession and then increased only temporarily in the subsequent periods, while it remained fairly stable over time with respect to females aged 36–45. By contrast, females at ages 46–55 and 56–65 faced the most pronounced increases in inequality until 2018. Their NGCs rose by 8.75 and 7.49%, respectively. Especially the wage component WI and, to a much lesser extent, the zero income component ZI contributed to these large increases of inequality, which were only slightly dampened by lower contributions of the remaining income components (in particular BI and AI). However, the NGC of females aged 66–75 increased by only 1.12% until 2018 due to much more pronounced declines of the asset income component AI that partly offset the similarly strong increases in WI between 2009 and 2018. Moreover, the NGC of females aged 76–85 temporarily rose by 6.24% until 2008, whereas the younger age group 66–75 faced a weak increase of only 2.29%. This was primarily attributable to higher contributions of AI, which decreased and even turned negative in the following years, so the NGC declined until 2011. Thereafter, inequality increased again due to the higher contributions of RI and WI, which outweighed the declines in AI and OI. The last two rows of Fig. 1 present the corresponding results for females with low levels of education. In contrast to highly educated females at ages 36–45, the NGC strongly increased by 4.98% among less educated females in the same age group until 2018. The decompositions show that this difference mainly resulted from very high contributions of the zero income component ZI to inequality since the effects of the remaining income components on inequality almost cancelled each other out. Furthermore, the NGCs of the other age groups followed qualitatively similar trends. Note, however, that the contributions of the zero income component ZI were also more pronounced in most of these age groups, in particular in the youngest age group comprising less educated females at ages 26–35.

Decomposition of Gini coefficients of total income - Males (M) with high (HE) and low (LE) education

Fig. 2 is analogous to Fig. 1 except that it displays the age-group-specific decompositions of inequality for males (M). Comparing highly (HE) and less (LE) educated males in the first row, the Gini coefficient of highly educated males at ages 26–35 was slightly lower and amounted to 0.39 in 2005, whereas the corresponding value was equal to 0.40 among less educated males. Then, the inequality among highly educated males increased to 0.48 up to age group 66–75, before it decreased to 0.47 in the oldest age group. In contrast, the Gini coefficient of males with low levels of education only increased to 0.45 up to age group 56–65 and then decreased to 0.42 in the oldest age group 76–85. Thus, the decline of inequality among less educated males in the oldest age groups was somewhat more pronounced. Compared with males holding a college degree, the associated decompositions show that especially the income components RI and AI contributed less to overall inequality among males with low educational levels in the two oldest age groups 66–75 and 76–85, so they dampened the higher contributions of SSBI to inequality. Moreover, the influence of the wage income component WI on overall income inequality became less important with increasing age for both education types across all age groups and was primarily replaced by the income components AI, RI, OI, and SSBI. Furthermore, the zero income component ZI explained, on average, only 2.17% of total income inequality in the youngest four age groups comprising highly educated males between ages 26–65. However, it accounted for a much higher share of total income inequality among males with low levels of education in these age groups, which was on average equal to 5.27%. Additionally, note that the business income component BI generally contributed more to overall inequality than ZI. On average across all age groups, BI explained 9.21 and 8.88% of total inequality among highly and less educated males, respectively.

The bottom four rows of Fig. 1 display the corresponding evolutions until 2018. Overall, inequality increased relatively uniformly among both highly and less educated males across all age groups. On average, across all age groups, the normlalized Gini coefficients of males with and without a college degree increased by 6.38% and 7.41% from 2005 to 2018, respectively. The associated growth decompositions show that the observed increases in inequality among both highly and less educated males were primarily attributable to increases in the wage income component WI up to age group 66–75, whereby the zero income component ZI, in particular, reinforced the increases of inequality among less educated males in the youngest three age groups 26–35, 36–45, and 46–55. Moreover, males at ages 66–75 and 76–85 with a low educational level also faced relatively large increases in SSBI, while retirement incomes RI mainly contributed to a higher level of inequality among highly educated males in the oldest age group 76–85. Moreover, irrespective of educational status and similar to the analysis with respect to females in Fig. 1, the contributions of the business income component BI were rather negligible in the oldest age groups, whereas they dampened the observed increases in inequality in younger age groups; in particular among highly educated males in the age groups 36–45, 46–55, and 56–65. Furthermore, asset incomes AI primarily contributed to the observed rises of inequality among both highly and less educated males in the oldest age groups 66–75 and 76–85 until 2008. Thereafter, this income component, however, rather dampened the increasing levels of inequality in most of these age groups up to 2018.