National Poverty Center Working Paper Series
#08-02
January 2008
Social Policy and Income Inequality
Christopher Bollinger, Department of Economics, University of Kentucky
James P. Ziliak, Department of Economics, Center for Poverty Research, University of
Kentucky
This paper is available online at the National Poverty Center Working Paper Series index at:
http://www.npc.umich.edu/publications/working_papers/
Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do
not necessarily reflect the view of the National Poverty Center or any sponsoring agency.
Social Policy and Income Inequality
Christopher Bollinger
Department of Economics
University of Kentucky
James P. Ziliak
Department of Economics
Center for Poverty Research
University of Kentucky
May 2007
Revised January 2008
* Address correspondence to James P. Ziliak, Department of Economics, University of
Kentucky, Lexington, KY 40506-0034; Email: jziliak@uky.edu; Phone: 859–257–2776. We
thank Luis Gonzalez for excellent research assistance, and seminar participants at the 2007
Institute for Poverty Research Summer Workshop for comments on an earlier version. All errors
are our own.
Social Policy and Income Inequality
Abstract: We document the economic, demographic, and social policy forces underlying
changes in income inequality among single mother families over the past twenty-seven years in
the United States. Using data from the 1980–2006 waves of the March Current Population
Survey, we construct additively decomposable measures of after-tax income-to-needs inequality
into the major income factors of earnings, transfers, other income, and taxes, and also into
within- and between-group inequality based on employment status, education attainment, age,
past marital status, and race. Our results indicate that income-to-needs inequality rose nearly 50
percent between 1980 and 2006. Employing Quandt-Andrews tests of unknown change point we
identify a trend break toward higher inequality centered in 1994 just as major tax and welfare
reform policies, and a business-cycle expansion were taking hold nationally. The post 1994 rise
in inequality is driven by a 75 percent increase in the cross-sectional variance of income accruing
in large part to strong income growth in the upper half of the distribution. A decomposition
focusing on the components of total income indicates that the rise in income inequality among
single mothers is driven by higher earnings inequality, and that most of the change in inequality
is occurring within demographic groups in part because of large, offsetting between-group
changes in population shares and relative incomes.
1
Documenting the sources of widening inequality in the United States continues to be a
focal research priority in economics. This vast literature has linked the growth in inequality to
expanding college-high school premiums (Bound and Johnson 1992; Katz and Murphy 1992),
rising returns to unobserved skills (Juhn, Murphy, and Pierce 1993), falling rates of unionization
and the real value of the minimum wage (DiNardo, Fortin, and Lemieux 1996; Lee 1999), social
norms (Piketty and Saez 2003), and the composition of the workforce (Lemieux 2006), among
others. While the debates on the relative contribution of each factor are ongoing, this research
has deepened our understanding of the fundamental mechanisms behind rising inequality
(Lemieux 2008). At the same time, much of the literature, and the complementary work on
volatility (Gottschalk and Moffitt 1994; Dynarski and Gruber 1997; Haider 2001; Blundell,
Pistaferri, and Preston 2006), has focused on men, and when women are considered, distinctions
are typically not made based on important demographics such as employment status, marital
status, and race. 1 This omission inhibits a more complete portrait of inequality in America, and
especially a greater understanding of the possible links between social policy reforms affecting
single mother families and inequality.
In this paper we present new evidence on the economic, demographic, and social policy
forces underlying changes in income inequality among single mother families over the past 27
years. Perhaps no other demographic group was singled out by policy in the 1980s and 1990s as
prominently as single mothers with dependent children. President Reagan set in motion the
retrenchment of the cash welfare program Aid to Families with Dependent Children by
increasing the implicit tax rate on earnings and reducing the liquid asset level necessary to
1
Notable exceptions are the articles by Karoly (1993), Gottschalk and Danziger (1993), and Cancian, Danziger, and
Gottschalk (1993). The data in these papers focus on the 1970s and 1980s, and thus do not span most of the major
reforms to social policy affecting single mother families. Gottschalk and Danziger (2005) do make some allowance
for nonemployment in some of their estimates of family income inequality. Keys (2007) is among the first to
examine women in the volatility literature.
2
qualify for benefits as part of OBRA 1981. This retrenchment was completed by President
Clinton with passage of the 1996 Personal Responsibility and Work Opportunity Reconciliation
Act, which abolished AFDC and replaced it with the new time-limited, block-grant program
Temporary Assistance to Needy Families (TANF). Concurrent to restrictions to cash welfare
were enhanced incentives for single mothers to work via expansions in the Earned Income Tax
Credit (EITC) as part of the Tax Reform Act of 1986 and OBRA 1990 and 1993, as well as
expansions in Medicaid program eligibility and later the introduction of the Supplemental
Children’s Health Insurance Program as part of OBRA 1997. In 1991 Congress was required to
modify rules for child eligibility in the Supplemental Security Income (SSI) program in light of
the Supreme Court’s 1990 Zebley decision that ruled unconstitutional previous guidelines. The
revised rules resulted in a large increase in children participating in SSI, including many from
single mother families on the AFDC program (Kubik 1999; Schmidt and Sevak 2004).
A burgeoning literature, much of which is summarized in the survey chapters in Moffitt
(2003), emerged in the wake of these reforms addressing outcomes such as employment, income,
poverty, welfare participation, childbearing, marriage, and health, among others. Virtually all
research on the effects of social policies on the well being of single mothers has focused on
average impacts, and while this frequently is of first-order importance to program evaluation, it
limits our understanding of program effects at other moments of the distribution including
inequality. There are some recent exceptions to the focus on the first moment. Mills, et al.
(2001) use non-parametric density re-weighting techniques to compare the single mother family
income distribution in 1993 to 1999, and their counterfactual experiments suggests that most of
the income gains in that six year period were from strong economic conditions and higher
education attainment and not welfare reform. Schoeni and Blank (2000) compare the effects of
3
welfare waivers and TANF across education groups at the 20th and 50th percentiles of family
income, and find that waivers did not alter the distribution of income but that TANF raised
incomes at the 50th percentile while leaving the 20th percentile unchanged. Meyer and Sullivan
(2006) compare trends in the distribution of income and consumption of single mother families
in the Consumer Expenditure Survey, arguing that consumption is a superior measure of well
being especially at the low end of the distribution. Bitler, et al. (2006) use data from a random
assignment experiment in Connecticut to examine heterogeneous treatment effects of welfare
waivers on employment. Bollinger, et al. (2007) estimate quantile treatment effects of social
policies and the business cycle on income and earnings, finding that TANF raised disposable
incomes an average of eight percent among higher skilled mothers, but that it also resulted in a
significant equal-size loss of after-tax total income among the low-skilled, and income fell
upwards of 20 percent in response to TANF in the lower-tail of the distribution.
We extend the literatures on inequality and on social policy by quantifying the
contributions of economic and demographic factors on changes in the level and trend of after-tax
income inequality among single mother families. Using data from the 1980-2006 waves of the
March Current Population Survey, our focal measure of inequality is the squared coefficient of
variation in age-adjusted disposable income-to-needs ratios. This index is in the family of
generalized entropy measures and has several desirable properties, the most important of which
for our purpose being that it is additively decomposable into the components of income as well
as into within-group and between-group inequality (Shorrocks 1980, 1982; Mookherjee and
Shorrocks 1982; Jenkins 1985). The additivity property is not guaranteed with more common
measures of inequality such as the Gini coefficient, the variance of log income, or 90-10 ratios.
We focus on income inequality rather than hourly wage inequality because of the large number
4
of non-working single mothers prior to the mid 1990s and the subsequent changes in the
composition of their income from transfers to earnings (Bollinger, et al. 2007). 2 This leads to
another key advantage of the squared coefficient of variation over other measures like the
variance of logs or 90-10 ratios because the squared CV is still defined even if some of the
income factors are zero, such as earnings for non-workers or transfers for non-welfare recipients.
Most of the inequality literature examines changes in trend inequality across decades or
by 5-year intervals, and we do so as well. However, there is no formal statistical basis for
decades or 5-year intervals, and so an additional contribution of our paper is to treat the break
point as an unknown parameter to estimate by employing Quandt-Andrews type tests of
structural change (Quandt 1960; Andrews 1993), coupled with confidence intervals around the
breakdate (Bai 1997). With the estimated breakdates in trend inequality we then use methods
proposed in Mookherjee and Shorrocks (1982) and Shorrocks (1982) to additively decompose
changes in inequality into changes in the key income factors of earnings, transfers, other
nonlabor income, and tax payments and EITC credits, as well as changes in within-group and
between-group inequality based on employment status, education, age, marital status, and race.
We identify a rise in disposable income inequality of about 50 percent among all single
mothers between 1979 and 2005, and this rise in inequality appears to have affected all major
subgroups of single mothers. The Quandt-Andrews tests of structural change, which control for
the business cycle, indicate that the trend break in inequality is centered around periods of policy
reforms—the breakdate for each of disposable income, earnings, and taxes is 1994 with a 95
percent confidence interval of one year, which coincides with the implementation of welfare
reform at the state level, the expansion of the EITC, and the robust macroeconomy. The post
2
As noted by Lemieux (2008) most of the inequality literature focuses on wages because trends in within-group
inequality of men were not robust to the use of weekly wages as in Juhn, et al. (1993). In future work we plan to
explore whether this non-robustness result extends to the single mother population as well.
5
1994 rise in the squared coefficient of variation is driven by a 75 percent increase in the crosssectional variance of income accruing in large part to strong income growth in the upper half of
the distribution, the latter of which corroborates recent work on wage inequality (Autor, et al.
2005). The results of our decompositions indicate that nearly all of the increase in income
inequality among single mothers is attributable to rising earnings inequality, though the rise in
inequality was tempered by the progressive income tax system including the EITC. Moreover,
most of the change in inequality is occurring within groups in part because of large, yet
offsetting, between-group changes in population shares and relative incomes.
II.
Data
The data derive from the 1980–2006 waves (1979–2005 calendar years) of the March
Annual Social and Economic Study of the Current Population Survey (CPS). The unit of
observation is single female family heads between the ages of 16 and 54 with dependent children
present under the age of 18. Single heads include never married women as well as those
divorced, separated, or widowed. In a bid to minimize measurement error in some of our
subgroup analyses we allocate each mother to one of forty-five five-year birth by education
cohorts, where three separate education groups of less than high school, high school graduate,
and more than high school are assembled, and drop cohort-education cells with fewer than 50
observations (Blundell et al. 1998).
The key variable of interest is disposable family income-to-needs, defined as gross
income less net tax payments relative to the family-size and year-specific poverty threshold. For
our purpose gross income is the sum of family income and the imputed value of public food
assistance programs. Family income is the same as that used in official Census Bureau
calculations of poverty and inequality and includes earnings, Social Security (retirement,
6
disability, and survivors benefits), Supplemental Security Income, Unemployment Insurance,
workers’ compensation, AFDC/TANF and other forms of public cash welfare, veterans’
payments, pension income, rent/interest/dividend income, royalties, income from estates, trusts,
educational assistance, alimony, child support, assistance from outside the household, and other
income sources. We define earnings as total family earnings from wage and salary income, nonfarm self employment, and farm self employment. Because the Census Bureau defines a family
as two or more persons related by birth, marriage, or adoption, family earnings contains earnings
of the mother as well as dependent children and other related adults such as a resident
grandparent. It does not contain earnings of cohabiting partners or other non-family members in
the household. We append to family income the (Census Bureau’s) imputed dollar value of
public food assistance programs, which includes the Food Stamp Program and the National
School Lunch and Breakfast Programs.
To construct after-tax total income we subtract tax payments from gross income and add
back refundable EITC income. Tax payments are the sum of Federal, state, and payroll taxes that
are estimated for each family in each year using the NBER TAXSIM program. The TAXSIM
module calculates Federal, state, and payroll marginal tax rates and tax payments using basic
information on labor income, taxable nonlabor income, dependents, and certain deductions such
as property tax payments and child care expenses. 3 The Federal and state taxes include the
respective EITC code for each tax year and state, thus allowing for the possibility of negative tax
payments. We assume that the family only bears the employee share of the payroll tax rate. To
control for changes in average family size over the twenty-seven years of our sample, we deflate
after-tax income by the family-size specific poverty threshold. Because the poverty thresholds
3
The CPS does not have information on certain inputs to the TAXSIM program such as annual rental payments,
child care expenses, or other itemized deductions. We set these values to zero when calculating the tax liability.
7
have been critiqued over the years on many dimensions (Citro and Michael 1995), including the
quality of the adult equivalent scale used, we also present our main inequality estimates
unadjusted for family size.
If the respondent refuses to supply earnings or transfer information, then the Census
Bureau uses a “hotdeck” imputation method to allocate income to those with missing data.
Bollinger and Hirsch (2006) argue that including allocated data generally leads to an attenuation
bias on estimated regression coefficients based on imputed data. Bollinger and Hirsch (2007)
also show that, for women, there appears to be no selection bias for dropping employed women
who fail to report earnings. Hence, we follow their recommendation and drop those mothers
with allocated earnings or transfer income. In addition, 0.7 percent of the remaining sample has
negative or zero values for total income, and we drop these observations. All income sources are
deflated by the personal consumption expenditure deflator with 2005 base year. The total number
of observations is 99,769 single female-headed families. Basic summary statistics are provided in
Appendix Table 1.
III.
Trends in Income Inequality of Single Mothers, 1979–2005
Our focal measure of inequality is a member of the generalized entropy class of
inequality indices, which is given as
(1)
κ
⎫⎪
1
1 n ⎧⎪⎛ yi ⎞
Iκ =
1
−
⎬, κ ≠ 0,1
∑⎨
κ (κ − 1) n i =1 ⎪⎩⎜⎝ y ⎟⎠
⎪⎭
where yi is disposable income-to-needs for family i, y is average disposable income-to-needs,
and κ reflects an ‘aversion to inequality’ with lower values implying greater aversion to
inequality (Shorrocks 1980; Cowell 2000). Although a wide variety of inequality measures are
available, the generalized entropy class has several desirable properties including that it satisfies
8
the Pigou-Dalton principle of transfers so that it records a rank-preserving increase in inequality
with transfers from a poor person to a less poor person, it is scale invariant which is useful for
making inequality comparisons across groups and time, it has useful stochastic dominance
properties for ranking income distributions (Fomby, et al. 1999), and perhaps most important for
our purpose here, the generalized entropy class provides consistent and additively decomposable
measures of inequality. These exact decompositions can be made by subpopulations such as
employment status, education, age, and race into within and between group inequality
(Mookherjee and Shorrocks 1982), and into income factors such as earnings and transfers both at
a point in time and over time (Shorrocks 1982). More common measures such as the Gini
coefficient, the Atkinson index, the variance of log income, or percentile ratios such as 90-10 are
not additively decomposable and thus do not provide consistent decompositions across groups.
For example, Cowell (1988) notes that it is possible with the log variance to have a change in the
income distribution that leaves between group inequality constant, raises inequality within each
group, and yet results in lower total inequality, which is clearly an undesirable property.
For most of our analyses we set κ = 2 , which yields I 2 = 0.5* CV 2 or one-half of the
squared coefficient of variation. Aside from the decomposability properties mentioned above a
key advantage of I2 is that this summary measure is still defined even when some of the income
components used in factor-share decompositions are zero. This is important in our sample
because many single mothers do not work, do not receive transfers, or do not have other forms of
nonlabor income (e.g. transfer income for the non-poor).
To net out any life-cycle age effects on income to needs we use an age-adjusted measure
of inequality. Specifically, we estimate via OLS the linear model of disposable income-to-needs
on a quartic in age. That is, for person i, i = 1,…, N, at time period t, t = 1,…, T, we estimate
9
(2)
yit = α + β1ageit + β 2 ageit2 + β3 ageit3 + β 4 ageit4 + ε it ,
where ε it is a mean zero random error. Because the mean of the fitted OLS residual, εˆit , used in
the denominator of equation (1) is zero, the residual-based version of I2 is undefined. Thus, in
order to ameliorate this shortcoming, we add to each observation in a given year the year-specific
mean of the predicted dependent variable, εˆi + yˆt , which results in a non-zero mean but has no
impact on the year-specific estimated variance.
A.
Aggregate Trends in Inequality
Figure 1 depicts the trends in inequality for disposable income-to-needs and for
comparison purposes we also depict inequality trends in disposable income levels. The trends in
both series are identical, but in most years the level of inequality is higher once adjustments are
made for family need standards. We also present the 95 percent confidence interval for the
income-to-needs measure of I2 constructed from 100 replications of the nonparametric bootstrap.
Because the unadjusted income inequality series is generally contained within the income-toneeds confidence interval we focus our ensuing discussion on income-to-needs.
Figure 1 shows a trend increase in inequality from 1979 to 1985, which coincides with
the inequality literature on men, but little change for the next decade except for 1987. After
1994, however, inequality begins a strong upward drift rising by over 60 percent between 1994
and 2004 before settling back down in 2005 at a level that is over 20 percent higher than 1994.
What is striking about the trend in inequality is how volatile it becomes after 1994. The time
series was relatively stable for the 15 years prior, but it becomes unstable after 1994 with large
spikes in 1996 and 2004. Even though the I2 is estimated precisely in each year (the bootstrap tstatistic rejects the null that it is zero with test statistics ranging from 7 to 22), the confidence
10
intervals widen markedly after 1994 such that the lower bound indicates little change over time
in inequality whereas the upper bound suggests that inequality has doubled.
Although the inequality series appears to change in the mid 1990s around the time of
major social policy reforms, it is also important to determine whether the series differs in a
statistical sense. One approach is to parametrically fit a series of trend break points in the mid
1990s and test for a structural change point. In lieu of arbitrarily choosing break points in the
inequality series, we instead turn to the recent time series literature on testing for structural
change with an unknown change point (Andrews 1993; Bai 1997; Hansen 2001). Because these
tests have not to our knowledge been applied in the inequality or social policy literatures a brief
summary of the procedure is warranted.
The tests build on an idea due to Quandt (1960), who proposed splitting the sample at
every possible breakdate, estimating the model parameters separately on the two sub samples,
and constructing the associated Chow test statistic for all possible sample splits (any subsample
must have more observations than parameters estimated). The estimated breakdate is the sample
split with the largest value of the Chow test statistic. If the breakdate is known a priori then one
can appeal to the usual chi-square tables for critical values. However, in many cases the
breakdate is not known and the chi-squared critical values are not valid. Andrews (1993)
developed the asymptotic theory for the case of unknown change point and provided tables of
critical values, and consequently the new tests are generally known as the Quandt-Andrews supWald statistic. As noted by Hansen (2001), this method of least squares testing for structural
change is valid for the linear regression model with homoskedastic variances, and Bai (1997)
proposed a straightforward method of constructing confidence intervals around the breakdate.
11
To implement the tests we take our estimated univariate time series of residual inequality
displayed in Figure 1 and run the following regression:
(3)
2
In
2 (t ) = σ 1 + θ1t + ζ 1 , t = 1,...,τ
(t ) = σ 2 + θ t + ζ , t = τ + 1,..., T
In
2
2
2
2
2
where In
2 (t ) is the estimated residual inequality, σ j , j = 1, 2 is a constant term (reflecting the
constant inequality), θ j , j = 1, 2 is the coefficient on the linear trend t, ζ is an iid random error
term, τ is the unknown breakdate, and T = 27 for the years calendar years 1979–2005. For each
possible breakdate, τ , we conduct the joint test of the null hypothesis of constant inequality
( σ 12 = σ 22 and θ1 = θ 2 ) by constructing the following Wald test statistic
(4)
W = ( SSE pooled − ( SSE1 + SSE2 )) / ( ( SSE1 + SSE2 ) /(T − 2 * l ) )
where SSE pooled is the sum of squared errors for the pooled regression with no break, SSE1 and
SSE2 are the sum of squared errors for the pre- and post-break periods, respectively, and l is the
number of parameters in each subsample. The estimated breakdate is the τˆ with the maximum
test statistic Ŵ , i.e. the supWald statistic. The associated Bai (1997) confidence interval for τˆ
c
⎡
⎤
with trending regressors is ⎢τˆ ± ( + 1) ⎥ . The term c is the critical value for a test of size α (c=7
Lˆ
⎣
⎦
when α = 0.1 and c=11 when α = 0.05 ) and L̂ is the outer product of the fitted valued of the
γˆ′ZZ ' γˆ′
, with γˆ = [σˆ j , θˆj ] and
regression standardized by the estimated error variance, Lˆ =
2
ˆ
σ
Z = [1, t ] and where t is set at the estimated breakdate τˆ (See Bai (p. 555) for additional details).
In Table 1 we report the Quandt-Andrews supWald test statistics for age-adjusted
residual inequality, along with the estimated breakdate, and the associated 95 percent confidence
interval. Because the determinants of income, and thus income inequality, are affected by the
12
business cycle (Solon, et al. 1994; Ziliak, et al. 1999), we conduct our Quandt-Andrews tests
controlling for the macroeconomy, including the unemployment rate, constructed by the Bureau
of Labor Statistics, and the growth rate in real chain-weighted GDP, constructed by the U.S.
Department of Commerce. Because our test contains a constant term, trend, and the two
business-cycle controls, l = 4 , which reflects the fact that by construction the tests allow for
structural change in the coefficients of all included regressors. The corresponding critical values
for the l = 4 case are 13.82, 15.84, and 20.24 for the 10 percent, 5 percent, and 1 percent levels
of significance, respectively (Andrews 1993).
In the first row of Table 1 the supWald statistic of 23.7 clearly rejects at the 1 percent
level the null hypothesis of no structural change for disposable income-to-needs inequality.
Moreover, what appears as obvious in Figure 1 is indeed statistically validated in that the
estimated breakdate occurs in 1994 and with a tightly estimated one-year confidence interval
between 1993 and 1995. Because the tests of structural change in Table 1 are not based on fullyspecified multivariate models we are cautious about making causal statements attributing
increasing inequality to welfare reform and the EITC, but we do note that the result is robust to
exclusion of business cycle factors in results not recorded (though with wider confidence
intervals).
To better understand why inequality is more volatile over the past decade in Figure 2 we
depict trends in the mean and variance of disposable income-to-needs. The figure makes
transparent that the instability in I2 in Figure 1 is driven by a massive increase in the variance of
income among single mother families. Mean income is stable through the early 1990s and then
begins a steady secular climb before plateauing in 2001. The variance likewise is stable into the
early 1990s, but then rises by 75 percent between 1994 and 2005, with an even larger spike in
13
2004. The rise in cross-sectional income variance in this population has not been previously
established and suggests that the social policies and macroeconomy of the mid 1990s affected
much more than the first moment of the income distribution.
Before proceeding it is important to address two measurement issues, one related to top
coding at the high end of the distribution and one related to income underreporting at the low end
of the distribution. Burkhauser, et al. (2007) recently showed that the Gini coefficient and 90-10
ratio are sensitive to income top coding in the CPS. Because the coefficient of variation, and thus
I2, is top sensitive, it is possible that our measure also is affected by top coding in the CPS. We
examined the extent of top coding across all the subcomponents of income in our sample of
single mother families and in most years there were no top-coded observations, but top coding
became more prevalent in beginning in 1998, which is consistent with Burkhauser, et al.;
however, unlike the general population, top coding never affected more than 0.2 percent of the
sample of single mother families. Thus, top coding appears to be an inconsequential issue for this
population. Meyer and Sullivan (2006), on the other hand, argue that income among single
mother families in the CPS at the lower tail of the distribution is mismeasured because of
underreporting of transfer income, especially beginning in the mid 1990s, and thus consumption
is a superior measure of well being. 4
Although a comparison of income to consumption is beyond the scope of the current
project, we first examine the possible influence of underreporting of transfers, as well as the
sensitivity of I2 to outliers at the high end of the distribution, by depicting various percentiles of
the income distribution from the 2nd percentile (p2) to the 99th percentile (p99) in Figure 3. We
present the percentiles in terms of real 2005 dollars, and not income to needs, in order to
4
Though Bollinger (1998), using data in the CPS matched to Social Security records, shows that if anything the
poor overstate earnings in the CPS relative to administrative Social Security data.
14
highlight the comparatively low incomes of this population relative to percentiles from the whole
population as presented in Piketty and Saez (2003). For example, among single mothers, the 99th
percentile in 1998 is $75,250 compared to over $230,000 reported for the entire tax-paying
population.
In Figure 3 we observe no discernable long-term downward trend in income at the low
end of the distribution. For example, the average level at the 2nd percentile is $533 from 1979–
1994 and $545 from 1995–2005 (recall 1994 is the estimated breakdate in inequality). Like
Meyer and Sullivan (2006) we do find a 30 percent reduction in after-tax income at the 2nd
percentile across the 1993–1995 and 1997–2000 periods, which spans the enactment of
PRWORA. But we also find a 42 percent reduction when comparing the 1980–1982 and 1983–
1986 periods which spans the major reforms to AFDC enacted by President Reagan, though
there is no evidence of an increase in transfer underreporting in the mid 1980s. We also note that
there is a 15 percent increase in after-tax income at the 2nd percentile when comparing the 1997–
2000 and 2001–2004 periods. Although this does not speak directly to the dominance of
consumption relative to income as a metric of well being, it does suggest that such a case be
based on strong theoretical arguments in addition to measurement because there is no consistent
long-term pattern of income declines among very poor single mothers (at least in the CPS).
At the same time Figure 3 does reveal evidence of a strong trend in income beginning in
the mid 1990s in the upper half of the distribution. We next attempt to gauge the impact of the
lower and upper tails of the distribution on our estimated inequality series in Appendix Figure 1.
In the figure we depict the original untrimmed series along with the estimated I2 where (a)
income at the second percentile and below is trimmed, and (b) income at the ninety-eighth
percentile and above is trimmed. The appendix figure shows that inequality is lower as expected
15
with the bottom 2 percent trimmed, but the series lies within the 95 percent confidence interval
of the untrimmed series. However, with the top 2 percent trimmed inequality is constant and lies
below the confidence region in every year. This suggests that among single mother families
rising inequality in the 1990s is an phenomenon heavily concentrated in the upper tail of the
income distribution similar to the trend in the general population (Piketty and Saez 2003; Autor,
et al. 2005). Indeed, in results not tabulated, the Quandt-Andrews test places the structural break
at 1998 for p75 thru p98 with a one-year confidence interval, and at 1993 with a three-year
confidence interval for p99.
B.
Factor Decomposition of Inequality
We now explore whether the rising inequality depicted in the previous section can be
attributed to changes in one or more of the income sources derived by families. As highlighted in
Grogger (2003) and Bollinger, et al. (2007), there have been substantial changes in the level and
composition of income among single mothers, with a massive shift away from transfers and
toward labor market earnings. We examine whether the shift in income composition contributed
to the rise in inequality. Specifically we decompose disposable income-to-needs into four factors
(5)
yit ≡ earningsit + transfersit + otherit − taxesit
where earnings refers to total labor market earnings in the family, transfers refers to income
from the AFDC/TANF program, the SSI program, the Social Security and Disability Insurance
programs, and the Food Stamp Program, other refers to other nonlabor income from both public
and private sources, and taxes refers to the sum of federal, state, and payroll tax payments
inclusive of the refundable portion of the federal and state EITC. These four major factors are
isolated to highlight the potential contribution of rising employment rates to earnings, the
contribution of declining welfare and food stamp income and rising disability payments in the
16
1990s, the contribution of income from other household members, and finally the inequality
reducing impact of progressive income taxes including the EITC. 5
Shorrocks (1982) shows that the generalized entropy class of inequality measures is
additively decomposable into the contributions of income factors such as that described in
equation (5), which implies that we can write I2 as
4
(6)
I2 = ∑ S f
f =1
where f = earnings, transfers, other , taxes and S f ≡ ρ f
σf
I . ρ f is the correlation coefficient
σy 2
between factor f and total disposable income to needs y, σ f is the standard deviation of income
factor f, and σ y is the standard deviation of disposable income-to-needs. Note that the product
of the correlation coefficient and the ratio of the standard deviations is simply the coefficient
from a least squares regression of disposable income-to-needs on income factor f. The advantage
of I2 is clear in this decomposition because the values of factor f may be zero for many
households, e.g. zero earnings for nonworkers or zero transfers for non welfare recipients, and
yet I2 is still defined in these cases (note that the variance of log income fails here).
Figure 4 depicts trends in the cross sectional decomposition of disposable income-toneeds inequality into its factor shares. 6 Both earnings and other nonlabor income lie above the
x-axis because they are ‘disequalizing’ and contribute to inequality and both transfers and taxes
lie below the x-axis as they are ‘equalizing’ factors in the distribution of income. The four
factors of income inequality shown in the figure are quite stable from 1979 to 1994, but after
1994 earnings inequality accelerates, and to a lesser extent so too inequality of other income but
5
See the series of papers in Slemrod (1994) on the role of tax policy on overall income inequality.
As with total income, we conduct our decomposition of factor shares based on residual earnings, transfers, other
nonlabor income, and taxes from a regression of each factor on a quartic in age.
6
17
only until 1998 when it falls back to the level in 1994 and remains constant thereafter. The
Quandt-Andrews tests reported in rows 2–5 of Table 1 generally corroborate the picture in
Figure 4 in that the null of no structural break in inequality of the income factors is rejected and
with the exception of transfers the estimated breakdate is 1994. Furthermore, Figure 4 suggests
that the bulk of the cross-section instability after 1994 depicted in Figure 1 emanates from rising
inequality in the labor market. The major equalizer is the tax system, both through the
refundable EITC and progressive marginal tax rates. In a typical year prior to 1994 the tax
system reduced inequality by about 33 percent, but after 1994 this share rose 8 percentage points
to 41 percent. Perhaps surprising, income transfers have never played a significant role in
reducing inequality among single mothers, averaging about 8 percent prior to 1994 and 3 percent
after 1994. So while there was a massive rundown in welfare caseloads after 1994, the transfer
income losses do not appear to be a major contributor to the significant rise in inequality.
C.
Sub-Group Decomposition of Inequality
The factor share decompositions indicated that the inequality of earnings is the major
factor determining the inequality of income among single mothers in any given year. The share
attributable to earnings rose further in the mid 1990s, which coincides with rising employment of
this demographic group (Meyer and Rosenbaum 2001; Grogger 2003; Bollinger, et al. 2007) and
suggests a potentially important role of employment for the trend in inequality. Figure 5 shows
the trend in I2,k where k represents workers and non-workers respectively. The figure shows that
income inequality actually rose much more dramatically among non-workers than workers—
between 1994 and 2005 a 90 percent increase for non-workers and 23 percent increase for
workers. Table 2 presents Quandt-Andrews tests of structural change for the group-specific
inequality series and the tests indicate structural breaks in 1994 for workers and 1998 for non-
18
workers, though the latter has a 4-year confidence interval. This highlights growing instability
among single mothers disconnected from the workforce (Blank 2007), but it also poses a prima
facie puzzle in light of the results indicating the primacy of earnings inequality in explaining
income inequality.
To examine in more detail the relative roles of between-group (e.g. workers versus nonworkers) inequality and within-group inequality, in this section we consider sub-group inequality
decompositions based on employment status. We also consider other demographic splits based
on education attainment, age, past marital status, and race because the groups historically at
highest risk of welfare use and thus likely affected by social policy reforms of the 1990s are the
less educated, the young, the never married, and African Americans (Moffitt 1992; Blank 1997).
The generalized entropy measure of inequality is once again useful here because it is additively
decomposable into within-group and between-group contributions to inequality, and only
depends on a few, easily obtained factors. Mookherjee and Shorrocks (1982) show that the I2
index can be decomposed as
K
(7)
I 2 = ∑ ωk μk2 I 2, k +
k =1
1 K
∑ ωk [μk2 − 1]
2 k =1
where the first term is within-group inequality and the second term is between-group inequality,
and the three determinants are the group-specific population share ωk ( k = 1,..., K ), the square of
2
⎛y ⎞
the relative mean of group k, μ ≡ ⎜ k ⎟ , and the group-specific inequality I 2,k .
⎝ y ⎠
2
k
Figures 6 through 10 depict the within- and between-group decomposition of equation (7)
for our selected demographic groups (employment status, educational attainment, age, marital
status, and race). For each figure we depict overall within- and between-group inequality, and
also show the contribution of each sub-group to within inequality. In Figure 6 this means that we
19
have a total of four lines based on employment status—overall within-employment and betweenemployment inequality, as well as the contributions to within-employment inequality by workers
and non-workers (the sum of these latter two figures yields the overall within-employment
inequality). Figure 6 reveals that most of the inequality in any given year is accounted for by
inequality within employment status (88 percent on average), and because approximately 90
percent of within-group inequality is attributable to workers, the figure also confirms the
importance of earnings to within-group inequality highlighted earlier. Figure 6, coupled with
Table 3, helps reconcile the puzzle raised earlier in Figure 5 which showed rising inequality
among non-working families. Note that the inequality trends of workers and non-workers in
Figure 5 do not account either for changes in the population shares of each group or the average
income accruing to each group. However, Table 3 shows that the population share and relative
mean income of non-working single mothers plummeted by over one-third between 1980 and
2005, and while inequality within the group of non-workers increased in Figure 5, the declining
population shares and relative incomes reduced their contribution to overall inequality as
depicted in Figure 6.
Figures 7–10 suggest that a similar story to Figure 6 in that nearly all of the inequality in
a given year is due to within-group inequality and very little is attributed to between group
differences. Within-group inequality among single mother families is most prominently affected
by those with more than a high school education, those age 31 and older, those widowed or
divorced, and those who are white. Table 3 provides five-year snapshots of population shares,
relative mean incomes of each group, and group-specific inequality. The table indicates that the
trend towards greater inequality (a) within higher educated mothers is explained in part by their
rising share of the population, (b) within older mothers is explained by an upward shift in the age
20
distribution of mothers, (c) within widowed and divorced mothers is explained both by the rising
inequality within the group and their rising share of relative income even though the population
share of never married single mothers more than doubled over the past 25 years, and (d) within
white mothers is explained by rising inequality within the group coupled with their sizable shares
of the population and mean income.
D.
Changes in Inequality over Time
The decompositions in Sections B and C are a time series of cross sectional relationships
and thus provide a snapshot at various points of time of the income sources and/or demographics
determining inequality. However, the trends do not speak directly to the underlying sources of
change in inequality over time. A long standing approach in the inequality literature to examine
changes in inequality is to adopt the so-called shift-share method that takes a given factor, say
education, and asks questions such as ‘what would inequality in 2000 be if education attainment
remained fixed at levels in 1980?’ (DiNardo, et al. 1996; Mills, et al. 2001; Autor, et al. 2005;
Lemieuz 2006). This approach is attractive because it offers transparent counter-factual
decompositions of income distributions. However, as argued by Mookherjee and Shorrocks
(1982) it is less useful when there are multiple changes occurring simultaneously (as affected
single mothers over the past two decades) because it is difficult to determine the relative
importance of each factor to trend inequality, and the combined effects of the changes do not
necessarily sum up to total inequality, i.e. it is possible to over- or under-explain trend inequality
with shift-share analyses.
A preferred alternative is to adopt the decompositions described in equation (6) and (7) as
they aggregate changes in sources exactly into the changes in total inequality; that is, changes in
income factors or changes in within and between group inequality add up to changes in total
21
inequality. Specifically in the case of determining how changes in income factors affect changes
in inequality between any two periods t and t+1 Jenkins (1985) shows that we can rewrite
equation (6) as
4
(8)
ΔI 2 ≡ I 2 (t + 1) − I 2 (t ) = ∑ ΔS f
f =1
which means that the change in inequality across any two years is the simple sum of changes in
the factor components. Likewise we can decompose the changes in within-group and betweengroup inequality by taking the difference in equation (7) between periods t and t+1 and
rearranging to yield
(9)
K
K
K
k =1
k =1
k =1
ΔI 2 = ∑ ωk (t ) μk2 (t )ΔI 2, k + ∑ Δωk μk2 (t + 1)[ I 2,k (t + 1) + 0.5] + ∑ ωk (t )Δμk2 [ I 2,k (t + 1) + 0.5]
which says that the change in inequality is due to (a) a change in within-group inequality, (b) a
change in population shares, and (c) a change in relative mean incomes. 7
The next step is to choose the relevant periods t and t+1 to conduct the decompositions of
inequality change. The bulk of the literature on both inequality and volatility proceeds by
choosing decades such as the 1970s, 1980s, and 1990s or 5-year intervals within decades to
conduct counter-factual experiments. This choice is based largely on convention. However,
Figure 1 and Table 1 are striking in that there is compelling evidence of a structural break in
trend inequality around 1994, and that this break point overlaps with major reforms to social
policies including welfare reform and EITC expansions. Consequently, we consider three time
decompositions—the change in inequality across the entire sample period of 1979 to 2005, the
change in inequality prior to the structural break (1979–1994) and the change after the structural
7
Mookherjee and Shorrocks (1982) note that there is an index number problem here in that the decomposition in
equation (9) uses current period values of population shares and (t+1) values of inequality and income shares, but it
is possible to reverse the order. For transparency we just present the results from equation (9).
22
break (1994–2005), and the change in inequality across five-year intervals (we include the extra
period in the first change of 1979 to 1985). To facilitate comparisons across the multiple
changes, and to guarantee adding up, we divide both sides of equations (8) and (9) by the base
year inequality I 2 (1979) and report the results as percentage changes. 8
Table 4 presents the results of the income factor change decompositions of equation (8).
In the first row of Table 4 we see that by 2005 inequality as measured by I2 rose by 49 percent
above the baseline value in 1979, and that in the absence of the progressive U.S. tax system
inequality would have been 18 percentage points higher. Prior to the 1994 breakdate, inequality
rose by 23 percent, and then it rose an additional 26 percent thereafter (relative to 1979).
Quantitatively there is little difference across periods in the relative contribution of each factor to
inequality, though transfers actually became disequalizing after 1994. The five-year inequality
change decompositions show considerable within-period variation in the relative roles of
earnings, transfers, other income, and taxes on inequality. In most cases inequality would be
significantly higher in the absence of income taxes, though there are some exceptions. Taxes
were disequalizing between 1985 and 1990 and again between 2000 and 2005, perhaps reflecting
the tax cuts associated with the 1986, 2001, and 2003 tax reforms. This merits future research on
both the population of single mothers as well as the broader population of taxpayers.
In Table 5 we record the results of the demographic change decompositions of equation
(9). Across the entire sample the bulk of the 49 percent rise in inequality is attributed to a rise in
within-group inequality regardless of the group selected to conduct the decomposition.
However, this is often because of large, offsetting changes in the two terms affecting betweengroup inequality. For example, there was a large and disequalizing increase in the share of single
8
In some cases rounding error after the calculations may result in some rows not adding up.
23
moms with more than high school between 1979 and 2005, but the relative mean incomes of this
population fell over the period suggesting a shift in the placement of higher educated single
mothers toward lower income earners relative to two decades ago (see Table 3). A similar
scenario unfolded based on employment status of single mothers as well as past marital status.
After 1994 there was a substantial increase in the contribution of employment to inequality, but
these new workers were placed in the lower end of the distribution and thus reducing the relative
mean income of workers, which equalized incomes in the overall population of single mothers.
In the case of marital status, there was an equalizing shift in the population toward never-married
mothers, but their relative mean incomes fell compared to widowed, separated, and divorced
mothers. Examining the inequality changes across sub-periods reveals a similar trend in favor of
within-group changes being the prominent factor in changes in inequality, but again often
because of substantial offsetting changes in relative population shares and relative mean
incomes. This suggests that the time-series of cross-sectional decompositions of within- and
between-group inequality in Figures 6–10 understate the role of important between group
changes in inequality over the past two decades arising from large shifts in employment status,
education attainment, age, and previous marital status.
IV.
Conclusion
We identify an increase in disposable income-to-needs inequality of about 50 percent
among single mothers in the United States over the past 27 years. Our statistical tests identified
a break in trend inequality toward higher inequality between the years 1993 and 1995—a period
that was characterized by major changes in the U.S. tax and transfer system, and was also in the
early stages of the longest post-war business-cycle expansion. Further analysis suggests that the
rise in income inequality was driven largely by higher earnings inequality, and most of the
24
increase was manifested in the form of higher within-group inequality rather than across broad
demographic groups of mothers. The role of between-group inequality was attenuated because
of offsetting changes in relative population shares and mean incomes across groups.
After-tax incomes of single mothers rose significantly between the mid 1990s and mid
2000s, ranging from 20 percent growth at the 25th percentile to nearly 40 percent growth at the
99th percentile. However, the rise in the cross-sectional variance swamps the increase in income
levels—the variance rose 75 percent on average—which fueled the rise in inequality identified in
the squared coefficient of variation. Much of this increase in income inequality comes from the
upper half of the income distribution, which corroborates recent work on the wage inequality of
men and women by Autor, et al. (2005). The latter finding begs the question as to what role
social policy played given that most of the policy changes were targeted to lower-income
populations. Here it is important to remember just how low incomes actually are among single
mothers compared to the general population. Median after-tax income of single mothers
averaged $20,590 in real terms, which is near the poverty line for a 4-person family in current
dollars, and after-tax income at the 75th percentile averaged $28,566 in real terms, which still
makes a single mother with two qualifying children income eligible for the EITC. This implies
that programs such as the EITC reach fairly high into the income distribution of single mothers,
such that the positive labor supply and earnings effects of TANF and the EITC reported in Meyer
and Rosenbaum (2001), Grogger (2003), and Bollinger, et al. (2007) likely contributed to the rise
in inequality. Although we are cautious in making explicit causal statements, our results add to
the mounting evidence summarized in Lemieux (2008) that institutions play a significant role in
accounting for rising inequality in America.
25
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Figure 1: Trends in Disposable Income Inequality of Single Mother Families
0.5
0.45
0.4
0.3
0.25
0.2
0.15
0.1
0.05
Year
Income Levels
Income to Needs
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
0
1979
0.5*Squared CV
0.35
Mean
Year
Variance
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
$2005
31
Figure 2: Trends in the Mean and Variance of Disposable Income to Needs
2.5
2
1.5
1
0.5
0
32
Figure 3: Trends in Percentiles of Disposable Income
120000
100000
80000
$2005
60000
40000
20000
-20000
Year
p2
p5
p10
p25
p50
p75
p90
p95
p98
p99
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
0
33
Figure 4: Factor Decomposition of Disposable Income to Needs Inequality
0.6
0.5
0.4
0.2
0.1
-0.1
-0.2
Year
earnings
transfers
other
taxes
total
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
0
1979
I(2), S(f)
0.3
34
Figure 5: Trends in Disposable Income to Needs Inequality by Employment Status
0.7
0.6
0.4
0.3
0.2
0.1
Year
non-workers
workers
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
0
1979
0.5*Squared CV
0.5
35
Figure 6: Trends in Within and Between Group Inequality by Employment Status
0.35
0.3
0.2
0.15
0.1
0.05
Year
within employment
within non-workers
within workers
between employment
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
0
1979
0.5*Squared CV
0.25
36
Figure 7: Trends in Within and Between Group Inequality by Education Attainment
0.4
0.35
0.25
0.2
0.15
0.1
0.05
Year
within education
< 12
12
> 12
between education
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
0
1979
0.5* Squared CV
0.3
37
Figure 8: Trends in Within and Between Group Inequality by Age
0.4
0.35
0.25
0.2
0.15
0.1
0.05
Year
within age
< 30
31-40
> 40
between age
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
0
1979
0.5*Squared CV
0.3
38
Figure 9: Trends in Within and Between Group Inequality by Martial Status
0.4
0.35
0.25
0.2
0.15
0.1
0.05
Year
within marital
separated
widowed/divorced
never married
between marital
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
0
1979
0.5*Squared CV
0.3
39
Figure 10: Trends in Within and Between Group Inequality by Race
0.4
0.35
0.25
0.2
0.15
0.1
0.05
Year
within race
within white
within black
within other
between race
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
0
1979
0.5*Squared CV
0.3
40
Appendix Figure 1: Trends in Disposable Income to Needs with the Lower and Upper 2
Percentiles Trimmed
0.5
0.45
0.4
0.3
0.25
0.2
0.15
0.1
0.05
0
19
79
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
0.5*Squared CV
0.35
Year
Untrimmed
Bottom 2% trim
Upper 2% trim
41
Table 1: Quandt-Andrews Tests of Structural Change of Unknown Breakdate in
Age-Adjusted Income-to-Needs Inequality of Single Mothers, 1979–2005
supWald Statistic
(with cycle)
Break Year
[95% CI]
Total Income
23.71
1994
[93,95]
Earnings
20.78
1994
[93,95]
Transfers
96.78
1986
[84,88]
Other Income
17.58
1994
[93,95]
Taxes
29.97
1994
[93,95]
Note: The years corresponding to the 95% confidence interval (CI) are reported in square brackets.
The supWald Statistic with cycle refers to tests of trend breaks after controlling for the unemployment
rate and growth in real GDP. For the case with k=4 parameters the critical values are 13.82, 15.84,
and 20.24 for the 10 percent, 5 percent, and 1 percent levels of significance, respectively.
42
Table 2: Quandt-Andrews Tests of Structural Change of Unknown Breakdate in
Age-Adjusted Income-to-Needs Inequality of Single Mothers, 1979–2005
supWald Statistic
(with cycle)
Break Year
[95% CI]
Earnings = 0
46.45
Earnings > 0
32.17
1998
[94,02]
1994
[93,95]
White
20.90
Black
25.15
Other Race
14.25
Separated
10.60
Widowed or Divorced
41.93
Never Married
12.76
Age <= 30
26.22
30 < Age <= 40
13.97
Age > 40
23.07
Less than High School
35.19
High School Education
36.45
More than High School
13.36
If:
1994
[93,95]
1994
[93,95]
1991
[88,94]
1994
[92,96]
1995
[94,96]
1995
[94,96]
1999
[98,00]
1999
[98,00]
1995
[94,96]
1999
[98,00]
1994
[93,95]
1995
[94,96]
Note: The years corresponding to the 95% confidence interval (CI) are reported in square brackets.
The supWald Statistic with cycle refers to tests of trend breaks after controlling for the unemployment
rate and growth in real GDP. For the case with k=4 parameters the critical values are 13.82, 15.84,
and 20.24 for the 10 percent, 5 percent, and 1 percent levels of significance, respectively.
43
Table 3: Trends in Inequality, Relative Means, and Population Shares for Selected Groups
1980
1985
1990
1995
2000
2
0.5*CV
0.133
0.188
0.314
0.170
0.299
Non-worker
Relative Mean
0.696
0.685
0.654
0.588
0.437
Population Share
0.263
0.290
0.273
0.226
0.125
2
0.5*CV
0.159
0.187
0.176
0.250
0.202
Worker
Relative Mean
1.108
1.129
1.130
1.120
1.080
Population Share
0.737
0.710
0.727
0.774
0.875
2
0.5*CV
0.161
0.297
0.187
0.351
0.305
Less than 12
Relative Mean
0.806
0.755
0.755
0.743
0.735
Population Share
0.355
0.300
0.276
0.231
0.180
2
0.5*CV
0.148
0.157
0.209
0.281
0.224
High School
Relative Mean
1.016
0.980
0.981
0.939
0.905
Population Share
0.419
0.433
0.436
0.342
0.349
2
0.5*CV
0.144
0.161
0.172
0.223
0.188
More than 12
Relative Mean
1.275
1.308
1.263
1.188
1.171
Population Share
0.226
0.267
0.288
0.427
0.471
2
0.5*CV
0.092
0.139
0.136
0.099
0.174
Under age 30
Relative Mean
1.040
1.007
1.007
0.992
1.008
Population Share
0.365
0.362
0.343
0.316
0.318
2
0.5*CV
0.178
0.216
0.242
0.384
0.213
Age 31-40
Relative Mean
1.021
1.030
1.021
1.011
0.994
Population Share
0.396
0.435
0.441
0.430
0.391
2
0.5*CV
0.388
0.417
0.355
0.346
0.340
Over age 40
Relative Mean
0.905
0.923
0.947
0.991
1.000
Population Share
0.239
0.203
0.216
0.254
0.291
2
0.5*CV
0.210
0.287
0.263
0.436
0.218
Separated
Relative Mean
0.875
0.880
0.883
0.895
0.910
Population Share
0.241
0.222
0.212
0.196
0.142
2
0.188
0.199
0.230
0.233
0.283
Widowed/divorced 0.5*CV
Relative Mean
1.072
1.092
1.113
1.107
1.103
Population Share
0.565
0.523
0.480
0.460
0.455
2
0.5*CV
0.103
0.194
0.152
0.291
0.142
Never married
Relative Mean
0.945
0.915
0.904
0.917
0.916
Population Share
0.194
0.255
0.308
0.344
0.403
2
0.5*CV
0.183
0.205
0.226
0.276
0.235
White
Relative Mean
1.036
1.043
1.050
1.036
1.041
Population Share
0.696
0.695
0.681
0.700
0.699
2
0.5*CV
0.164
0.254
0.195
0.333
0.229
Black
Relative Mean
0.915
0.886
0.886
0.907
0.913
Population Share
0.274
0.279
0.280
0.258
0.256
2
0.5*CV
0.138
0.195
0.255
0.177
0.207
Other race
Relative Mean
0.939
1.056
0.939
0.963
0.866
Population Share
0.031
0.027
0.039
0.042
0.045
2005
0.424
0.435
0.164
0.209
1.111
0.836
0.211
0.703
0.169
0.221
0.852
0.337
0.224
1.202
0.494
0.108
0.972
0.298
0.286
0.995
0.377
0.356
1.032
0.325
0.266
0.899
0.132
0.282
1.129
0.436
0.196
0.901
0.431
0.277
1.036
0.683
0.202
0.914
0.250
0.215
0.959
0.067
44
Table 4: Decomposition of Percentage Changes in Income-to-Needs Inequality by Income Source
Total Period
1979-2005
Pre Break
1979-1994
Post Break
1994-2005
Five-Year Change
1979-1985
1985-1990
1990-1995
1995-2000
2000-2005
Percent Change in I2
Contribution of earnings
Contribution of transfers
Contribution of other income
Contribution of taxes
49
65
2
0
-18
23
34
-2
-1
-8
26
31
4
1
-10
26
4
35
-29
13
24
3
63
-31
6
-3
0
1
5
-2
23
-12
6
-18
2
-17
12
-36
15
7
Note: The decompositions as calculated add up exactly, but some rows may not because of rounding error in converting to integer percentages.
45
Table 5: Decomposition of Percentage Changes in Income-to-Needs Inequality by Subgroups
Percent Change in I2
Total Period
1979-2005
Pre Break
1979-1994
Post Break
1994-2005
Five-Year Change
1979-1985
1985-1990
1990-1995
1995-2000
2000-2005
Pre Break
1979-1994
Post Break
1994-2005
Five-Year Change
1979-1985
1985-1990
1990-1995
1995-2000
2000-2005
47
28
-26
23
13
-11
20
26
33
40
-47
26
4
35
-29
13
23
3
32
-22
6
-20
6
20
39
-16
23
-5
-17
-46
24
Pre Break
1979-1994
Post Break
1994-2005
Five-Year Change
1979-1985
1985-1990
1990-1995
1995-2000
2000-2005
Education Level
Changes in withinChanges in
group inequality
population shares
Changes in relative
mean income
49
44
116
-111
23
18
80
-74
26
27
34
-35
26
4
35
-29
13
24
7
44
-25
9
28
11
41
17
9
-26
-15
-50
-22
-5
Percent Change in I2
Total Period
1979-2005
Changes in relative
mean income
49
Percent Change in I2
Total Period
1979-2005
Employment Status
Changes in withinChanges in
group inequality
population shares
Age
Changes in withinChanges in
group inequality
population shares
Changes in relative
mean income
49
29
17
3
23
16
2
5
26
15
12
-2
26
4
35
-29
13
27
1
29
-31
6
2
2
5
4
6
-3
1
1
-2
1
46
Table 5 continued: Decomposition of Percentage Changes in Income-to-Needs Inequality by Subgroups
Percent Change in I2
Total Period
1979-2005
Pre Break
1979-1994
Post Break
1994-2005
Five-Year Change
1979-1985
1985-1990
1990-1995
1995-2000
2000-2005
Pre Break
1979-1994
Post Break
1994-2005
Five-Year Change
1979-1985
1985-1990
1990-1995
1995-2000
2000-2005
Changes in relative
mean income
49
59
-35
25
23
28
-25
20
26
30
-9
5
26
4
35
-29
13
27
4
35
-25
13
-9
-10
-4
-1
-5
8
10
3
-3
6
Changes in
population shares
Changes in relative
mean income
Percent Change in I2
Total Period
1979-2005
Marital Status
Changes in withinChanges in
group inequality
population shares
Race
Changes in withingroup inequality
49
56
-1
-7
23
26
-3
0
26
27
2
-4
26
4
35
-29
13
28
4
36
-29
16
0
-2
3
0
-2
-2
1
-5
0
0
Note: The decompositions as calculated add up exactly, but some rows may not because of rounding error in
converting to integer percentages.
47
Appendix Table 1: Summary Statistics
Mean
Disposable Income
Disposable Income to Needs
Earnings
Transfers
Other Nonlabor Income
Taxes
Less than High School
High School
More than High School
Age
White
Black
Other Race
Separated
Widowed or Divorced
Never Married
Observations
23134.400
1.502
18347.980
4195.346
3181.597
2590.528
0.246
0.384
0.370
34.698
0.689
0.266
0.045
0.187
0.485
0.327
99,769
Standard Deviation
17168.020
1.127
22857.640
5933.211
8021.257
7770.095
0.430
0.486
0.483
8.140
0.463
0.442
0.207
0.390
0.500
0.469