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What Does Increased Economic Inequality Imply
about the Future Level and Dispersion of Human Capital?
Mary Campbell
Robert Haveman
Gary Sandefur
Barbara Wolfe
University of Wisconsin–Madison
May 6, 2004
We thank the Russell Sage Foundation and its program on the Social Dimensions of Inequality for support for this
research. Special thanks to Andrea Voyer for her insights and help thinking through dilemmas as they arose, to
Susan Mayer for providing us with state gini coefficients and to Kathryn Wilson for calculating models for us that
include measure of school district expenditures. We are very grateful for everything they have added to our study
and for their generous willingness to share both their time and their effort. The authors are listed in alphabetical
order; all contributed equally to the paper.
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Abstract
Does the well-recognized increase in economic inequality among families and neighborhoods
have implications for children who have experienced this development? Are children growing up in a
more unequal economic environment likely to choose less human capital investment (schooling) than they
would if the economic environment were more equal? Or, might a higher level of economic inequality be
related to more schooling (reflecting greater implicit returns to schooling)? Is the disparity in levels of
schooling of a cohort growing up in a more unequal environment likely to be more or less than that of a
cohort reared in a less unequal environment?
In this study we attempt to shed light on these questions. We estimate a stylized model of
children’s attainments using longitudinal data on about 1200 children from the Panel Study of Income
Dynamics. We observe these children over a period of at least 20 years, and statistically estimate the
relationship of the family and regional/neighborhood factors that exist while they are growing up to the
educational choices that they make when young adults. Our human capital variables are completed years
of schooling, graduation from high school and college attendance. The family and neighborhood/regional
economic variables inequality are family income (relative to needs), family net worth (wealth), a state
measure of inequality (the Gini coefficient), and a measure of the accessibility of higher education (the
cost of tuition at state colleges).
We then use the estimated relationships to simulate the effects of changes in the inequality of
family and neighborhood/regional economic variables on the level of youth schooling attainments. We
indicate the effects of changes in economic inequality of the family and regional/neighborhood variables
on both the average level of educational attainment of our cohort of youths, and on the inequality among
these youths in educational attainment.
We conclude that increases in the inequality of economic circumstances of both families and
regions/neighborhoods will have small but slightly positive effects on the average level of schooling.
However, increased inequality in family and regional/neighborhood circumstances is associated with
substantial increases in the inequality of schooling attainments among these youths.
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The past three decades have witnessed substantial growth in economic inequality among families.
For example, between 1973 and 1998, the gini coefficient of income among families rose from .356 to
.430, an increase of 21 percent (see Haveman, Sandefur, Wolfe, and Voyer, 2001). This increase in family
income inequality reflects the net effect of changes in inequality of labor market attainments (wage rates,
working time)1 and public income transfers.
Growing inequality among the geographic areas in which people live—and hence the social
isolation of economic and racial/ethnic groups—has also been studied. Jargowsky (1997) has documented
the social decline in the urban neighborhoods in which many poor and minority children are concentrated,
and Massey (1996) shows that both affluence and poverty became more concentrated between 1970 and
1990.2 Given the conjectures of economists and sociologists concerning the adverse effects on children’s
attainments of growing up in low quality family and neighborhood environments, these trends in
between-jurisdiction inequality are of concern.
In this paper, we explore the relationship between the growth in economic inequality (in both
family and geographic dimensions) and the disparity among youths in their educational attainments. We
study human capital indicators of children’s attainments—the years of completed schooling that they
attain, the probability that they will graduate from high school and the probability they will attend college
or another form of post-secondary schooling. We relate changes in the level and the dispersion of
schooling attainment among a group of young adults to changes in the level of inequality in family
economic position and regional economic performance that may occur during the years when they were
growing up (ages 2–15).
Our analysis rests on two primary conjectures. First, we expect that higher levels of inequality in
family and neighborhood/regional circumstances while growing up will be associated with lower average
1
For example, the inequality of both female and male full-time worker earnings increased by nearly 30
percent over the 1975 to 2000 period.
2
In fact, affluence (persons living in families with an income at least four times the poverty line for a family
of four) is more concentrated than poverty. In 1990, the average affluent person lived in a neighborhood in which
over 50 percent of his neighbors were also affluent while the average poor person lived in a neighborhood in which
just over 20 percent of his neighbors were poor.
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3
levels of educational attainment. This conjecture reflects findings from numerous studies of deleterious
effects of inequality on a variety of social performance measures (See Adler et al., 1994; Marmot et al.,
1991; Diez-Roux et al., 1997; Kawachi and Kennedy 1997). Second, we expect a positive and robust
relationship between both family and neighborhood/regional economic circumstances and measures of
children’s attainments, reflecting the numerous studies of intergenerational linkages in attainments (See
Haveman and Wolfe, 1994, 1995, McLanahan and Sandefur, 1994, and more recently Haveman,
Sandefur, Wolfe, and Voyer, 2001). Because of this relationship, we expect increased inequality in both
family and neighborhood/regional economic characteristics to be associated with greater schooling
disparities among youth.
Mayer (2001) has explored the relationship between inequality in family and regional
circumstances while children are growing up with the level and the disparity in economic attainments
among them during young adulthood. Using data from the Michigan Panel Survey of Income Dynamics
(PSID), she estimates the relationship between state-level economic inequality during adolescence and
eventual educational attainment, distinguishing potentially differential impacts on rich vs. poor children.4
Within-state inequality is measured by a gini coefficient calculated over family income using data from
the decennial census, interpolated linearly to obtain a state inequality measure for each observation at age
14. Control variables include estimated measures of returns to education, region, year, percentage of the
state population that is African-American and Hispanic, mean within-state household income, and
unemployment rate, the log of family income, and a measure of economic segregation within the state.
Separate estimates are made over high- and low-income observations, defined as living in a family above
or below the median level of family income (at ages 12–14).
3
This effect may be mitigated in that decreases in educational attainment may be constrained by legal and
institutional factors (e.g., mandatory school attendance regulations), while choices involving additional schooling
(e.g., college attendance) are less so.
4
Mayer’s sample of children consists of all observations in the data set at ages 12–14, and ages 20 and 23
(when the relevant educational outcome data were available). Measures of within-state economic inequality and
control variables were obtained when the respondents were between the ages of 12 and 14. Mayer considers four
educational outcomes: the probability of high school completion by age 20; the probability of beginning college by
age 23; the probability of completing four years of post-secondary education by age 23; and the number of years of
completed schooling by age 23.
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While Mayer finds very low zero-order correlations between the state ginis and the educational
outcomes—less than -.04 for each outcome—changes in within-state income inequality are positively
related to the educational attainment of higher income children, and negatively related to that of lower
income children in multivariate estimates. She finds that mean educational attainment increases as withinstate income inequality increases. Significant positive coefficients on within-state income inequality are
estimated for higher income observations when years of education (with the base set of controls) and for
college graduation (after adding controls for state educational policies) are dependent variables. Among
lower income respondents, within-state income inequality is significantly and negatively related to only
the years-of-schooling variable.
Mayer concludes that increased within-state inequality is associated with increased overall
educational attainment (primarily due to increasing post-secondary education entrance choices) and
increased inequality in youth educational attainment. Variables reflecting changes in returns to education,
parental income and state-level investments in education are positively related to youth educational
inequality, as these effects tend to be concentrated on youth from higher-income families.
Our study addresses a similar question. We also relate hypothesized changes in a variety of
dimensions of family and geographic inequality to both the average level and the dispersion of children’s
educational attainment. However, rather than relating only changes in within-state inequality to
educational attainments, we directly alter—through simulation analysis—the level of inequality among
the families of children (family income/needs, wealth) and among the states in which children live (as
measured by state-specific gini coefficients of family income/needs and the level of in-state higher
5
education costs). The other unique features of our study are the inclusion of data over nearly all years of
5
While Mayer relates changes in mean educational attainment to within-state income inequality, we adjust
family income/needs, wealth, and across-state inequality and higher education costs back to the original mean, and
then test how changes in these variables influence the mean and distribution of youth educational outcomes. Mayer
suggests that increased returns to schooling contribute to increased income inequality, and hence the level of
educational attainment. However, she argues that redistribution of income from the rich to the poor will increase
mean educational attainment more than would an equivalent increase in incomes across the distribution, provided
the relationship between family income and educational attainment is semi-logarithmic. If a semi-logarithmic
relationship between family income/needs (and wealth and state income inequality and education costs) and
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a child’s life (e.g., family characteristics beginning at the child’s age 2), data measuring the childcare
experiences of the child, information that tracks all the locations a child has lived, and a direct measure of
the cost of post-secondary schooling.
In Section I, we briefly describe the research strategy on which our analysis rests. In effect, we
model the relationship of relevant family and regional/neighborhood characteristics observed for a sample
of children while they were growing up to their educational attainments when they are young adults. We
also describe the data set that we use for the analysis in this section. Section II summarizes the findings
from our analysis in a series of figures and summary measures of levels and disparities among children in
the years of schooling attained. The final section concludes.
I.
RESEARCH STRATEGY AND DATA
In this analysis, we view the schooling choices of youths to be the outcome of a production
process in which both parental choices (or family circumstances) and regional/neighborhood
6
characteristics influence youth outcomes. We estimate the relationship between these family and
regional/neighborhood variables measured for a large sample of children during the childhood years (ages
2–15) to their educational attainments when they become young adults. We use a sparse model that is
motivated by the identification of those relevant family and regional/neighborhood characteristics
variables that are persistently found to be significantly related to years of schooling in the existing
7
research literature.
Our basic data set consists of 21 years of information on 2609 children from the Michigan Panel
Survey of Income Dynamics (PSID). We selected children who were born from 1966 to 1970, and follow
educational attainment exists, increasing the dispersion of family income/needs by a fixed percentage (as we do) will
leave the mean unchanged.
6
Haveman and Wolfe (1994, 1995) discuss the implications of this framework for empirical estimation. In
some formulations, youth choices are modeled as a response to incentives, with family and neighborhood
environment having both direct effects on outcomes, and indirect effects through their influence on incentives. See
Haveman, Wolfe, and Wilson (1997).
7
In Haveman, Sandefur, Wolfe, and Voyer (2001), we present the results of a review of this literature.
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them from 1968, the first year of the PSID (or their year of birth, if later) until 1994–1999. Only those
8
individuals who remained in the survey until they reached age 21 are included. After omitting
observations with missing information in core variables, we have a sample of 906–1210 children
(depending on the outcome of interest), each of whom is observed over a period of at least 21 years.
Our data set contains extensive longitudinal information on the status, characteristics, and choices
of family members, family income (by source), living arrangements, neighborhood characteristics, and
background characteristics such as race, and location for each individual. In order to make comparisons of
individuals with different birth years, we index the time-varying data elements in each data set by age:
that is, rather than have the information defined by the year of its occurrence (say, 1968 or 1974), we
convert the data so that this time-varying information is assigned to the child by the child’s age. Hence,
we are able to compare the process of attainment across individuals with different birth years. All
monetary values are expressed in 1993 dollars using the Consumer Price Index for all items.
We merged Census tract (neighborhood) information from the 1970 and 1980 Censuses onto our
PSID data. The Census data are matched to the specific location of the children in our sample for each
9
year over the years 1968–1985. Based on this link, we are able to include in our data information
describing a variety of social and economic characteristics of rather narrowly defined areas for each
8
Some observations did not respond in an intervening year but reentered the sample the following year.
Such persons are included in our analysis, and the missing information was filled in by averaging the data for the
two years contiguous to the year of missing data. For the first and last years of the sample, this averaging of the
contiguous years is not possible. In this case, the contiguous year’s value is assigned, adjusted if appropriate using
other information that is reported. Studies of attrition in the PSID find little reason for concern that attrition has
reduced the representativeness of the sample. See Becketti et al. (1988), Lillard and Panis (1994), and Haveman and
Wolfe (1994). A more recent study by Fitzgerald, Gottschalk, and Moffitt (1998) finds that, while “dropouts” from
the PSID panel do differ systematically from those observations retained, estimates of the determinants of choices
such as schooling and teen nonmarital childbearing estimated from the data do not appear to be significantly
affected.
9
The links between the neighborhood in which each family in the PSID lives and small-area (census tract)
information collected in the 1970 and 1980 Census have been (painfully and painstakingly) constructed by Michigan
Survey Research Center (SRC) analysts. For the years 1968 to 1970, the 1970 Census data are used in this matching;
for the years 1980 to 1985, the 1980 Census data are used. In most cases, this link is based on a match of the
location of our observations to the relevant Census tract or block numbering area (67.8 percent for 1970 and 71.5
percent for 1980). For years 1971 to 1979, a weighted combination of the 1970 and 1980 Census data are used. The
weights linearly reflect the distance from 1970 and 1980. For example, the matched value for 1972 equals
[(.8 x 1970 value) + (.2 x 1980 value)].
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10
family in our sample, based on their residence in each of the years from 1968 to 1985. In this paper we
use the variables for percent who are high school drop outs and percent in the neighborhood with low
incomes.
From these data, we can also observe a number of measures of educational attainment when a
young adult for each of the children in our sample. We concentrate on three such outcomes—years of
completed schooling, completion of high school, and college attendance—all measured as of age 25.
We have selected four family and neighborhood/regional variables for our exploration of the
effects of changes in inequality on educational attainments. They are:
•
Logarithm of the ratio of the income of the family in which the child grew up to the
poverty line for the family,
•
Level of Net Worth of the family in which the child grew up,
•
Gini coefficient for the state in which the child grew up11, and
•
Cost of state tuition and fees in the state in which the child lived in 1985–1990.12
Table 1 provides unweighted descriptive statistics on all of the variables included in our models.
Three-fourths of our sample youth graduated from high school, nearly thirty percent attended college and
they have a mean educational attainment of 12.18 years of schooling. The corresponding weighted values
10
These characteristics include racial composition, measures of family income and its distribution
(including the proportion of families with incomes below $10,000 and those above $15,000), the proportion of
persons living in poverty, the proportion of young adults who are high school dropouts, the adult and male
unemployment rates, the proportion of families that are female headed, the proportion of those in the labor force in
managerial (professional) occupations, and an underclass count (See Rickets and Sawhill, 1988).
11
If a child moved over ages 12–15, the gini coefficient is a weighted average of the states that the child
lived in where the weights are the years lived in each state.
12
The income variable is measured over the child’s ages 2–15 and included as averages over the preschool
years (2–5), elementary school years (6–11) and secondary school years (12–15); the wealth indicator is measured in
1984 when the youth are age 14–18. The gini coefficient of the state where the child lived (averaged over ages 12–
15, the age when our tests found that there was the greatest impact on outcomes) and the cost of tuition and fees of
the public higher education institutions in the state in which they live (measured in 1987, when the youth were ages
17–21) are neighborhood/geographic variables. Our measure of the gini coefficient is that used by Susan Mayer
(2001). We also planned to explore the effect of changes in the average income of the neighborhood in which the
child grew up over ages 2–15. However in numerous estimates of the effect of a variety of factors on years of
schooling, these neighborhood variables were never statistically significant.
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are 84 percent graduated high school, nearly 40 percent attended college and mean years of schooling
were 12.63.
II.
THE EFFECTS OF FAMILY AND NEIGHBORHOOD/REGIONAL ECONOMIC
CIRCUMSTANCES ON EDUCATIONAL ATTAINMENT
In assessing the effects of increases in the inequality of family and neighborhood/geographic
economic circumstances on children’s schooling attainments, we statistically relate these characteristics to
years-of-completed-schooling, high school graduation, and college attendance. Results from our
estimated models are shown in Table 2.
Our review of the numerous studies of the determinants of children’s attainments available in the
literature (See Haveman, Sandefur, Wolfe, and Voyer, 2001) identified those variables whose relationship
to attainments is persistent, robust and statistically significant. Such variables include parental schooling
attainments, family economic resources (family income and wealth), family structure (for example,
growing up in a single parent family), and the number of geographic moves during childhood. We have
supplemented these with variables describing neighborhood and state circumstances. More specifically
we have measures at the county level (unemployment rate), the neighborhood or census tract level
(percent of individuals who drop out of high school and percent in the neighborhood in low income
families), and at the state level (the state gini coefficient and public tuition and fees). Our estimate
distinguishes the race and gender of the observations. In addition, given the renewed interest in young
children’s experiences we include a variable indicating whether or not more than $1000 was spent on
childcare from ages 2 to 5 as a proxy for having spent extended periods in non-family childcare. The
model we have selected includes all the substantively relevant variables.
The estimated relationships in Table 2 are generally as expected. After controlling for family and
location characteristics, African Americans have higher educational attainment than others, and women
have higher educational attainment than men.13 Women have higher educational attainment than men
13
The positive effect of being African-American after controls is a common finding in studies of
educational attainment.
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before and after controls. Individuals from families where the head is foreign born also have higher levels
of educational attainment.
Parental schooling is positively and significantly related to years of completed schooling and high
school graduation. Surprisingly, parental education is not significantly associated with college attendance
14
after controlling for other variables. In this model the effects of parental education occur through its
effects on family income and family wealth. Family income at ages 2–5 and at ages 12–15 is significantly
associated with years of completed schooling while family income at ages 6–11 is not. We see similar
effects of family income at ages 2–5 and 12–15 on high school graduation whereas family income at ages
6–11 is negatively associated with high school graduation. Only the measure of income for children at
15
ages 12–15 is significantly associated with college attendance. These results provide some evidence to
support other research that appears to show that incomes during early childhood and adolescence are
important determinants of educational attainment, and that family income during adolescence is most
16
important in determining college attendance. Wealth is strongly associated with years of completed
schooling and high school graduation, but not with college attendance. These results imply that wealth
affects college attendance and years of completed schooling through both its effect on high school
graduation and its association with family income during the adolescent years. These results suggest that
family socioeconomic status is strongly associated with educational attainment.
14
We also estimated models in which we specified interactions between race and parental education, an
equation that also included interactions between race and income, unemployment, childcare and tuition and fees (see
Appendix Table 1). The only significant interaction between race and parental education was between race and at
least one parent graduating from high school in the years of education and high school graduation models. The
interaction effect suggested that this variable had a smaller effect for Blacks than for Whites.
15
One must be cautious in interpreting these effects, however, since the measures of family income at the
different ages have correlations ranging from .75 (2–5 and 12–15) and .86 (6–11 and 12–15).
16
The interactions between the income/poverty measure at ages 6–11 and race in the models that included
race and income interactions (see note 14) were significant in the years of schooling models. The interactions
suggested that the ratio of income to the poverty line at ages 6–11 had a positive effect on years of education for
blacks but a negative effect for whites, while the income/poverty ratio at ages 12–15 had a positive effect for whites,
but no effect for blacks. The interaction between the ratio of income to poverty at ages 6–11 and race was also
significant in the model for attending college. This interaction indicated that the income/poverty measure had
positive effects on college attendance for blacks but not for whites.
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The proportion of years that a child has lived with a single parent is not associated with any of the
three educational outcomes. Having lived with a single parent is associated with educational attainment
before controls but its effects are not significant after controlling for the socioeconomic attributes of the
family. The average number of siblings living at home over the course of childhood is associated with
years of education and college attendance but not with high school graduation. The number of residential
moves during childhood, on the other hand, is associated (negatively) with years of completed schooling
and high school graduation, but not with college attendance. Having spent considerable time in formal
childcare as a 2–5 year old is negatively associated with years of completed schooling but not with high
17
school graduation, or college attendance. If we interpret this together with results for higher income
while 2–5, it suggests that the positive association of higher income (due in part to greater work effort) is
partly offset by the negative association of formal childcare.
Finally we look at characteristics of the areas in which people live. We begin with indicators of
the neighborhood in which individuals live. These results show that each schooling outcome is negatively
associated with the percent of the neighborhood that has dropped out of high school. Our county-level
indicator—the average county unemployment rate—is significantly associated with years of completed
schooling and high school graduation, but not college attendance. The state gini is not significantly
associated with any of the educational outcomes. The tuition and fees for attending a public institution in
the state are significantly associated with high school completion and years of completed schooling but
not with college attendance. These effects are reflected in the interaction terms that suggest tuition costs
affect the outcomes for those individuals for which the tuition costs were measured closest to when they
were in their last year of high school.18
17
The model that includes race interactions suggests the negative association between considerable formal
child care and education outcomes is only significant for whites. For whites the associate is significant for both years
of schooling and whether or not a child graduates from high school.
18
In estimates not reported here, we also included a variable measuring school expenditures per pupil. This
required a trade-off as the data set to which we could match school expenditures was a slightly different population
for whom we only had data beginning at age 6. Estimates from this sample, conducted by Kathryn Wilson,
suggested a positive, insignificant and small association between school district expenditures and the educational
outcomes.
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While most of these results are as expected, two comments are in order. First the lack of effects of
some key variables on college attendance may be due, at least in part, to the inclusion of only of
individuals who have completed high school in this part of the analysis. Further, some variables affect
college attendance through their effects on high school graduation. Second, unlike Mayer (2001) we do
not find any significant effects of the state ginis on educational outcomes in the Table 2 estimates, or
when we separately analyzed the high-income and low-income sub-samples. The differences in our
results and those of Mayer are in part due to the smaller sample that we use, but also suggest that the
effects of characteristics such as state ginis with very low correlations with educational outcomes are very
sensitive to model specification.
III.
ESTIMATES OF THE EFFECT OF INCREASED INEQUALITY IN FAMILY AND
NEIGHBORHOOD/REGIONAL ECONOMIC CIRCUMSTANCES ON EDUCATIONAL
ATTAINMENT
We assume that the relationships estimated in this model are reasonable proxies for true causal
relationships. Then, using the relevant estimated coefficients, we simulate the effect of increasing the
inequality in the distribution of four of these family and regional/neighborhood variables (family
income/needs, family wealth, state gini coefficients and state college tuition) on the mean level and the
variance of the distribution of educational attainment.
The simulated increase in inequality is obtained in two steps. In the first step, we increase the
standard deviation of each independent variable (e.g., family income/needs) by an amount consistent with
real changes in inequality between 1970 and 1990.19 To preserve the mean for each variable, we then
adjust each simulated value by the constant required to retain the actual mean level for that variable. As a
19
These changes in inequality were based on changes in inequality from 1970 to 1990 for income and
wealth. The standard deviation of the log of family income increased 9 percent between 1970 and 1990, while the
standard deviation of wealth increased about 25 percent. Changes in inequality in college tuition proved more
difficult to estimate; while the average level of public tuition increased fourfold from 1970 to 1990, information on
inequality between states of public tuition levels is difficult to uncover. Hence, we use a 10 percent increase in
inequality of college tuition at this stage of our analysis, as this value is approximately the increase in tuition
inequality between public 4-year universities and 2-year colleges during this time period. State gini coefficients are
widely available. We have used an estimate of changes in gini coefficients taken from the Current Population
Survey. We increased the gini in each state to correspond with the actual changes that took place between 1970 and
1990.
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second step, we use the estimated coefficients from the model shown in Table 2 together with the adjusted
(more unequal) values of those independent variables being studied (and the actual values of the
remaining independent variables), and predict the value of the relevant schooling attainment outcome for
each observation.
We estimate both the aggregate level of children’s schooling attainment (mean and median years
of schooling) and the inequality of children’s schooling attainment (the standard deviation of years of
schooling). We also estimate the proportion of children who are simulated to not graduate high school and
the proportion not expected to complete 11 years of school, using the adjusted variables of interest. Then,
we compare these medians, standard deviations and proportions with the actual levels recorded in the
data. We present results that are weighted to reflect national levels of attainment for this cohort of
individuals.
Table 3 shows the predicted values of both outcomes, before and after simulated increases in
inequality. The first row in Table 3 shows the mean, median, and standard deviation of predicted values
of years of schooling based on the estimates in Table 2. The last two columns in this row give the
percentage of individuals with less than 12 years of schooling and the percent below 11 years of
schooling. The next four rows summarize the impact on years of schooling of the simulated increases in
inequality in our four independent variables of interest.
The results in the top of Table 3 show that an increase in inequality of family income or wealth
results in an increase in the inequality of schooling outcomes. Changes in the state gini or tuition, on the
other hand, do not lead to changes in inequality in years of completed schooling. The standard deviation
of years of schooling increases by approximately 4 percent when income or wealth inequality increases.
Further these simulated changes increase the percentages of individuals who have less than a high school
education (less than 12 years) and the percentage that completes less than 11 years of school.
In reality, however, we would never expect an increase in income inequality without an increase
in wealth inequality, and it is impossible to see those changes without a corresponding increase in the gini
index. The best indicators of real changes in the inequality of outcomes, therefore, are the predicted
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values when all four factors change. With this scenario, the standard deviation of schooling outcomes
increases even more—by over 8 percent—and there are significant increases in the number of youth not
achieving 11 years of education.20
These numbers are not surprising; they reflect commonly estimated relationships between family
income, wealth, inequality and college tuition and educational outcomes. Importantly, they suggest that
increased inequality in these dimensions increases the disparity in educational attainment among members
of the next generation.
The middle of Table 3 shows the mean, median and standard deviation of the probability of
graduating from high school under different simulated conditions. Not surprisingly, this outcome
indicates a smaller response to simulated increases in family and regional economic inequality. In all
cases, including the base estimate and the simulated estimates, most of the sample is predicted to graduate
from high school. Increases in the inequality of family income and wealth do result in small increases in
the inequality of this outcome as well, although the changes are smaller.21 We conclude that although high
school graduation probabilities are fairly high today in most contexts, increases in family income and
especially wealth inequality would probably result in small increases in inequality for this outcome as
well. When inequality of income, wealth and tuition are jointly increased, the standard deviation increases
by 7.5 percent. The biggest contributor to this increase in inequality is the increase in inequality of wealth.
The last section of Table 3 shows the mean, median and standard deviation of the probability of
attending college for those who graduated from high school. In this case an increase in family income
inequality or wealth inequality is associated with very small changes (around 1 percent) in the probability
20
If we instead base our simulations on the model in which we include race interactions (see note 14
above,) we find similar patterns. In these we simulate that the standard deviation would increase by 7 percent among
whites when all four changes are simulated (from .848 to .906) while for Blacks it would increase by 9 percent or
from .654 to .712. The proportion with less than 12 years of schooling would increase from 17.3 percent (36.9
percent) to 17.6 percent (39.6 percent), respectively, while the proportion simulated to have less than 11 years
increases from 2.8 percent (3.9 percent) to 3.3 percent (4.4 percent). (See Appendix Table 2)
21
The simulated increase in the state gini coefficients suggests an increase in the mean probability of high
school graduation, and a decrease in the variation in this outcome; however, the coefficient on this variable is
marginally significant and the conceptual linkage between college costs and high school graduation is less
convincing than between these costs and years of schooling.
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of attending college when they are considered alone. However, when all four factors changed (or three
factors) change, there is an increase of around 7 percent in the standard deviation or our measure of
inequality of educational outcomes.
We use several other measures of inequality in an attempt to better understand the nature of the
change in schooling in response to the changes in our indicators of changing income and wealth
inequality (income, wealth, state ginis and state public university tuition.). We report the distribution of
probabilities by quintiles (see table 4), which is descriptive. We report the gini coefficient, and a series of
other summary inequality measures (the coefficient of variation, the Theil index, the Theil entropy
measure, the Theil mean log deviation measure, and the Kakwani index).22 These measures were selected
to reflect a variety of inequality attributes of the distributions. The measures we include rank the
distribution of education outcomes with equal weights above and below the average (gini and Theil
index), weights that values observations farthest from the average most highly (coefficient of variation or
CV and Kakwani), and that weights changes in the lower end of the distribution most highly (Theil mean
log deviation and the Theil entropy index) The results are reported in table 5 using both three changes
(income, wealth and tuition) and four (the three plus changes in the state ginis.)
Turning first to the change in the probability of high school graduation, we find that the Gini
coefficient suggests that the probability of high school graduation has become slightly more equal when
we model the four changes, but slightly more unequal if we consider only the three changes. All of the
other measures show an increase in the inequality in the probability of graduating. Most suggest the
22
The gini coefficient is sensitive to changes across the distribution. It meets the criteria of mean
independence (double everyone’s income and the value of the index remains the same), symmetry (it does not
matter is poor only the number who are poor), independence from sample size, and the so-called Pigou-Dalton
transfer sensitivity or inequality is increased when a transfer is made from a poor person to a rich one. It is not
decomposable and tests of significant differences must rely on bootstrapping techniques. We also report the three
Theil entrophy measures which meet all the above criteria including decomposability. The entrophy measure is most
sensitive to changes in the lower end of the distribution while the Theil index is more balanced in giving weight
across the distribution and so is closer to the gini in that regard, the mean log deviation is intermediate giving more
weight to the lower end but less than the entrophy measure. The coefficient of variation is more sensitive to higher
and lower values though it does not meet all of these criteria. The CV is the square root of the variance divided by
the mean. A CV of zero indicates no inequality within a distribution; however, its upper limit, in theory, is infinite.
The Kakwani index is similar to the Gini, which is 1 minus the area under the Lorenz curve measuring the inequality
in the distribution of education (or the probability of achieving a specified level of education), except that the
Kakwani index squares the area under the Lorenz curve so that larger values are given greater weight.
Russell Sage 16
increase is small; the exception is the entropy index which places more emphasis on the change for those
closest to the bottom of the distribution; it shows about a nine percent increase in inequality. Overall the
measures suggest a small increase in inequality in the probability of high school graduation due to the
changes in income, wealth, tuition and the state gini coefficient. The results simulating the three changes
(excluding changes in the state ginis) suggest more substantial increases in the inequality of the
probability of completing high school. Again those that emphasize low valued observations show the
largest increase in inequality.
The results for years of education are more consistent. All of the reported measures of inequality
suggest that the distribution of years of education has become more unequal after the observed changes in
inequality of income, wealth, state incomes and public tuition, or for the three changes excluding state
ginis. The gini coefficient increases by about 8 percent in both simulations; the three Theil indices by
about 16–17 percent; and the CV by about 8 percent or by the same percentage as the gini coefficient. The
simulations are remarkably similar for the three and four income/wealth changes. The pattern suggests an
overall increase in inequality including a considerably greater loss of opportunity at the bottom end of the
distribution.
By every measure simulating inequality for all four changes (income wealth, state ginis and
college tuition), inequality is greater for college attendance than for years of schooling or the probability
of graduating high school. All of the inequality measures show increases in inequality in terms of the
probability of attending college in response to the changes we simulate. In this case we find an increase
that varies from about a three percentage increase for the gini coefficient for all four changes to 17
percent for the two Theil indices that emphasize those at the lower end when including only three changes
in income/wealth inequality. All suggest sizeable increases in the inequality of the probability of
attending college due to the changes in income, wealth and tuition that have taken place in the United
States.
In Appendix Table 2 we present the results for the two racial groups in our sample: whites and
blacks. In all cases we observe the lower levels of education among blacks compared to whites. However,
Russell Sage 17
with few exceptions, the increase in inequality of outcomes is similar for the two groups. The increase in
family income and in family wealth is associated with a substantial increase in inequality of years of
education and the proportion predicted to have less than 11 or 12 years of education. When simulating the
expected change due to an increase in either all 4 or all 3 factors, the standard deviation of each group
increases by about 8.6 percent. However, among non-whites there appears to be a larger difference in the
increase in the standard deviation of years of schooling in response to the simulation of an increase of 25
percent in family wealth (5.6 percent compared to 4 percent.)
Comparing the simulations of mean, median and standard deviation for high school graduates, it
appears that non-whites show a larger expected increase in inequality especially in response to increases
in inequality of family wealth and in response to the changing of the three factors simultaneously (in the
latter case the predicted increase is about 11 percent for non-whites and 6 percent for whites. In the case
of attending college, the exception to the similar pattern among whites and non-whites is the response to
an increase in inequality in family wealth that appears to decrease inequality among whites while
increasing it somewhat among non-whites.
In viewing these simulations, it is important to keep in mind that while we model actual changes
in income, wealth, public tuition and state ginis we do so in a particular way that may not reflect the
pattern of actual changes.
IV.
CONCLUSION
The social science and the policy communities have been concerned for some time about the
possible implications of increases in inequality during the past several years. We know that our society
has experienced increases in inequality in both family income and wealth. We also know that there is
some evidence that individuals and families are becoming increasingly concentrated in either very
affluent or very impoverished areas. The research of Mayer and others suggests that increases in income
inequality as measured at the state level have increased inequality in educational outcomes. Similarly, as
Russell Sage 18
postsecondary education rises in importance, the influence of college tuition levels also gains significance
for understanding educational inequality.
In this paper we pose a related but different question: What may have been the impact of
increases in inequality measured at the family level on educational outcomes in the next generation? Our
results suggest that increases in family income inequality and family wealth inequality have likely
produced an upward influence on the dispersion of educational outcomes. Ceteris paribus, increases in
family economic inequality are associated with increases in inequality in educational attainment in the
next generation. Given the linkage between schooling attainments and labor market success, it seems
likely that increases in inequality in educational attainment will also result in an increase in earnings
inequality. In sum, increases in inequality have important intergenerational effects that we as a society
cannot afford to ignore. If such increases persist across generations, the bottom and top of the education
and income distributions are likely to grow farther and farther apart.
Public policy can be used to alleviate some of the effects of growing inequality on inequality in
educational attainment in the next generation. Compulsory schooling and free public education through
high school creates a threshold of high school graduation below which few people need be. Unfortunately
some people continue to be below that threshold. Efforts to assist low-income students to obtain postsecondary education also help to alleviate some of the impacts of growing income and wealth inequality.
The large increases in the inequality as captured by those indices that emphasize the lower part of the
distribution seem to call for intervention. It appears that without additional public intervention, the
inequality in schooling will increase sizably, and with it prospects for decreasing inequality in income and
wealth in the future.
Russell Sage 19
Table 1
Unweighted Descriptive Statistics
High school graduate
Attended College
Years completed education
African American
Female
Average number of siblings 2–15
At least one parent graduated H.S.
At least one parent attended college
Education info missing for both parents
Log of family income/poverty level, 2–5
Log of family income/poverty level, 6–11
Log of family income/poverty level, 12–15
Proportion years with single parent, 2–15
Number of moves 2–15
Head foreign born
Average county unemployment 2–15
Percent NH dropouts 2–15
Percent NH persons low income 2–15
Log of positive wealth, 1984
Negative wealth, 1984
Wealth missing, 1984
State gini index ages 2–5
State gini index ages 5–11
State gini index, ages 12–15
Tuition & fees per FTE student/1000, Public 85–
90
Public tuition * youngest kids
Child care costs above $1000, age 2–5
Obs
Mean
S.D.
Min
Max
1350
1348
1348
1426
1426
1423
1426
1426
1426
1336
1396
1421
1414
1368
1410
1412
1368
1420
1426
1426
1426
1416
1419
1417
0.73
0.29
12.18
0.45
0.47
2.09
0.61
0.25
0.08
0.58
0.65
0.66
0.27
2.80
0.02
6.61
16.83
27.80
6.77
0.05
0.20
0.37
0.37
0.38
0.44
0.45
1.67
0.50
0.50
1.48
0.49
0.43
0.27
0.64
0.68
0.76
0.37
2.56
0.15
2.12
8.69
14.28
5.03
0.22
0.40
0.03
0.02
0.02
0.00
0.00
2.00
0.00
0.00
0.00
0.00
0.00
0.00
-2.27
-1.48
-1.77
0.00
0.00
0.00
1.50
0.00
2.07
0.00
0.00
0.00
0.33
0.34
0.34
1.00
1.00
17.00
1.00
1.00
8.43
1.00
1.00
1.00
2.79
3.38
3.59
1.00
12.00
1.00
30.67
67.29
75.30
16.12
1.00
1.00
0.43
0.43
0.44
1321
1321
1416
1.59
0.34
0.15
0.54
0.71
0.36
0.705
0.00
0.00
4.78
4.78
1.00
Russell Sage 20
Table 2
Regression Results
African American
Female
Average number of siblings 2–15
At least one parent grad h.s.
At least one parent attend college
Education info missing for both parents
Family income/poverty level, 2–5, logged
Family income/poverty level, 6–11, logged
Family income/poverty level, 12–15, logged
Proportion yrs w/single parent 2–15
# moves 2–15
Head foreign born
Average county unemployment 2–15
Percent NH dropouts 2–15
State gini, avg 12–15
Log of positive wealth, 1984
Negative wealth, 1984
Wealth missing, 1984
Tuition & fees per FTE student, PUBLIC 87
Tuition & fees* youngest cohort
Child care costs above $1000, 2–5
Constant
Observations
Years of Completed
Schooling
OLS Coeff.
0.486***
(0.109)
0.338***
(0.085)
-0.075**
(0.035)
0.381***
(0.113)
0.159
(0.114)
0.462**
(0.181)
0.384***
(0.132)
-0.168
(0.161)
0.336***
(0.118)
0.095
(0.155)
-0.057***
(0.018)
1.189***
(0.306)
-0.053**
(0.023)
-0.024***
(0.005)
0.682
(2.621)
0.050***
(0.017)
0.194
(0.232)
-0.769***
(0.196)
-0.036
(0.091)
-0.154**
(0.064)
-0.210*
(0.123)
11.813***
(1.102)
1209
Standard errors in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
High School
Graduation
Logit Coeff.
0.599***
(0.197)
0.443***
(0.155)
-0.057
(0.059)
0.764***
(0.189)
0.298
(0.241)
0.526*
(0.294)
0.616***
(0.233)
-0.711**
(0.281)
0.625***
(0.205)
-0.078
(0.267)
-0.071**
(0.030)
2.087*
(1.097)
-0.094**
(0.043)
-0.030***
(0.010)
5.076
(4.787)
0.100***
(0.027)
0.252
(0.353)
-0.940***
(0.303)
0.261
(0.170)
-0.224**
(0.114)
-0.349
(0.227)
-1.405
(2.024)
1210
Attend
College
Logit Coeff.
0.694***
(0.202)
0.554***
(0.149)
-0.169**
(0.069)
-0.007
(0.217)
0.196
(0.185)
0.604*
(0.346)
0.384
(0.252)
-0.097
(0.308)
0.574**
(0.226)
-0.081
(0.290)
-0.040
(0.034)
1.114**
(0.505)
-0.011
(0.039)
-0.029***
(0.010)
1.832
(4.592)
0.043
(0.036)
-0.021
(0.504)
-0.766
(0.503)
-0.103
(0.155)
-0.050
(0.117)
-0.040
(0.213)
-1.633
(1.927)
906
Russell Sage 21
Table 3
Comparison of Predicted Values under Simulated Conditions (Weighted)
Years of Education
Predicted Actual
SD of log family income/needs +10%
SD of wealth +25%
Gini + State change in gini
SD of tuition +10%
All four factors changed
Three factors changed
High School Graduation
Predicted Actual
SD of log family income/needs +10%
SD of wealth +25%
Gini + State change in gini
SD of tuition +10%
All four factors changed
Three factors changed
Attend College
Predicted Actual
SD of log family income/needs +10%
SD of wealth +25%
Gini + State change in gini
SD of tuition +10%
All four factors changed
Three factors changed
Mean Years
Median
Years
12.597
12.612
12.636
12.615
12.593
12.665
12.647
12.643
12.670
12.696
12.668
12.639
12.727
12.706
Mean Pred
Prob
Median Pred
Prob
0.829
0.828
0.833
0.843
0.829
0.845
0.831
Mean Pred
Prob
0.428
0.434
0.436
0.438
0.427
0.450
0.441
0.887
0.888
0.896
0.899
0.887
0.908
0.898
Median Pred
Prob
0.415
0.422
0.428
0.429
0.416
0.440
0.430
Standard
Deviation
0.816
0.848
0.852
0.817
0.816
0.885
0.884
Standard
Deviation
0.161
0.164
0.169
0.152
0.161
0.164
0.173
Standard
Deviation
.0198
0.207
0.202
0.199
0.198
0.213
0.211
Percent <12
years
Percent <11
years
19.1%
19.9%
19.6%
19.0%
19.5%
19.1%
19.7%
1.9%
2.1%
2.5%
1.9%
1.9%
2.5%
2.5%
Russell Sage 22
Table 4
Weighted Quintile Probabilities
SD of Wealth
+25%
Gini + State
Change in
Gini
SD of Tuition
+10%
All Four
Factors
Changed
High School Graduation — All respondents
0–0.2
0.4%
0.4%
0.2–0.4
3.8%
4.2%
0.4–0.6
10.2%
10.9%
0.6–0.8
22.5%
22.0%
0.8–1.0
63.0%
62.5%
0.7%
4.7%
10.2%
20.5%
63.8%
0.4%
2.9%
9.3%
21.6%
65.8%
0.5%
3.7%
10.1%
22.5%
62.6%
0.5%
3.9%
10.1%
19.7%
65.2%
High School Graduation — whites
0–0.2
0.5%
0.2–0.4
2.8%
0.4–0.6
7.5%
0.6–0.8
15.7%
0.8–1.0
73.5%
0.5%
3.7%
6.6%
15.5%
73.7%
0.5%
3.9%
5.9%
15.3%
74.4%
0.5%
2.1%
6.4%
14.9%
76.0%
0.5%
2.8%
7.7%
15.7%
72.6%
0.5%
3.0%
5.3%
13.7%
76.7%
High School Graduation — blacks
0–0.2
0.8%
0.2–0.4
5.6%
0.4–0.6
13.9%
0.6–0.8
33.9%
0.8–1.0
45.9%
0.8%
5.6%
14.7%
34.4%
44.5%
0.8%
6.4%
16.5%
28.8%
47.5%
0.3%
4.5%
11.5%
33.9%
49.9%
0.8%
5.3%
14.1%
33.3%
46.4%
0.8%
4.5%
17.3%
29.6%
47.7%
SD of Log
Family
Income/Needs
+10%
SD of Wealth
+25%
Gini + State
Change in
Gini
SD of Tuition
+10%
All Four
Factors
Changed
College Attendance — All high school graduates
0–0.2
14.0%
15.1%
0.2–0.4
32.1%
31.6%
0.4–0.6
35.2%
32.5%
0.6–0.8
15.9%
17.5%
0.8–1.0
2.8%
3.3%
13.9%
31.0%
34.4%
17.9%
2.9%
13.0%
31.6%
35.1%
17.5%
2.9%
14.2%
32.0%
34.8%
15.7%
2.8%
14.6%
29.0%
32.7%
19.4%
3.8%
College Attendance — white high school graduates
0–0.2
9.5%
10.1%
0.2–0.4
31.2%
30.4%
0.4–0.6
37.1%
35.0%
0.6–0.8
18.6%
20.3%
0.8–1.0
3.6%
4.2%
8.4%
30.4%
36.7%
20.5%
4.0%
8.0%
29.5%
36.7%
21.3%
4.4%
9.5%
30.8%
37.1%
18.4%
3.4%
8.4%
27.2%
33.8%
24.5%
5.3%
College Attendance — black high school graduates
0–0.2
22.7%
24.8%
0.2–0.4
33.0%
34.4%
0.4–0.6
29.8%
25.5%
0.6–0.8
12.4%
13.1%
0.8–1.0
2.1%
2.1%
23.0%
31.2%
30.1%
13.5%
2.1%
22.3%
30.9%
30.5%
13.8%
2.5%
22.7%
33.3%
28.7%
13.1%
2.1%
24.1%
31.2%
27.7%
13.8%
3.2%
Predicted
Actual
Predicted
Actual
SD of Log
Income/Needs
+10%
Russell Sage 23
Table 5
Expanded Measures of Inequality
Years of Education
High School Graduation
4 Changes 3 Changes
Actual
4 Changes 3 Changes
College Attendance
Inequality Measures
Actual
Actual
4 Changes 3 Changes
Coefficient of variation
0.065
0.070
0.070
0.194
0.194
0.208
0.462
0.473
0.480
Gini coefficient
0.036
0.039
0.039
0.098
0.095
0.103
0.264
0.271
0.275
Kakwani measure
0.001
0.001
0.001
0.014
0.014
0.016
0.067
0.071
0.073
Theil index (GE(a), a = 1)
0.002
0.002
0.002
0.022
0.022
0.026
0.114
0.121
0.124
Mean Log Deviation (GE(a), a = 0)
0.002
0.002
0.002
0.027
0.028
0.033
0.138
0.150
0.154
Entropy index (GE(a), a = -1)
0.002
0.003
0.003
0.038
0.041
0.048
0.206
0.232
0.241
Russell Sage 24
0
.1
.2
Density
.3
.4
.5
Years of ed: Weighted predicted values, simulated
8
10
12
14
Predicted values, combined ed sim, 4 changes
16
Russell Sage 25
0
.2
Density
.4
.6
Years of ed: Weighted predicted values for whites, actual
10
11
12
13
Fitted values
14
15
0
.1
.2
Density
.3
.4
.5
Years of ed: Weighted predicted values for whites, simulated
8
10
12
14
Predicted values, ed sim by race, 4 changes
16
Russell Sage 26
0
.2
Density
.4
.6
.8
1
Years of ed: Weighted predicted values for blacks, actual
10
11
12
Fitted values
13
14
0
.2
Density
.4
.6
Years of ed: Weighted predicted values for blacks, simulated
10
11
12
13
Predicted values, ed sim by race, 4 changes
14
Russell Sage 27
Appendix Table 1
Regression Results: Interactions with Race
African American
Female
Average number of siblings 2–15
At least one parent grad h.s.
At least one parent attend college
Education info missing for both parents
Family income/poverty level, 2–5, logged
Family income/poverty level, 6–11, logged
Family income/poverty level, 12–15, logged
Proportion yrs w/single parent 2–15
# moves 2–15
Head foreign born
Average county unemployment 2–15
Percent NH dropouts 2–15
State gini, avg 12–15
Log of positive wealth, 1984
Negative wealth, 1984
Wealth missing, 1984
Tuition & fees per FTE student, PUBLIC 87
Tuition & fees* youngest cohort
Child care costs above $1000, 2–5
Years of
Completed
Schooling
High School
Graduation
Attend
College
OLS Coeff.
Logit Coeff.
Logit Coeff.
0.809**
(0.360)
0.322***
(0.085)
-0.083**
(0.035)
0.623***
(0.163)
0.163
(0.136)
0.336
(0.428)
0.307
(0.192)
-0.457**
(0.225)
0.585***
(0.154)
0.139
(0.159)
-0.058***
(0.018)
1.184***
(0.307)
-0.042
(0.030)
-0.024***
(0.006)
1.303
(2.629)
0.049***
(0.017)
0.172
(0.234)
-0.795***
(0.199)
-0.049
(0.091)
-0.177**
(0.084)
-0.334**
(0.153)
1.107*
(0.646)
0.411***
(0.157)
-0.065
(0.060)
1.106***
(0.271)
0.365
(0.302)
-0.049
(0.689)
0.602
(0.374)
-1.021**
(0.435)
0.765***
(0.294)
0.003
(0.273)
-0.074**
(0.030)
2.055*
(1.104)
-0.059
(0.062)
-0.031***
(0.010)
6.019
(4.801)
0.092***
(0.028)
0.155
(0.357)
-1.048***
(0.313)
0.235
(0.171)
-0.210
(0.158)
-0.556*
(0.294)
0.573
(0.668)
0.570***
(0.151)
-0.172**
(0.070)
0.246
(0.332)
0.185
(0.218)
-0.011
(0.982)
0.306
(0.343)
-0.607
(0.422)
0.906***
(0.298)
0.086
(0.300)
-0.044
(0.035)
1.104**
(0.503)
-0.010
(0.051)
-0.032***
(0.011)
2.856
(4.654)
0.044
(0.037)
-0.033
(0.514)
-0.780
(0.516)
-0.134
(0.157)
0.017
(0.148)
-0.290
(0.263)
(table continues)
Russell Sage 28
Appendix Table 1, continued
Years of
Completed
Schooling
OLS Coeff.
INTERACTIONS
Black*parent completed HS
Black*parent attended college
Black*parent ed missing
Black*family income/poverty, logged, 2–5
Black*family income/poverty, logged, 6–11
Black*family income/poverty, logged, 12–15
Black*unemployment, 2–15
Black*Tuition and fees, youngest cohort
Black*Child care costs above $1000, 2–5
Constant
Observations
-0.467**
(0.227)
-0.104
(0.262)
0.071
(0.471)
0.134
(0.260)
0.635**
(0.317)
-0.556**
(0.230)
-0.033
(0.046)
0.054
(0.129)
0.325
(0.255)
11.502***
(1.105)
1209
Standard errors in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
High School
Graduation
Attend
College
Logit Coeff.
Logit Coeff.
-0.683*
(0.378)
-0.285
(0.517)
0.618
(0.764)
0.016
(0.474)
0.612
(0.563)
-0.243
(0.405)
-0.068
(0.085)
-0.027
(0.224)
0.530
(0.466)
-1.854
(2.047)
1210
-0.523
(0.451)
-0.007
(0.442)
0.556
(1.043)
0.142
(0.496)
1.198*
(0.618)
-0.709
(0.452)
0.002
(0.080)
-0.217
(0.246)
0.659
(0.441)
-1.911
(1.943)
906
Russell Sage 29
Appendix Table 2
Racial Comparison of Predicted Values under Simulated Conditions (Weighted)
Mean Years
Median Years
Standard
Deviation
Percent <12
years
Percent <11
years
Years of Education
WHITE RESPONDENTS
Predicted Actual
SD of log family income/needs +10%
SD of wealth +25%
Gini + State change in gini
SD of tuition +10%
All four factors changed
Three factors changed
12.686
12.704
12.731
12.720
12.683
12.781
12.746
12.750
12.758
12.794
12.784
12.747
12.843
12.812
0.848
0.876
0.876
0.850
0.850
0.908
0.906
17.3%
17.2%
17.5%
17.0%
17.4%
17.3%
17.6%
2.8%
3.0%
3.1%
2.6%
2.9%
2.9%
3.3%
BLACK RESPONDENTS
Predicted Actual
SD of log family income/needs +10%
SD of wealth +25%
Gini + State change in gini
SD of tuition +10%
All four factors changed
Three factors changed
12.141
12.121
12.135
12.172
12.141
12.146
12.115
12.076
12.043
12.118
12.122
12.084
12.108
12.080
0.654
0.665
0.699
0.650
0.654
0.708
0.712
36.9%
39.2%
38.6%
36.2%
37.1%
38.7%
39.6%
3.9%
3.9%
4.5%
3.2%
4.2%
4.4%
4.4%
Mean
Pred Prob
Median Pred
Prob
Standard
Deviation
High School Graduation
WHITE RESPONDENTS
Predicted Actual
SD of log family income/needs +10%
SD of wealth +25%
Gini + State change in gini
SD of tuition +10%
All four factors changed
Three factors changed
0.848
0.847
0.853
0.862
0.847
0.866
0.852
0.910
0.909
0.917
0.920
0.909
0.929
0.917
0.160
0.163
0.164
0.151
0.161
0.158
0.167
BLACK RESPONDENTS
Predicted Actual
SD of log family income/needs +10%
SD of wealth +25%
Gini + State change in gini
SD of tuition +10%
All four factors changed
Three factors changed
0.730
0.724
0.722
0.755
0.730
0.741
0.716
0.775
0.769
0.780
0.790
0.773
0.790
0.773
0.174
0.176
0.191
0.163
0.174
0.181
0.193
(table continues)
Russell Sage 30
Appendix Table 2, continued
Mean
Pred Prob
Median Pred
Prob
Standard
Deviation
Attend College
WHITE RESPONDENTS
Predicted Actual
SD of log family income/needs +10%
SD of wealth +25%
Gini + State change in gini
SD of tuition +10%
All four factors changed
Three factors changed
0.440
0.447
0.450
0.456
0.440
0.470
0.455
0.432
0.439
0.444
0.447
0.431
0.466
0.452
0.198
0.205
0.202
0.200
0.198
0.211
0.210
BLACK RESPONDENTS
Predicted Actual
SD of log family income/needs +10%
SD of wealth +25%
Gini + State change in gini
SD of tuition +10%
All four factors changed
Three factors changed
0.343
0.335
0.344
0.356
0.343
0.349
0.336
0.293
0.280
0.292
0.306
0.294
0.288
0.271
0.189
0.194
0.195
0.192
0.189
0.202
0.199
Russell Sage 31
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