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Federal Reserve Bank of Chicago

Black-White Differences in
Intergenerational Economic
Mobility in the US
Bhashkar Mazumder

WP 2011-10

Black-White Differences in Intergenerational Economic Mobility in the US 

Bhashkar Mazumder
Federal Reserve Bank of Chicago

November, 2011

Abstract: Traditional measures of intergenerational mobility such as the intergenerational
elasticity are not useful for inferences concerning group differences in mobility with
respect to the pooled income distribution. This paper uses transition probabilities and
measures of “directional rank mobility” that can identify inter-racial differences in
intergenerational mobility. The study uses two data sources including one that contains
social security earnings for a large intergenerational sample. I find that recent cohorts of
blacks are not only significantly less upwardly mobile but also significantly more
downwardly mobile than whites. This implies a steady-state distribution in which there is
no racial convergence in income. A descriptive analysis using covariates reveals that test
scores in adolescence can explain much of the racial difference in both upward and
downward mobility. Family structure can account for some of the racial gap in upward
mobility but not downward mobility. Completed schooling and parental wealth also
appear to account for some of the racial gaps in intergenerational mobility.



I thank Katherine Meckel, Nathan Chan, Benjamin Jakes, Weiting Zhang and especially Jon Davis for
excellent research assistance. I thank Nathan Grawe and Gregory Clark for their helpful suggestions and
seminar participants at the UC Davis 2010 conference on social mobility, the Chicago Fed, 2011 ASSA
Meeting and the 2011 World Bank-IAE meetings on socioeconomic mobility in Latin America for helpful
comments. The views expressed here do not reflect the views of the Federal Reserve system. Any
opinions and conclusions expressed herein are those of the author and do not necessarily represent the
views of the U.S. Census Bureau. All results have been reviewed to ensure that no confidential information
is disclosed.

1.

Introduction
The large and persistent gap in economic status between blacks and whites in the United

States has been a topic of considerable interest among social scientists and policy makers for
many decades. The historical legacy of slavery and segregation raises the question of how long
blacks may expect to remain a disadvantaged minority in the United States. Despite the enormous
literature on black-white inequality and its historical trends, few studies have directly measured
black-white differences in intergenerational mobility. Estimates of current rates of
intergenerational mobility by race can provide insight on whether racial differences in the US are
likely to be eliminated and if so, how long it will take.
A further question of interest is whether blacks today enjoy the same opportunities for
economic success as whites, despite differences in family background. Finally, understanding the
causes behind racial differences in intergenerational mobility might also shed light on the more
general question of the underlying mechanisms behind the relatively high degree of
intergenerational persistence of inequality in the US.
Surprisingly, only a few studies in the literature (e.g. Hertz, 2005) have sought to
examine black-white differences in intergenerational mobility.1 This first reason for this is that a
key measure of intergenerational income mobility, the intergenerational elasticity (IGE) is not
well suited for comparing black-white differences in mobility with respect to the entire income
distribution (comprising of both blacks and whites). This is because the IGE for any particular
subgroup only estimates the rate of regression to the mean for that particular subgroup and not for
the overall distribution.2 Figure 1 provides a hypothetical and stylized example to illustrate this

1

Other notable exceptions are Hertz (2008), Isaacs, Sawhill and Haskins (2008) and Bhattacharya and
Mazumder (forthcoming). Datcher (1981) and Corcoran and Adams (1997) have also studied the racial
dimension of the intergenerational transmission of status more generally, but have not used summary
measures of intergenerational mobility. None of the previous studies have used the samples considered
here.
2
A similar criticism applies to the intergenerational correlation. Measured within groups it is only
informative about mobility within each group and not about mobility across the broader distribution. Hertz
(2008) also proposes an alternative estimator to deal with this limitation.

1

point. The chart plots the log income of children against the log income of parents. The open
circles in blue represent white families while the red boxes represent blacks. The slopes of the
lines represent the IGE for each group with a flatter slope indicating a smaller IGE and greater
mobility. In Figure 1, although the slope of the line for blacks is flatter than for whites it is clear
that blacks are regressing to a lower mean and hence are not more mobile with respect to the
overall income distribution.3 In principle, therefore, it is possible that blacks do not regress to the
overall mean, even if there is regression to the mean within each group and apparent regression to
the mean for the overall population.
A second reason for the paucity of studies of racial differences in intergenerational
mobility is that intergenerational samples of black families are relatively small making it hard to
make meaningful inferences about group differences.4
This study expands upon recent methodological contributions made by Bhattacharya and
Mazumder (forthcoming) that overcome the pitfalls of relying on the IGE to measure group
differences in intergenerational mobility.

First, they develop the distribution theory for

estimating transition probabilities with covariates. Transition probabilities measure the
probability of moving across specific quantile intervals of the income distribution over
generations and can therefore be used to compare group differences in mobility with respect to a
common distribution. The inclusion of covariates makes it possible to better understand which
factors (e.g. education, family structure) are associated with racial differences in mobility.5
In addition, Bhattacharya and Mazumder also introduce a new set of measures of
“upward mobility” that compare the relative positions of parents and children in the income

3

I thank Nathan Grawe for suggesting that I make this point graphically.
For example, Solon (1992) using the representative portion of the PSID, reports that only 6% of his
multiple sons sample of 428 individuals is black. This yields only 26 black father-son pairs. There are also
concerns about the use of the oversample of poorer families in the PSID due to a technical problem in the
collection of the initial list of households used for the sampling frame (Lee and Solon, 2008). In addition
about two-thirds of the oversample was dropped starting in 1997 due to budget cutbacks (Isaacs, 2008).
5
Hertz (2005) and Isaacs, Sawhill and Haskins (2008) also use transition probabilities to estimate racial
differences in mobility using the PSID.
4

2

distribution of each respective generation. For example, upward mobility can be measured by an
indicator for whether the child’s rank in the distribution is higher than the parents’ rank in the
prior generation. Although, Bhattacharya and Mazumder’s study was focused solely on upward
movements, their measures can easily be adapted to study downward movements. Therefore, I
refer to these measures as “directional rank mobility”. Like transition probabilities, estimates of
directional rank mobility are also well suited for comparing group differences with respect to a
common distribution since one can easily calculate the percent of individuals who experience
upward or downward mobility relative to their parents within each racial group. Bhattacharya
and Mazumder use these measures to produce new estimates of upward mobility in earnings for
black and white men using the National Longitudinal Survey of Youth (NLSY79). They also
show that cognitive skills during adolescence appear to explain much of the difference in the
racial gap in men’s upward mobility.
This paper expands upon this previous work along several key dimensions yielding some
important new findings. First, in addition to the NLSY, I also use a second intergenerational
dataset that matches families in the Survey of Income and Program Participation (SIPP) to
administrative earnings data from the Social Security Administration, hereafter, “SIPP-SSA”.
Compared to the NLSY, the SIPP-SSA data provides many more years of data on parents’
earnings that are potentially less prone to measurement error since they are derived from tax
records. In addition, the SIPP contains data on key characteristics of the parents (e.g. wealth,
marital history) that are lacking in the NLSY and which could help explain racial differences in
intergenerational mobility. The two data sources, viewed in conjunction may provide a more
robust set of facts concerning intergenerational mobility differences by race and mechanisms that
may account for these differences.
Second, I broaden the analysis to consider racial differences in downward mobility.
Suppose it were the case that blacks were not only less upwardly mobile than whites but also less
downwardly mobile, then this might suggest that the relative economic disadvantage faced by

3

blacks might not be as severe as an analysis that only considered upward mobility. In general, in
order to understand the long-term prospects for racial inequality in the “steady-state”, one must
consider rates of both upward and downward mobility. Third, the analysis here further extends
the NLSY sample to include women and to use family income as an outcome. Fourth, and
perhaps most importantly, I explore how estimates of both upward and downward mobility, and
racial gaps in these outcomes, are affected by a wide array of covariates that encompass factors
such as cognitive skill, non-cognitive skills, wealth and family structure.6
These extensions lead to several important new findings. First, the results show that
blacks are both substantially less upwardly mobile and substantially more downwardly mobile
than whites. Should these patterns of mobility persist, the implications for racial differences in
the steady state distribution of income would be alarming. Instead of “regressing to the mean” as
the standard IGE estimates would imply, these results would instead imply that blacks would
largely remain a permanent underclass. In contrast, if we were to use the population wide
estimate of the IGE of around 0.6 from Mazumder (2005), then even this high level of
intergenerational persistence would still imply eventual convergence in black-white earnings.
This study also uses non-parametric regressions and a statistical decomposition to shed
light on which factors are associated with the racial gaps in upward and downward mobility.
While the analysis is descriptive and not causal, it nonetheless provides some highly suggestive
“first order” clues for the underlying mechanisms leading to black-white differences in
intergenerational mobility. It appears that cognitive skills during adolescence as measured by
scores on the Armed Forces Qualifying Test (AFQT) are strongly associated with these gaps. For
example, conditional on having the median AFQT score, the racial gaps in both upward and
downward mobility are relatively small. As with previous studies linking AFQT scores to racial
differences in adult outcomes (e.g. Neal and Johnson, 1996; Cameron and Heckman, 2001), I do

6

I also lengthen the time span of the data used in the NLSY to 2006. Bhattacharya and Mazumder’s
analysis only uses NLSY data through 2002.

4

not interpret these scores as measuring innate endowments but rather they reflect the accumulated
differences in family background and other influences. Indeed, a growing literature suggests that
black-white differences in tests scores can be strongly affected by environmental influences.
A commonly proposed explanation for racial gaps in achievement has been the relative
high rates of black children growing up with single mothers. I find evidence that for blacks, the
lack of two parents in the household throughout childhood does indeed hamper upward mobility.
However, patterns in downward mobility are unaffected by family structure for either blacks or
whites. Importantly, the negative effects of single motherhood on blacks are only identified in
the SIPP where the entire marital history during the child’s life is available. This highlights the
importance of access to data on family structure over long windows of time rather than a single
snapshot at a point in time.
I also find that black-white gaps in both upward and downward mobility are significantly
smaller for those who have completed 16 years of schooling. Low levels of parental wealth
among blacks also inhibit the prospects for upward mobility. In contrast, I find that measures of
non-cognitive skills available in these data do not appear to play a significant role in explaining
intergenerational mobility gaps. A caveat is that previous research (e.g. Heckman, Stixrud and
Urzua 1996) has emphasized the importance of using dynamic structural models that better deal
with measurement and selection issues to identify the long-term effects of non-cognitive skills.
The rest of the paper proceeds as follows: section 2 presents the measures of mobility,
section 3 describes the data, section 4 presents the unconditional mobility estimates, section 5
analyzes the effects of including covariates and section 6 concludes.
2.

Measures of Mobility

Transition Probabilities
The upward transition probability (hereafter “UTP”) used in this analysis is the
probability that the child’s income percentile (Y1) exceeds a given percentile s, in the child’s

5

income distribution by an amount  , conditional on the parent’s income percentile (Y0) being at
or below s in the parent’s income distribution:7
(1) UTP  , s  Pr( Y1  s   | Y 0  s )
For example, in a simple case where = 0 and s =0.2, the upward transition probability
(UTP0,s) would represent the probability that the child exceeded the bottom quintile in the child’s
generation, conditional on parent income being in the bottom quintile of the parent generation.8
The empirical analysis of upward transition probabilities will vary s in increments of 10
percentiles throughout the bottom half of the distribution (i.e. 10, 20,…50). Using this approach
implies that the samples will overlap as progressively more families are added to the sample as s
increases.

This approach is helpful in making comparisons with the directional mobility

estimator that will be introduced shortly. I will also show results that use non overlapping
percentile intervals of the parent income distribution (e.g. s <= 10th percentile, 10th percentile > s
<= 20th percentile,..., 40th percentile > s <= 50th percentile).
It is straightforward to see that this estimator can be modified to measure downward
transition probabilities by altering the inequality signs:
(2) DTP ,s  Pr(Y1  s   | Y0  s )
In this case I will vary s from 50 to 90. I will also consider intervals such as the 90th percentile <
s <=100th percentiles, 80th percentile < s <=90th percentiles,…, 50th percentile < s <=60th
percentile.
Formby, Smith and Zheng (2004) develop the distribution theory for marginal transition
probabilities that can be easily extended to the case of discrete covariates. Unfortunately, for
many covariates of interest that are commonly treated as continuous, such as years of schooling
7

Bhattacharya and Mazumder (forthcoming) use a more general notation that allows for a less restricted set
of transition probabilities. For example, transition probabilities can be estimated conditional on parent
income lying within any specific percentile interval.
8
In a transition matrix using quintiles of the income distribution, this example would measure 1 minus the
probability of remaining in the bottom quintile. The introduction of  is useful to parallel variations on the
URM estimator that are introduced later.

6

or test scores, this is not of much practical value. Bhattacharya and Mazumder (2011) show how
the transition probability can be estimated conditional on continuous covariates using
nonparametric regression techniques and demonstrate that bootstrapping is a valid approach for
calculating standard errors.9

Using this methodology one can, for example, estimate the

difference in transition probabilities between blacks and whites while controlling for the effects
of children’s test scores, and determine whether these differences are statistically significant.
Directional Rank Mobility
Following Bhattacharya and Mazumder (2011), I use a measure of upward rank mobility
(“URM”) which estimates the likelihood that an individual will surpass their parent’s place in the
distribution by a given amount, conditional on their parents being at or below a given percentile.10
(3) URM  ,s  Pr(Y1  Y0   | Y0  s )
In the simple case where τ = 0, this is simply the probability that the child exceeds the
parents place in the distribution.

As with the UTP measure, positive values of τ enable one to

measure the amount of the gain in percentiles across generations. Results will be shown for a
range of values for τ and also as s is progressively increased. Bhattacharya and Mazumder show
that the URM measure can also be estimated conditional on continuous covariates using
nonparametric regressions.
Similarly one can construct a measure of downward rank mobility (“DRM”) using an
analogous approach:
(4) DRM  ,s  Pr(Y0  Y1   | Y0  s )
Comparison of transition probabilities and directional rank mobility

9

In order to implement the TP estimator one must first estimate quantiles of the income distribution. Since
the TP estimates conditional on continuous covariates will involve non-smooth functions of these initially
estimated functions, it is technically challenging to show that one can bootstrap the standard errors.
10
Bhattacharya and Mazumder (forthcoming) refer to this measure as “UP”.

7

Since there are an infinite number of possible transition probabilities, depending on the
specific quantiles that are chosen, a criticism of transition probabilities is that they require using
arbitrarily chosen cutoffs. In contrast, the directional rank mobility measures simply compare the
child’s rank to the parent’s rank rather than to an arbitrarily chosen quantile.11
The two measures may also produced biased measures of group differences depending on
the properties of the group-specific distribution. For example, Bhattacharya and Mazumder
(forthcoming) show that since the white income distribution lies to the right of the black
distribution over virtually the entire support, the upward transition probability will be biased in
favor of whites. This is because at any point of the overall income distribution an equivalent
increase in income given to both whites and blacks would mechanically allow more whites to
surpass any specified threshold.

A similar argument suggests that the URM measure is

potentially biased in favor of blacks. Overall, then it seems reasonable to consider both measures
and to examine a range of estimates.
3.

Data

NLSY79
The first source of data I use is the National Longitudinal Survey of Youth 1979 cohort
(NLSY79), a dataset that has been neglected by most previous studies of intergenerational
mobility despite having several attractive features.12 Most notably there is a very large sample of
over 6000 individuals for whom we know both family income in adolescence (1978-1980) and
various economic outcomes as adults (1997-2005).

11

When making comparisons between population subgroups this is an unambiguous advantage to using the
URM. However, Bhattacharya and Mazumder (2011) show that when using the full sample (i.e. pooling all
subgroups), the URM measure is only meaningful if there is some cutoff, s used to condition the sample.
The choice of s of course, is likely to be arbitrary. Even in this case, however, children’s ranks are still
directly compared to their parents’ rank as opposed to an arbitrary quantile.
12
Exceptions include Bratsberg et al (2007) and Aaronson and Mazumder (2008). Some previous studies
such as Zimmerman (1992) have used an earlier NLS cohort of young men and women

8

The NLSY began with a sample of individuals who were between the ages of 14 and 21
as of January 1, 1979 and who have since been tracked through adulthood. The NLSY conducted
annual interviews until 1994 and has since shifted to biennial surveys. The analysis is restricted
to the sample of youth who were living at home with their parents during the first three years of
the survey and for whom family income was directly reported by the parents in any of these
years. Respondents also must have stayed in the sample to adulthood and been interviewed in
one of the surveys beginning with 1998 and ending in 2006. The analysis includes individuals
from both the cross-sectional representative samples as well as the supplemental samples (e.g.,
blacks and Hispanics). Following Neal and Johnson (1996) and Cameron and Heckman (2001) I
combine the cross-sectional and supplemental samples of blacks. However, as a group, blacks
and Hispanics are overrepresented in the sample. Therefore, all of the analyses utilize the 1979
sampling weights. The final sample includes 3,440 men and 3,250 women.
The measures of mobility utilize data on the family income of the children during the
years 1997, 1999, 2001, 2003 and 2005 when sample members were between the ages of 33 and
48. The measures of permanent family income are constructed for each generation by using
multiyear averages using any available years of data. Years of zero income are included in the
averages. Family income is converted into 2004 dollars using the headline CPI series.
A nice feature of the NLSY is that it also includes a rich set of covariates pertaining to
the children. Measures of human capital include completed years of education and scores on the
Armed Services Vocational Aptitude Battery test (ASVAB) which was given to all NLSY
respondents. I will focus on the composite AFQT score which is used as a screening device by
the military and has been used in many previous economic studies. Non-cognitive measures
include self-esteem and the Rotter scale of locus of control. The NLSY also has information on
parent education and family structure at age 14.
SIPP-SSA

9

The second data source pools the 1984, 1990, 1991, 1992 and 1993 panels of the Survey
of Income and Program Participation (“SIPP”) matched to administrative earnings records
maintained by the Social Security Administration (SSA).13 The Census Bureau attempted to
collect the social security numbers (SSN) of all individuals in the surveys and they were
subsequently matched to SSA administrative data bases of Summary Earnings Records (SER) and
Detailed Earnings Records (DER). Davis and Mazumder (2011) show that the match rates are
high for most SIPP panels and that selection does not appear to be a serious concern.14
The SER data covers annual earnings both from employers and self-employment over the
period from 1951 to 2007. In the SER data the earnings of individuals who are not covered by
the social security system will have their earnings recorded as zero. Further, the SER data are
censored at the maximum level of earnings subject to the social security tax. While the DER data
is not subject to either of these issues it is only available since 1978. Further, the DER data used
in this paper only covers labor market earnings reported on W-2 form and not self-employment
earnings. Therefore, I combine information from both the SER and DER in order to use earnings
data from both labor market earnings and self-employment and only use the data beginning in
1978.15
In order to satisfy Census Bureau disclosure avoidance review requirements and to
maximize the sample size, I use a relatively liberal set of sample selection rules. I start with a

13

This data source is not publicly available. Researchers must apply to obtain the data through the Center
for Economic Studies at the US Census Bureau (http://www.ces.census.gov/)
14
For example, the matched SIPP-SSA samples slightly over-represent individuals with financial assets and
those who received government transfer programs since such individuals are more likely to have SSNs.
15
Subsequent to having all of the results in this paper released through the Census Bureau’s disclosure
avoidance review process, I learned that the self-employment earnings in the DER were available to me but
that I had not been making use of it. Therefore, for a small set of self-employed individuals whose earnings
were above the taxable maximum, the use of the SER rather than the DER self-employment earnings
understates their true earnings. To address this, I have redone all the calculations in this paper using only
the full DER data (including the non-topcoded self-employed earnings) and found that it has an
imperceptible effect on the results (typically only changing estimates at the third decimal place). Since
there are procedural difficulties in releasing a second set of statistical results through the Census Bureau
disclosure avoidance review process in cases where revised estimates lead the sample size to change by just
1 or 2 individuals, and since the current results are virtually identical to the corrected ones, I have opted to
show the current results that combines both the SER and DER data.

10

sample of white or black males who were living with their parents at the time of the SIPP and
who were no older than 25 years old.16 I also require that the adult earnings of these men are
observed when they are at least 21 years old. Sons’ earnings are taken over the five years
spanning 2003 through 2007. Although, years of zero earnings are included in the average, sons
must have positive earnings in at least one year to be included. This produces a sample of 16,782
men who could have been born anytime between 1959 and 1982 and who are observed as adults
between the ages of 21 and 48.17
Both parents’ earnings are combined and are averaged over all years between 1978 and
1986 to construct a measure of permanent earnings. For those who lived with their fathers at the
time of the SIPP, the parent earnings are recorded as the fathers’ earnings. The earnings of the
mother are used for those children who were not living with their fathers. To be included in the
sample, parents must have had positive earnings in at least one year.
A limitation of the SIPP-SSA data is that there is little information available for the
children during their adult years aside from their administrative earnings records. However,
unlike the NLSY, a rich set of data on the parents is available. For example, information is
available on parental wealth and the complete marital histories of the parents.
Comparison of NLSY79 and SIPP-SSA
Table 1 presents summary statistics for each sample. There are a number of potentially
important differences between the samples.

The NLSY79 sample includes both sons and

daughters and uses family income for both generations. Family income is useful as a way of
including daughters in the sample and avoiding issues dealing with selective labor force
participation. The administrative data in the SIPP-SSA only has earnings, and only for the

16

Restricting the sample to whites and blacks avoids implicitly disclosing any information concerning men
who are neither white nor black thereby making it easier to pass Census Bureau disclosure avoidance
review. The age restriction avoids using individuals who continued to live with their parents throughout
adulthood. The results are not sensitive to restricting the age cutoff to 18. There is no lower bound on the
age when living at home.
17
As I discuss later the results are not sensitive to requiring sons to be at least 28 years old.

11

individuals (not the spouse). Since there is no ideal way of dealing with selection of which
daughters participate in the labor force, the analysis with the SIPP-SSA only uses sons. The
NLSY79 covers individuals born between 1957 and 1964 while the SIPP sample covers those
born over a much longer time span, 1959-1982. Parent income is measured over just a three year
period (1978 to 1980) in the NLSY79 but over a nine year period from 1978 to 1986 in the SIPP.
Finally, all ranks and quantiles used in the NLSY are based on distributions that include
individuals who are neither white nor black. The SIPP-SSA data in contrast is restricted to just
whites and blacks. Table 1 provides some summary statistics for the two samples.
Haider and Solon (2006) demonstrate that lifecycle bias affects estimates of the
intergenerational elasticity in permanent income and the extent of the bias depends on the ages at
which the incomes of children and parents are measured. They find that such bias is minimized
in the US when income is measured around the age of 40. It is not clear whether a similar bias
would arise with respect to the measures utilized here and I do not consider the possible
implications of age bias. In the NLSY, the mean age of the kids in 2001 (the middle year of the
sample) is 39 which is close to ideal according to Haider and Solon (2006). In the SIPP-SSA
sample, the mean age of the sons in 2005 (the middle year of the sample) is 33.

4.

Unconditional Estimates of Intergenerational Mobility

Upward Transition Probabilities (UTP)
I begin by presenting race-specific estimates of upward transition probabilities in Table
2.18 Panel A shows the results from the NLSY while panel B presents analogous results from the
SIPP-SSA. The first entry in panel A shows that among white men and women in the NLSY
whose parents’ income was at or below the 10th percentile, 84 percent exceed the 10th percentile
as adults. Moving across the first row demonstrates the effect of raising τ, the percentile cutoff in
the child’s generation. For example, only about 42 percent of whites starting in the bottom decile
18

Results for the pooled samples are available from the author upon request.

12

exceed the 40th percentile (τ =0.3). Moving down the columns shows the effect of raising the
cutoff percentile in the parent generation. For example, among whites starting below the 40th
percentile in the parent generation only 54 percent exceed the 40th percentiles as adults.
In all cases, the comparable UTP estimates are much lower among blacks. For example,
among blacks starting in the bottom decile only 65 percent exceed the bottom decile as adults, a
19 percentage point difference compared to whites. The black-white gap in the probability of
rising out of the bottom quintile is even higher at 27 percent.19 Owing to the large samples in the
NLSY, all of the estimated gaps in Table are highly statistically significant. Figure 2 plots the
race-specific upward transition probabilities along with confidence bands as the sample is
progressively increased.
In panel B the SIPP-SSA sample consists only of sons, includes only blacks and whites,
includes many more recent cohorts and uses administrative earnings data rather than family
income. Despite these different concepts and measures, the UTP estimates are very similar to
those shown in Panel A. This is evident visually in Figure 2 which plots estimates from both
datasets. The general pattern of large and statistically significant differences in point estimates is
also evident in the SIPP-SSA data. Across the 20 entries for each race, it appears that white
transition probabilities are typically about 1.5 percentage points higher for whites in the NLSY
compared to the SIPP-SSA and about 1.5 percentage points lower for blacks. The fact that the
key findings are so similar across the datasets is advantageous since each dataset has its own
exclusive set of covariates.
Downward Transition Probabilities (DTP)
Table 3 presents an analogous set of downward transition probabilities. Using either
dataset, I find that blacks are clearly more downwardly mobile. For example, about 60 percent of
19

For ease of exposition I will refer to the “black-white” gap in the text in terms of the absolute value of the
difference in levels between the groups. The tables and charts actually report the white level minus the
black level (“W-B”) and will typically report a positive number for this racial difference in upward
mobility and a negative number for the racial difference in downward mobility.

13

blacks whose parents were in the top half of the income distribution fall below the 50th percentile
in the subsequent generation. The analogous figure for whites is 36 percent. Although the
datasets provide broadly similar patterns, there is a somewhat notable difference between the two
datasets in the degree of downward mobility out of the top decile for blacks which is visually
evident in Figure 3. In the NLSY which uses family income in both generations, 81 percent of
black children whose parents were in the top decile fall below the top decile as adults. The
comparable figure is 88 percent in the SIPP-SER data, where the income concept is earnings.
Upward Rank Mobility (URM)
Table 4 shows estimates of upward rank mobility based on equation (3). As might be
expected, the rates of upward mobility using this measure are somewhat higher than for the
upward transition probability. For example, using the NLSY I find that 75 percent of blacks
whose parents were below the 20th percentile, surpass their parents’ percentile in the family
income distribution. In table 2, it is shown that 48 percent of this same subsample exceeds the
20th percentile, implying that although about 37 percent of blacks starting in the bottom quintile
exceed their parents’ percentile, they do not transition out of the bottom quintile. For whites, the
difference in upward mobility between the two measures is much smaller. Therefore, the upward
rank mobility estimator (for τ = 0, and s= 0.2 ) shows a much smaller black-white gap of about
0.12. Interestingly, using this measure, the estimates are now nearly identical across the two
datasets as is apparent in figure 4. This suggests that the URM is an especially robust measure.
The finding of a smaller black white gap using the URM rather than the UTP measure is
sensitive to the chosen value of τ. For example, if τ is set to 0.2, then the black-white differences
in upward rank mobility rise considerably. For example, among men and women in the NLSY
whose parents’ family income placed them in the bottom quintile, blacks are nearly 25 percent
less likely to surpass their parents’ rank by 20 percentiles or more. Using the SIPP-SSA data the

14

analogous black-white difference for men is 21 percent. Figure 5 plots the full set of estimates
for the case where τ equals 0.2
Downward Rank Mobility (DRM)
In Table 5 and Figure 6 I present estimates of downward rank mobility. Using the simple
measure (τ equals 0), I again observe higher rates of downward mobility among blacks than
whites that is less pronounced in the top two deciles. Compared to the estimates of DTP,
however, the estimates of DRM are higher. For example, among whites in the NLSY sample
whose parents’ income was in the top half of the income distribution, 69 percent were in a lower
rank in the distribution than their parents even though only 36 percent fell below the median. For
blacks starting in the top half of the income distribution, 79 percent fell below their parents and
61 percent also dropped below the median. Therefore, the estimates of the black-white gap in
downward mobility using the baseline DRM measure are considerably smaller than the analogous
estimates using DTP.
As was the case with the pair of upward mobility measures, the comparison of the two
downward mobility measures is also sensitive to the choice of τ. For example, if we consider the
probability of those in the top half of the distribution falling 20 percentiles or more, the blackwhite gap is 18 percent in the NLSY and 14 percent in the SIPP-SSA. The racial differences in
DRM when τ =0.2 show somewhat different patterns across the income distribution depending on
the dataset used as is shown in Figure 7.

For example, the black-white difference in the

probability of falling 20 percentiles below one’s parents, among those who start in the top decile
is only 7 percent in the NLSY but is 23 percent in the SIPP-SSA. This likely reflects differences
that are due to the relevant concept of income. Compared to whites, blacks starting in the top
decile are more likely to suffer larger drops in their earnings rank than in their family income
rank.
Upward Mobility Using Interval-based Samples

15

Thus far all the estimates have used samples that have progressively cumulated deciles
beginning at either the bottom or the top of the income distribution. One might instead be
interested in estimates of upward or downward mobility within narrower percentile ranges and
how these estimates vary along the distribution. Table 6 and Figure 8 address this by presenting
estimates of UTP and URM using interval based samples using deciles in the bottom half of the
income distribution and for the case where τ = 0. The UTP estimates are drawn from the NLSY
sample while the URM estimates are drawn from the SIPP-SSA sample. Figure 8 shows that
aside from the bottom decile, the racial differences in upward mobility are consistently between
20 and 30 percent. The greater similarity between the UTP and URM estimates is not surprising
since as the interval range becomes smaller, the two estimates will converge.20 Partially for this
reason, I have chosen to emphasize the estimates using the cumulative samples so as to highlight
the differences between the transition probabilities and the directional rank mobility estimates.
The cumulative samples, of course, also have the virtue of having larger sample sizes and
therefore, providing more precise estimates.
Implications of transition probabilities on the steady state distributions by race
The transition matrix of movements across quintiles of the income distribution over
generations, for blacks and whites based on the SIPP-SSA are shown in Table 7. The general
patterns concerning racial differences in upward and downward mobility are again evident. For
example, over 50 percent of blacks who start in the bottom quintile in the parent generation
remain there in the child generation but only 26 percent of whites remain in the bottom quintile in
both generations. Whites are less likely to transition out of the top quintile compared to Blacks
suggesting a distribution that may not be exhibiting racial convergence. Assuming that these
probabilities are a permanent feature of the US economy, they can be used to calculate an implied

20

This is obvious at the limit since the probability of exceeding one’s parents percentile (URM) and the
probability of exceeding any given percentile threshold (UTP) will be identical if the sample is conditioned
on the same percentile in each case.

16

steady state distribution using standard matrix algebra methods for solving Markov chains. The
results show, for example, that in the steady state, 39 percent of blacks would occupy the bottom
quintile of the income distribution and only 8 percent would be in the top quintile.21 This
suggests that rather than convergence, blacks would perpetually remain an underclass in
American society if mobility patterns continue to evolve as they have for the cohorts studied in
this paper.

5.

Estimates of Intergenerational Mobility Conditional on Covariates
Ideally, we would like to understand the causal factors that explain the observed patterns

of intergenerational mobility and the possible implications for policies designed to address racial
differences in mobility. For example, we might like to know whether a particular schooling
intervention such as smaller classes might improve the prospects for upward mobility and
whether this could reduce the racial gap in upward mobility. Such a study would not only require
a convincing research design to address standard concerns about endogeneity bias but would also
likely require high quality income data spanning multiple years of adulthood for two generations
for the same set of families. Instead, I opt for a more modest goal and conduct a descriptive
analysis to explore how the inclusion of other available covariates of the parents and children
affect the racial differences in upward and downward intergenerational mobility. Such a “first
pass” analysis may yield important clues about which factors are potentially important.
The use of characteristics from the parent generation (e.g. father’s education) provides a
somewhat more straightforward interpretation than characteristics from the child generation,
since they are “predetermined” and may be viewed as more clearly exogenous to children’s future
income. The use of children’s own characteristics, even if they are measured prior to entering the
labor market, may be somewhat more difficult to interpret since there may still be latent

21

Further, 22 percent of blacks would be in the second quintile, 17 percent in the third quintile and 14
percent would be in the fourth quintile. The share of whites across the distribution, from the bottom to top
quintiles is as follows: 17 percent, 20 percent, 20 percent, 21 percent and 22 percent.

17

unobserved factors (e.g. patience) that could affect both long-run income of the child as well as
the covariate. In any event, none of the estimates described in this section should be given a
causal interpretation and are more akin to an accounting exercise that may still provide some
meaningful descriptive evidence.
Upward Mobility Conditional on Covariates
Since there are a large number of potential estimates of upward mobility I simplify the
analysis in this section by focusing only on the transition probability of moving out of the bottom
quintile over a generation. In order to estimate how the inclusion of a particular continuous
covariate affects this measure using a non-parametric approach, I start with samples of families
starting in the bottom quintile and estimate locally weighted regressions, by race, where the
outcome is an indicator for the son or daughter exceeding the bottom quintile as an adult. I then
produce a series of plots of the upward transition probability at each value of the covariate for
each racial group. In addition, I plot the black-white difference, along with 95 percent confidence
bands.22 Finally, as a point of reference, I include the unconditional transition probabilities in
lightly shaded horizontal lines.

In the NLSY sample the unconditional upward transition

probability of leaving the bottom quintile is 0.75 for whites and 0.48 for blacks yielding a blackwhite gap of 0.27. A covariate with a positive association with upward mobility will produce an
upward sloped line and may reduce the black-white gap in upward mobility for certain values of
the covariate.
The left hand side panels in Figure 9 show the results for upward mobility when using
own education, father’s education, AFQT scores, self esteem, the Rotter scale and having a single
mother at age 14 as covariates. Figure 10 shows the results when using wealth as a covariate.
Panel A shows that, as would be expected, more years of completed schooling are associated with
a greater likelihood of rising out of the bottom quintile. For example, 89 percent of whites with
22

These are produced by using the bootstrap method. Bhattacharya and Mazumder (forthcoming) show
that the bootstrap method is a valid method of inference for these measures.

18

exactly 16 years of schooling will escape the bottom quintile compared to 75 percent of whites
with exactly 12 years of schooling. For blacks, rates of upward mobility are extremely low for
those with less than a high school education but begin to rise sharply for those who attain more
than a high school education. For example, for blacks with exactly 10 years of schooling only 28
percent will transition out of the bottom quintile compared to 69 percent of blacks with exactly 14
years of schooling.
With respect to the racial gap in upward mobility, controlling for education provides
something of a mixed picture. The racial gap in upward mobility among those with less than a
high school education is actually higher than the unconditional estimate. On the other hand the
racial gap narrows sharply with additional years of post secondary education. Indeed among
those with 16 years of schooling the racial gap in upward mobility gap is essentially closed.
Nevertheless, the racial gap is still quite large among those with some post-secondary education
but who have not completed college. For example, the black white gap among those with 14
years of schooling is still sizable at 16 percent. Given that only 17 percent of blacks in the NLSY
attained more than 14 years of schooling, this suggests that marginal improvements in educational
attainment may not do a great deal to improve the overall upward mobility prospects of blacks.
Panel C of Figure 9 suggests a somewhat different story when including father’s
education. In this case the slopes of the lines, though positive, are not nearly as upward sloping
as they were for one’s own education. However, in this case the point estimates of the blackwhite gap are consistently below the unconditional estimates throughout the distribution of
fathers education although the one cannot reject that they are statistically the same. For example
the black–white gap in upward mobility among those whose fathers had only 9 years of education
is 20 percentage points or about 25 percent lower than the unconditional gap of 27 percentage
points.

As with own education, the black-white gap is essentially closed if one’s father

completed 16 years of schooling.

19

The effects of including one’s AFQT score on rates of upward mobility are shown in
Panel E of Figure 9. Here the results provide a relatively clean and compelling story. For both
blacks and whites upward mobility rises with AFQT scores in a fairly similar fashion. There are
especially sharp gains in upward mobility associated with increases in test scores at the low end
of the AFQT distribution. Upward mobility continues to rise at a somewhat slower but still
strong rate in the middle and upper half of the AFQT distribution. Remarkably, the lines for
blacks and whites are relatively close throughout the AFQT distribution. For example, the blackwhite gap in moving out of the bottom quintile is only 5.2 percentage points for those with
median AFQT scores compared to the unconditional gap of 27 percentage points. This suggests
that cognitive skills measured at adolescence can “account” for much of the black-white
difference in upward mobility. This result echoes previous findings by Neal and Johnson (1996)
and Cameron and Heckman (2001) who have also found that AFQT scores can account for much
of the racial gap in adult earnings and college enrollment rates. As with these aforementioned
studies I interpret this finding as reflecting the cumulative effect of family background influences
rather than reflecting innate differences. A growing number of studies (Neal and Johnson 1996,
Hansen, Heckman, and Mullen 2004, Cascio and Lewis 2001, Chay, Guryan, and Mazumder
2008 and Aaronson and Mazumder, forthcoming) have shown that environmental influences can
have large effects on military test scores and narrow racial differences.
The effects of the two non-cognitive measures, self-esteem and the Rotter scale are
shown in Panels G and I of Figure 9. For self esteem, the slopes of the lines are in the expected
direction however the inclusion of this variable does relatively little to narrow black-white
differences as the gap is above 20 percentage points throughout the distribution and the
confidence intervals always include the unconditional gap. The Rotter scale appears to provide
suggestive evidence that the black-white gap is lower among individuals who exhibit less internal
control but the confidence intervals are too wide to say anything meaningful. There also appears
to be little effect among those who report high levels of internal control.

20

In Panel K of Figure 9, I use a simple dichotomous measure of family structure, namely
whether the NLSY respondent lived only with his or her mother at age 14. The black-white gap
in upward mobility does appear to be smaller for those coming from two parent families but this
appears to be driven mainly by lower upward mobility among whites in two parent families rather
than higher mobility among black families. Overall, the evidence from the NLSY suggests that
family structure does not play much of a role in accounting for the black-white gap in upward
mobility.
The effects of family structure on upward mobility differ, however, when using the SIPP
sample which contains the entire marital history of parents over the child’s lifetime. In Figure 10
I compare the upward mobility rates for those sons who according to the SIPP always lived with
both parents to those sons who ever lived with just a single parent.23 For whites upward mobility
out of the bottom quintile actually declines slightly from 0.75 (0.02) for those who ever lived with
just one parent to 0.71 (0.02) for those who always lived two parents. For blacks, however, we
see an increase in the transition probability from 0.47 (0.02) to 0.58 (0.02). The black-white gap
declines from 0.28 (0.02) to 0.13 (0.06). This 15 percentage point improvement in upward
mobility for blacks relative to whites is statistically significant at the 5 percent level.
Another key variable concerning parental status that could plausibly influence patterns of
upward mobility is wealth.

Becker and Tomes (1979, 1986) have suggested that rates of

intergenerational mobility could be lower for families who face borrowing constraints and who
therefore cannot optimally invest in their children’s human capital. While the wealth of parents is
not available in the NLSY, detailed data on assets and liabilities are collected in the SIPP. Figure
12 shows how the upward transition probability out of the bottom quintile varies over distribution
of net worth in the SIPP-SSA sample. It is notable that in contrast to some of the other
covariates, the pattern for wealth appears to be more nonlinear. For whites upward mobility rises
23

The latter category includes those whose parents were ever separated, divorced or widowed. The sample
includes those who were given the marital history topical module in the SIPP and who had non-missing dat.
There are no significant differences between this subsample and the full SIPP analysis sample

21

with wealth in the bottom half of the wealth distribution but is fairly flat in the top half of the
distribution. For blacks, there is a more striking upward slope at the bottom end of the wealth
distribution and a similar leveling off in the middle of the distribution. Although the point
estimates suggest a decline in upward mobility for the wealthiest blacks, this is driven by a small
number of observations and is accompanied by very large confidence bands. Conditional on
wealth, the black-white gap is about 20 percentage points or about 20 percent lower than the
unconditional estimates. The fact that wealth only appears to matter at the bottom of the wealth
distribution is consistent with the idea that wealth reflects borrowing constraints and that such
constraints may inhibit upward mobility.
Downward Mobility Conditional on Covariates
For downward mobility I focus on the probability of moving out of the top half of the
income distribution over the course of a generation. Using the NLSY data, the probability of
such a downward transition is 36 percent for whites and 61 percent for blacks yielding a blackwhite gap (in absolute value) of 0.25. The right hand side panels of Figure 9 (and Figures 11 and
13) present the plots for the downward transition probability. As was the case with the upward
mobility figures, the charts show the transition probability for each value of the covariate, by race
and for the black-white difference, based on locally weighted regressions. In this case the racial
gaps are negative since they are calculated as the white level minus the black level.
The effects of education on downward mobility are shown in Panel B of Figure 9. As
expected the lines slope downward. Since I am conditioning on individuals whose parents are in
the top half of the income distribution, the samples of individuals with less than a high school
education are quite thin so the estimates for these values are especially noisy. As was the case
with upward mobility, additional years of post-secondary schooling are associated with a
reduction in the racial gap in downward mobility. Among those with 16 years of schooling, the
black white gap is reduced to just 14 percentage points and entirely disappears among those with

22

17 years or more of schooling. Panel D of Figure 9 shows the patterns when using fathers’
education. Here the slopes are a bit flatter and there is a much less pronounced reduction in the
racial gap in downward mobility.
The effects of AFQT scores on downward mobility (Panel F of Figure 9) are quite
striking. The lines for whites and blacks converge quite a bit and for a broad swath of the AFQT
distribution the racial gap is below 10 percentage points and is not statistically different from 0.
Therefore as was the case with upward mobility, test scores during adolescence are strongly
associated with rates of downward mobility. In panels H and J of Figure 9, the effects of self
esteem and the Rotter scale on downward mobility are shown. These variables do not appear to
have much effect on reducing the black-white gap in downward mobility. In some areas of the
distribution of these covariates, the point estimates suggest a narrowing but the confidence
intervals are far too large to draw meaningful inferences. Panel L of Figure 9 shows that there is
little difference in the prospects for downward mobility among blacks by family structure when
using the NLSY but that whites from single mother headed families are far more likely to be
downwardly mobile. In Figure 11, using data from the SIPP where I have data on family
structure throughout the child’s life, I find virtually no difference in downward mobility by
whether sons always lived with two parents or not, for either blacks or whites.
Finally, Figure 13 suggests that accounting for wealth modestly reduces the black-white
downward mobility gap. In the SIPP-SSA data the racial difference in the probability of dropping
out of the top half of the distribution is 20 percentage points. At both the very top and the very
bottom of the wealth distribution, there is suggestive evidence that the racial gap narrows
considerably, though the estimates are very noisy. Throughout most of the wealth distribution,
the racial gap appears to be between 10 and 15 percentage points.
Regression Based Accounting Framework

23

It would of course, be useful to include many of the covariates simultaneously in a
multivariate framework to investigate the relative importance of the different factors. Since it is
difficult to implement this non-parametrically I consider a simpler exercise where I simply use a
linear regression framework to estimate the mean black-white mobility gaps conditional on the
covariates.24 The results are shown in Table 8. For this exercise I use only the NLSY sample and
show the effects on both the upward and downward mobility racial gaps when I separately
include each covariate or include several simultaneously. The inclusion of parent characteristics
(father’s education, mother’s education, and having a single mother at age 14) reduces the upward
mobility gap from 27.1 to 25.1 percentage points or a reduction of 7.5 percent. These variables,
however, can account for a larger reduction in the downward mobility gap from 25.3 to 19.8
percentage points or a reduction of about 22 percent.
Table 8 further shows how accounting for children’s own characteristics affects the racial
mobility gaps. What is most striking is that only AFQT scores appear to have a noticeable effect.
Including AFQT scores reduces the black-white gap in the probability of leaving the bottom
quintile to 16 percentage points and reduces the black-white gap in the probability of leaving the
top half of the income distribution to just 10 percentage points.

5.

Conclusion
One can potentially gain insight into the dynamics of the racial gap in economic status in

the U.S. and better understand how long it will take before there is complete convergence by
examining rates of intergenerational income mobility. However, commonly used measures of
intergenerational mobility such as the rate of regression to the mean for the pooled sample may
mask the possibility of non-convergence, if groups are regressing toward very different means.
Using measures of intergenerational mobility that are better suited to describing racial differences
in mobility with respect to a common distribution I find dramatically lower rates of upward
24

This is similar to the approach used by Neal and Johnson (1996) to demonstrate the extent to which test
scores in adolescence can account for the black-white gap in adult wages.

24

mobility from the bottom of the income distribution and dramatically higher rates of downward
mobility from the top of the distribution among blacks born between the late 1950s and early
1980s.
In combination the estimates imply a steady state income distribution that shows no racial
convergence. In other words if future generations of white and black Americans experience the
same rates of intergenerational mobility as these cohorts, we should expect to see that blacks
would make no relative progress and would remain a “permanent underclass”. While these
results are provocative, it is clear that over the course of American history there have been
periods of steady progress in reducing racial differentials. These findings therefore, should not be
taken to imply that racial progress is impossible but rather to highlight what current trends
suggest about the future.
These results also underscores the importance of understanding what kinds of policies
can potentially foster greater upward mobility and reduce downward mobility for blacks. While
this paper does not seek to identify definitive causal channels, the use of statistical models that
include covariates suggests a few potential areas for policy makers to consider. Similar to
previous studies that have looked at static gaps in black-white earnings and college-going rates
using NLSY data (e.g. Neal and Johnson, 1996; Cameron and Heckman, 2001), it is apparent that
the cumulative effects of a variety of influences that affect cognitive ability by adolescence play a
critical role in accounting for racial differences in upward and downward mobility. A growing
literature has shown that black-white differences in test scores, and military test scores in
particular, have been narrowed through large scale policy interventions throughout American
history (e.g. Chay, Guryan and Mazumder, 2009; Aaronson and Mazumder, forthcoming). Other
studies (e.g. Dobbie and Fryer, 2011) have also shown the potential for modern educational
interventions to improve the black-white gap in educational achievement.
Educational attainment also appears to matter for both upward and downward mobility
but the results from non-parametric models suggest that the effects of education on reducing

25

racial mobility differentials occur primarily at the margin of acquiring higher education. If racial
gaps in college attainment are primarily due to skill differences determined in adolescence
(Cameron and Heckman, 2001) then this also points to the importance of interventions earlier in
life. Still, there may be some scope for higher education policies that ease credit constraints for
those families for whom such constraints bind. Indeed evidence from the SIPP suggests that
upward mobility is sharply lower for black families with especially low levels of wealth which is
consistent with the hypothesis that credit constraints may impede intergenerational mobility
(Becker and Tomes, 1979, 1986).
Many commentators have pointed to prevalence of black children raised by single
mothers as a source of racial gaps in economic success. I find supportive evidence that blacks
raised in two parent families throughout childhood experience significantly greater upward
mobility. Interestingly, family structure appears not to matter for whites or for rates of downward
mobility for either blacks or whites.
Finally, the analysis here finds much less of a role for measures of non-cognitive skills,
though the effects of such measures may be better revealed in structural models that account for
measurement and selection issues (Heckman, Stixrud and Urzua, 2006).

26

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Haider, Steven J. and Gary Solon. 2006. “Life Cycle Variation in the Association Between Current and
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28

Table 1: Summary Statistics
Panel A: NLSY

Family Income (1997-2005)
Child Age in 2001
Education
AFQT
Self Esteem
Rotter
SF Physical health
SF Mental health
Parent Income (1978-1980)
Dad's Education
Single Mother at age 14

N
6690
6690
6673
6432
6446
6621
6315
6315
6690
5714
6690

All
Mean
69395
39.1
13.0
46.0
17.3
5.9
23.7
24.2
57760
11.8
0.13

SD
58953
2.2
2.3
28.5
4.0
2.0
6.8
7.4
36299
3.5
0.33

N
3205
3205
3199
3080
3103
3178
3018
3018
3205
3006
3205

Whites
Mean
76284
39.1
13.2
52.5
17.4
5.8
24.0
24.1
64354
12.3
0.08

SD
61316
2.2
2.3
27.0
4.0
2.0
6.7
7.3
35965
3.2
0.27

N
2143
2143
2136
2082
2069
2118
2036
2036
2143
1588
2143

Blacks
Mean
42289
39.2
12.4
21.6
17.2
6.3
22.8
24.4
33743
10.2
0.3

SD
39070
2.2
2.1
19.8
4.0
2.2
7.3
8.0
26725
3.4
0.5

Blacks
Mean
9.48
30.66
0.53
0.27
0.23
0.12
0.19
0.18
9.63
33.11

SD
1.32
5.55
0.50
0.45
0.42
0.33
0.40
0.38
1.26
9.14

Panel B: SIPP-SSA

Son Log Earnings
Son Age in 2005
Single Parent
1984 Panel
1990 Panel
1991 Panel
1992 Panel
1993 Panel
Parent log Earnings
Dads Age in 1982
Net Worth

N
16782
16782
16782
16782
16782
16782
16782
16782
16782
15354

All
Mean
10.14
30.93
0.21
0.26
0.23
0.14
0.20
0.18
10.32
35.72

SD
1.07
5.69
0.41
0.44
0.42
0.35
0.40
0.38
1.06
8.85

N
14757
14757
14757
14757
14757
14757
14757
14757
14757
13467

Whites
Mean
10.23
30.97
0.17
0.25
0.23
0.15
0.20
0.18
10.42
36.09

SD
1.00
5.71
0.38
0.43
0.42
0.35
0.40
0.38
1.00
8.75

N
2025
2025
2025
2025
2025
2025
2025
2025
2025
1887

Table 2: Upward Transition Probability Estimates by Race, cumulative samples
Panel A: NLSY sample
Percent of children exceeding their parents percentile range by the amount, τ
Parent
percentile
range
1 to 10
[N w =197, N b =676]

1 to 20
[N w =468, N b =1127]

1 to 30
[N w =754, N b =1449]

1 to 40
[N w =1081, N b =1640]

1 to 50
[[N w =1425,, N b =1767]]

Whites
0.841
(0.031)

τ =0
Blacks
0.650
(0.020)

W-B
0.191
(0.040)

Whites
0.754
(0.035)

τ =0.1
Blacks
0.449
(0.021)

W-B
0.304
(0.042)

Whites
0.605
(0.039)

τ =0.2
Blacks
0.322
(0.021)

W-B
0.283
(0.043)

Whites
0.423
(0.039)

τ =0.3
Blacks
0.237
(0.019)

W-B
0.186
(0.019)

0.748
(0.022)

0.477
(0.018)

0.271
(0.029)

0.604
(0.024)

0.341
(0.018)

0.262
(0.030)

0.448
(0.027)

0.250
(0.016)

0.198
(0.032)

0.328
(0.023)

0.188
(0.015)

0.140
(0.015)

0.649
(0.018)

0.368
(0.013)

0.281
(0.025)

0.513
(0.019)

0.274
(0.013)

0.239
(0.026)

0.388
(0.018)

0.203
(0.013)

0.185
(0.023)

0.284
(0.018)

0.128
(0.010)

0.156
(0.010)

0.537
(0.013)

0.286
(0.011)

0.251
(0.018)

0.425
(0.014)

0.215
(0.011)

0.210
(0.019)

0.314
(0.014)

0.141
(0.009)

0.173
(0.018)

0.227
(0.013)

0.097
(0.008)

0.130
(0.008)

0.451
(0.0 )
(0.011)

0.220
(0.0 )
(0.012)

0.232
(0.0 9)
(0.019)

0.343
(0.0 )
(0.011)

0.145
(0.0 0)
(0.010)

0.198
(0.0 6)
(0.016)

0.240
(0.0 0)
(0.010)

0.099
(0.008)

0.141
(0.0 3)
(0.013)

0.160
(0.008)

0.057
(0.007)

0.103
(0.007)

0.835
(0.009)

0.632
(0.019)

0.203
(0.025)

0.701
(0.011)

0.451
(0.020)

0.250
(0.027)

0.544
(0.011)

0.331
(0.017)

0.213
(0.027)

0.424
(0.009)

0.254
(0.013)

0.170
(0.024)

0 737
0.737
(0.007)

0 492
0.492
(0.013)

0 245
0.245
(0.020)

0 592
0.592
(0.009)

0 370
0.370
(0.010)

0 222
0.222
(0.018)

0 470
0.470
(0.009)

0 285
0.285
(0.010)

0 185
0.185
(0.018)

0 361
0.361
(0.011)

0 188
0.188
(0.013)

0 173
0.173
(0.017)

0.619
(0.004)

0.408
(0.009)

0.211
(0.016)

0.494
(0.008)

0.319
(0.016)

0.175
(0.016)

0.385
(0.005)

0.220
(0.016)

0.165
(0.015)

0.283
(0.007)

0.147
(0.009)

0.137
(0.013)

0.515
(0.010)
(0
010)

0.329
(0
(0.014)
014)

0.186
(0
(0.015)
015)

0.404
(0
(0.006)
006)

0.234
(0
(0.016)
016)

0.170
(0
(0.014)
014)

0.301
(0
(0.005)
005)

0.155
(0
(0.009)
009)

0.146
(0
(0.012)
012)

0.204
(0
(0.005)
005)

0.097
(0
(0.009)
009)

0.106
(0
(0.009)
009)

0.427
(0.004)

0.246
(0.012)

0.181
(0.012)

0.319
(0.005)

0.166
(0.009)

0.153
(0.011)

0.216
(0.005)

0.103
(0.009)

0.113
(0.009)

0.128
(0.002)

0.051
(0.005)

0.077
(0.007)

Panel B: SIPP-SSA sample
1 to 10
[N w =1197, N b =481]

1 to 20
[N w =2510, N b =846]

1 to 30
[N w =3902, N b =1132]

1 to 40
[N w =5325,
5325 N b =1387]
1387]

1 to 50
[N w =6808, N b =1583]

Notes: See text for a description of the estimator. Panel A uses a sample of 6690 individuals from the NLSY and uses multiyear averages of son or daughter's
family income over 1997-2005 and parent family income measured over 1978-1980. NLSY analysis incorporates the 1979 sampling weights. Panel B uses
a sample of 16,782 men from the SIPP-SSA data and uses a multiyear average of sons' earnings over 2003-2007 and parent earnings over 1978-1986.
Bootstrapped standard errors are in parentheses.

Table 3: Downward Transition Probability Estimates by Race, cumulative samples
Panel A: NLSY sample
Percent of children at or below the bottom of their parents percentile range by the amount, τ
Parent
percentile
range
91 to 100
[N w =368, N b =46]

81 to 100
[N w =724, N b =116]

71 to 100
[N w =1088, N b =183]

61 to 100
[N w =1431, N b =268]

51 to 100
[[N w =1780,, N b =376]]

Whites
0.725
(0.020)

τ =0
Blacks
0.813
(0.069)

W-B
-0.087
(0.072)

Whites
0.548
(0.024)

τ =0.1
Blacks
0.579
(0.082)

W-B
-0.031
(0.084)

Whites
0.426
(0.023)

τ =0.2
Blacks
0.562
(0.079)

W-B
-0.136
(0.083)

Whites
0.318
(0.022)

τ =0.3
Blacks
0.467
(0.081)

W-B
-0.149
(0.081)

0.603
(0.015)

0.685
(0.047)

-0.082
(0.051)

0.471
(0.018)

0.620
(0.048)

-0.148
(0.053)

0.363
(0.016)

0.507
(0.054)

-0.144
(0.057)

0.270
(0.015)

0.475
(0.054)

-0.204
(0.054)

0.509
(0.012)

0.685
(0.038)

-0.177
(0.040)

0.396
(0.012)

0.583
(0.038)

-0.187
(0.040)

0.298
(0.013)

0.531
(0.038)

-0.233
(0.039)

0.202
(0.011)

0.398
(0.037)

-0.195
(0.037)

0.436
(0.010)

0.643
(0.033)

-0.207
(0.036)

0.332
(0.010)

0.588
(0.034)

-0.256
(0.037)

0.232
(0.009)

0.459
(0.036)

-0.227
(0.037)

0.159
(0.009)

0.356
(0.032)

-0.197
(0.032)

0.357
(0.007)

0.610
(0.0 9)
(0.029)

-0.253
(0.03 )
(0.031)

0.255
(0.007)

0.491
(0.0 9)
(0.029)

-0.236
(0.030)

0.175
(0.007)

0.372
(0.0 8)
(0.028)

-0.197
(0.0 9)
(0.029)

0.105
(0.005)

0.270
(0.0 7)
(0.027)

-0.165
(0.0 7)
(0.027)

0.720
(0.009)

0.882
(0.059)

-0.162
(0.059)

0.561
(0.012)

0.765
(0.076)

-0.204
(0.076)

0.455
(0.012)

0.676
(0.082)

-0.222
(0.085)

0.374
(0.012)

0.618
(0.082)

-0.243
(0.082)

0 620
0.620
(0.007)

0 764
0.764
(0.043)

-0 144
-0.144
(0.044)

0 498
0.498
(0.007)

0 652
0.652
(0.051)

-0 154
-0.154
(0.052)

0 404
0.404
(0.008)

0 573
0.573
(0.055)

-0 169
-0.169
(0.056)

0 323
0.323
(0.007)

0 449
0.449
(0.053)

-0 126
-0.126
(0.053)

0.529
(0.006)

0.726
(0.034)

-0.197
(0.036)

0.429
(0.006)

0.626
(0.038)

-0.196
(0.039)

0.342
(0.006)

0.525
(0.037)

-0.183
(0.038)

0.263
(0.006)

0.441
(0.036)

-0.178
(0.037)

0.459
(0.005)
(0
005)

0.646
(0
(0.029)
029)

-0.188
(0
(0.030)
030)

0.365
(0
(0.005)
005)

0.554
(0
(0.031)
031)

-0.188
(0
(0.032)
032)

0.279
(0
(0.005)
005)

0.471
(0
(0.029)
029)

-0.193
(0
(0.029)
029)

0.203
(0
(0.004)
004)

0.357
(0
(0.028)
028)

-0.155
(0
(0.029)
029)

0.382
(0.004)

0.577
(0.025)

-0.195
(0.027)

0.290
(0.004)

0.495
(0.022)

-0.205
(0.024)

0.207
(0.004)

0.382
(0.024)

-0.175
(0.025)

0.132
(0.003)

0.285
(0.022)

-0.153
(0.023)

Panel B: SIPP-SSA sample
91 to 100
[N w =1645, N b =34]

81 to 100
[N w =3268, N b =89]

71 to 100
[N w =4856, N b =179]

61 to 100
[N w =6433,
6433 N b =280]
280]

51 to 100
[N w =7949, N b =442]

Notes: See text for a description of the estimator. Panel A uses a sample of 6690 individuals from the NLSY and uses multiyear averages of son or daughter's
family income over 1997-2005 and parent family income measured over 1978-1980. NLSY analysis incorporates the 1979 sampling weights. Panel B uses
a sample of 16,782 men from the SIPP-SSA data and uses a multiyear average of sons' earnings over 2003-2007 and parent earnings over 1978-1986.
Bootstrapped standard errors are in parentheses.

Table 4: Upward Rank Mobility Estimates by Race, cumulative samples
Panel A: NLSY sample
Percent of children exceeding their parents exact percentile by the amount, τ
Parent
percentile
range
1 to 10
[N w =197, N b =676]

1 to 20
[N w =468, N b =1127]

1 to 30
[N w =754, N b =1449]

1 to 40
[N w =1081, N b =1640]

1 to 50
[[N w =1425,, N b =1767]]

Whites
0.908
(0.026)

τ =0
Blacks
0.824
(0.019)

W-B
0.084
(0.033)

Whites
0.801
(0.032)

τ =0.1
Blacks
0.540
(0.023)

W-B
0.262
(0.040)

Whites
0.675
(0.033)

τ =0.2
Blacks
0.386
(0.021)

W-B
0.288
(0.040)

Whites
0.490
(0.043)

τ =0.3
Blacks
0.274
(0.018)

W-B
0.216
(0.043)

0.864
(0.018)

0.745
(0.016)

0.119
(0.025)

0.709
(0.023)

0.502
(0.016)

0.207
(0.029)

0.603
(0.026)

0.357
(0.016)

0.246
(0.031)

0.453
(0.024)

0.257
(0.014)

0.195
(0.028)

0.827
(0.014)

0.688
(0.013)

0.139
(0.019)

0.690
(0.017)

0.480
(0.015)

0.210
(0.024)

0.575
(0.019)

0.339
(0.014)

0.236
(0.023)

0.435
(0.017)

0.242
(0.013)

0.193
(0.021)

0.775
(0.011)

0.658
(0.013)

0.116
(0.017)

0.636
(0.014)

0.463
(0.013)

0.173
(0.019)

0.529
(0.015)

0.333
(0.013)

0.196
(0.020)

0.396
(0.015)

0.238
(0.012)

0.158
(0.020)

0.721
(0.0 )
(0.011)

0.632
(0.0 )
(0.012)

0.089
(0.0 7)
(0.017)

0.593
(0.0 )
(0.012)

0.445
(0.0 3)
(0.013)

0.147
(0.0 9)
(0.019)

0.485
(0.0 )
(0.012)

0.318
(0.0 3)
(0.013)

0.167
(0.0 8)
(0.018)

0.358
(0.0 )
(0.011)

0.228
(0.0 )
(0.011)

0.130
(0.0 7)
(0.017)

0.919
(0.005)

0.807
(0.009)

0.112
(0.021)

0.764
(0.009)

0.538
(0.018)

0.225
(0.026)

0.623
(0.009)

0.399
(0.020)

0.224
(0.026)

0.475
(0.009)

0.297
(0.013)

0.178
(0.028)

0 870
0.870
(0.005)

0 740
0.740
(0.014)

0 130
0.130
(0.018)

0 731
0.731
(0.008)

0 520
0.520
(0.012)

0 211
0.211
(0.020)

0 600
0.600
(0.012)

0 392
0.392
(0.020)

0 207
0.207
(0.020)

0 463
0.463
(0.007)

0 284
0.284
(0.014)

0 179
0.179
(0.019)

0.820
(0.006)

0.699
(0.011)

0.121
(0.015)

0.683
(0.006)

0.508
(0.016)

0.176
(0.017)

0.555
(0.007)

0.389
(0.022)

0.166
(0.017)

0.429
(0.004)

0.278
(0.016)

0.151
(0.015)

0.769
(0.007)
(0
007)

0.650
(0
(0.010)
010)

0.119
(0
(0.014)
014)

0.639
(0
(0.005)
005)

0.476
(0
(0.018)
018)

0.163
(0
(0.014)
014)

0.516
(0
(0.008)
008)

0.359
(0
(0.018)
018)

0.157
(0
(0.015)
015)

0.391
(0
(0.005)
005)

0.254
(0
(0.015)
015)

0.137
(0
(0.013)
013)

0.726
(0.003)

0.618
(0.013)

0.108
(0.013)

0.597
(0.005)

0.451
(0.008)

0.146
(0.014)

0.473
(0.005)

0.337
(0.007)

0.136
(0.013)

0.353
(0.002)

0.236
(0.008)

0.117
(0.011)

Panel B: SIPP-SSA sample
1 to 10
[N w =1197, N b =481]

1 to 20
[N w =2510, N b =846]

1 to 30
[N w =3902, N b =1132]

1 to 40
[N w =5325,
5325 N b =1387]
1387]

1 to 50
[N w =6808, N b =1583]

Notes: See text for a description of the estimator. Panel A uses a sample of 6690 individuals from the NLSY and uses multiyear averages of son or daughter's
family income over 1997-2005 and parent family income measured over 1978-1980. NLSY analysis incorporates the 1979 sampling weights. Panel B uses
a sample of 16,782 men from the SIPP-SSA data and uses a multiyear average of sons' earnings over 2003-2007 and parent earnings over 1978-1986.
Bootstrapped standard errors are in parentheses.

Table 5: Downward Rank Mobility Estimates by Race, cumulative samples
Panel A: NLSY sample
Percent of children below their parents exact percentile by the amount, τ
Parent
percentile
range
91 to 100
[N w =368, N b =46]

81 to 100
[N w =724, N b =116]

71 to 100
[N w =1088, N b =183]

61 to 100
[N w =1431, N b =268]

51 to 100
[[N w =1780,, N b =376]]

Whites
0.870
(0.017)

τ =0
Blacks
0.912
(0.056)

W-B
-0.042
(0.059)

Whites
0.630
(0.024)

τ =0.1
Blacks
0.661
(0.077)

W-B
-0.032
(0.084)

Whites
0.491
(0.027)

τ =0.2
Blacks
0.562
(0.077)

W-B
-0.071
(0.080)

Whites
0.371
(0.025)

τ =0.3
Blacks
0.522
(0.077)

W-B
-0.151
(0.082)

0.815
(0.015)

0.842
(0.037)

-0.027
(0.038)

0.611
(0.014)

0.685
(0.051)

-0.074
(0.053)

0.477
(0.017)

0.588
(0.052)

-0.111
(0.055)

0.360
(0.019)

0.520
(0.051)

-0.160
(0.054)

0.771
(0.011)

0.842
(0.033)

-0.071
(0.034)

0.575
(0.012)

0.699
(0.037)

-0.123
(0.040)

0.451
(0.013)

0.613
(0.039)

-0.162
(0.041)

0.342
(0.013)

0.526
(0.037)

-0.185
(0.039)

0.733
(0.010)

0.823
(0.028)

-0.090
(0.030)

0.557
(0.012)

0.716
(0.031)

-0.159
(0.034)

0.435
(0.010)

0.630
(0.031)

-0.196
(0.033)

0.327
(0.010)

0.535
(0.032)

-0.208
(0.033)

0.693
(0.009)

0.788
(0.0 5)
(0.025)

-0.094
(0.0 6)
(0.026)

0.528
(0.0 0)
(0.010)

0.682
(0.0 8)
(0.028)

-0.154
(0.030)

0.408
(0.009)

0.591
(0.0 7)
(0.027)

-0.184
(0.030)

0.299
(0.009)

0.473
(0.0 7)
(0.027)

-0.173
(0.030)

0.852
(0.008)

0.882
(0.053)

-0.031
(0.054)

0.633
(0.011)

0.824
(0.061)

-0.191
(0.062)

0.503
(0.011)

0.735
(0.078)

-0.232
(0.080)

0.410
(0.013)

0.618
(0.083)

-0.208
(0.084)

0 808
0.808
(0.006)

0 820
0.820
(0.039)

-0 012
-0.012
(0.040)

0 619
0.619
(0.008)

0 742
0.742
(0.048)

-0 123
-0.123
(0.048)

0 495
0.495
(0.008)

0 652
0.652
(0.053)

-0 156
-0.156
(0.054)

0 392
0.392
(0.008)

0 551
0.551
(0.055)

-0 159
-0.159
(0.056)

0.761
(0.005)

0.821
(0.030)

-0.060
(0.031)

0.591
(0.006)

0.732
(0.032)

-0.141
(0.034)

0.473
(0.006)

0.637
(0.038)

-0.163
(0.039)

0.372
(0.005)

0.547
(0.039)

-0.175
(0.040)

0.721
(0.005)
(0
005)

0.793
(0
(0.024)
024)

-0.072
(0
(0.025)
025)

0.567
(0
(0.005)
005)

0.696
(0
(0.029)
029)

-0.129
(0
(0.030)
030)

0.451
(0
(0.005)
005)

0.614
(0
(0.030)
030)

-0.163
(0
(0.031)
031)

0.352
(0
(0.005)
005)

0.525
(0
(0.032)
032)

-0.173
(0
(0.033)
033)

0.682
(0.004)

0.749
(0.020)

-0.066
(0.021)

0.535
(0.004)

0.652
(0.024)

-0.116
(0.024)

0.420
(0.004)

0.563
(0.025)

-0.143
(0.026)

0.319
(0.005)

0.471
(0.023)

-0.152
(0.024)

Panel B: SIPP-SSA sample
91 to 100
[N w =1645, N b =34]

81 to 100
[N w =3268, N b =89]

71 to 100
[N w =4856, N b =179]

61 to 100
[N w =6433,
6433 N b =280]
280]

51 to 100
[N w =7949, N b =442]

Notes: See text for a description of the estimator. Panel A uses a sample of 6690 individuals from the NLSY and uses multiyear averages of son or daughter's
family income over 1997-2005 and parent family income measured over 1978-1980. NLSY analysis incorporates the 1979 sampling weights. Panel B uses
a sample of 16,782 men from the SIPP-SSA data and uses a multiyear average of sons' earnings over 2003-2007 and parent earnings over 1978-1986.
Bootstrapped standard errors are in parentheses.

Table 6: Comparison of Upward Transition Probability and Upward Rank Mobility Race Using interval samples
Panel A: Upward Transition Probability
Percent of children exceeding their parents percentile range by the amount, τ
Parent
percentile
range
1 to 10
[N w =197, N b =676]

11 to 20
[N w =468, N b =1127]

21 to 30
[N w =754, N b =1449]

31 to 40
[N w =1081, N b =1640]

41 to 50
[[N w =1425,, N b =1767]]

Whites
0.841
(0.031)

τ =0
Blacks
0.650
(0.020)

W-B
0.191
(0.040)

Whites
0.754
(0.035)

τ =0.1
Blacks
0.449
(0.021)

W-B
0.304
(0.042)

Whites
0.605
(0.039)

τ =0.2
Blacks
0.322
(0.021)

W-B
0.283
(0.043)

Whites
0.423
(0.039)

τ =0.3
Blacks
0.237
(0.019)

W-B
0.186
(0.019)

0.744
(0.031)

0.519
(0.027)

0.226
(0.044)

0.603
(0.032)

0.371
(0.026)

0.233
(0.044)

0.465
(0.036)

0.268
(0.026)

0.197
(0.047)

0.346
(0.034)

0.197
(0.023)

0.149
(0.023)

0.711
(0.029)

0.458
(0.031)

0.253
(0.043)

0.602
(0.031)

0.353
(0.032)

0.249
(0.043)

0.469
(0.032)

0.250
(0.029)

0.220
(0.041)

0.359
(0.030)

0.159
(0.022)

0.200
(0.022)

0.584
(0.028)

0.376
(0.038)

0.209
(0.047)

0.499
(0.029)

0.307
(0.034)

0.191
(0.044)

0.374
(0.029)

0.238
(0.032)

0.135
(0.043)

0.279
(0.027)

0.169
(0.030)

0.110
(0.030)

0.524
(0.0 7)
(0.027)

0.275
(0.0 )
(0.044)

0.249
(0.053)

0.425
(0.0 7)
(0.027)

0.194
(0.036)

0.232
(0.0 6)
(0.046)

0.279
(0.0 5)
(0.025)

0.130
(0.03 )
(0.034)

0.149
(0.0 )
(0.044)

0.194
(0.0 )
(0.022)

0.072
(0.0 6)
(0.026)

0.123
(0.0 6)
(0.026)

0.908
(0.026)

0.824
(0.019)

0.084
(0.033)

0.801
(0.032)

0.540
(0.023)

0.262
(0.040)

0.675
(0.033)

0.386
(0.021)

0.288
(0.040)

0.490
(0.043)

0.274
(0.018)

0.216
(0.043)

0 834
0.834
(0.026)

0 628
0.628
(0.027)

0 206
0.206
(0.040)

0 646
0.646
(0.033)

0 446
0.446
(0.024)

0 200
0.200
(0.041)

0 555
0.555
(0.035)

0 314
0.314
(0.026)

0 241
0.241
(0.043)

0 427
0.427
(0.036)

0 232
0.232
(0.023)

0 195
0.195
(0.043)

0.776
(0.026)

0.496
(0.030)

0.281
(0.040)

0.664
(0.032)

0.408
(0.032)

0.255
(0.048)

0.536
(0.030)

0.279
(0.029)

0.257
(0.041)

0.411
(0.033)

0.190
(0.025)

0.221
(0.042)

0.672
(0.025)
(0
025)

0.440
(0
(0.039)
039)

0.233
(0
(0.048)
048)

0.532
(0
(0.027)
027)

0.332
(0
(0.037)
037)

0.199
(0
(0.047)
047)

0.440
(0
(0.027)
027)

0.286
(0
(0.033)
033)

0.154
(0
(0.043)
043)

0.320
(0
(0.027)
027)

0.207
(0
(0.033)
033)

0.112
(0
(0.041)
041)

0.570
(0.026)

0.314
(0.044)

0.256
(0.052)

0.469
(0.029)

0.232
(0.043)

0.237
(0.052)

0.360
(0.029)

0.140
(0.038)

0.220
(0.049)

0.250
(0.025)

0.106
(0.030)

0.144
(0.040)

Panel B: Upward Rank Mobility
1 to 10
[N w =197, N b =676]

11 to 20
[N w =468, N b =1127]

21 to 30
[N w =754, N b =1449]

31 to 40
[N w =1081,
1081 N b =1640]
1640]

41 to 50
[N w =1425, N b =1767]

Notes: See text for a description of the estimator. Panel A uses a sample of 6690 individuals from the NLSY and uses multiyear averages of son or daughter's
family income over 1997-2005 and parent family income measured over 1978-1980. NLSY analysis incorporates the 1979 sampling weights. Panel B uses
a sample of 16,782 men from the SIPP-SSA data and uses a multiyear average of sons' earnings over 2003-2007 and parent earnings over 1978-1986.
Bootstrapped standard errors are in parentheses.

Table 7: Transition Matrices by Race Using SIPP-SSA sample
Panel A: Whites

1

2
Parent's
Income
Quintile

3

4

5

1
0.263
(0.008)
2510
0.205
(0.009)
2815
0.156
(0.007)
2999
0.147
(0.007)
3165
0.113
(0.006)
3268

Child's Income Quintile
2
3
4
0.267
0.208
0.159
(0.007)
(0.006)
(0.005)
2510
2510
2510
0.239
0.219
0.204
(0.008)
(0.007)
(0.006)
2815
2815
2815
0.203
0.236
0.223
(0.007)
(0.007)
(0.006)
2999
2999
2999
0.162
0.206
0.234
(0.006)
(0.007)
(0.006)
3165
3165
3165
0.136
0.155
0.217
(0.006)
(0.006)
(0.007)
3268
3268
3268

5
0.103
(0.005)
2510
0.133
(0.005)
2815
0.182
(0.006)
2999
0.250
(0.006)
3165
0.380
(0.007)
3268

Child's Income Quintile
2
3
4
0.207
0.155
0.092
(0.021)
(0.025)
(0.034)
846
846
846
0.246
0.203
0.129
(0.020)
(0.023)
(0.028)
541
541
541
0.212
0.176
0.190
(0.018)
(0.021)
(0.030)
358
358
358
0.236
0.173
0.178
(0.012)
(0.019)
(0.028)
191
191
191
0.180
0.180
0.191
(0.011)
(0.015)
(0.026)
89
89
89

5
0.038
(0.048)
846
0.065
(0.041)
541
0.081
(0.045)
358
0.141
(0.042)
191
0.236
(0.048)
89

Panel B: Blacks

1

2
Parent's
Income
Quintile

3

4

5

1
0.508
(0.017)
846
0.357
(0.013)
541
0.341
(0.012)
358
0.272
(0.010)
191
0.213
(0.007)
89

Notes: See text for a description. Both panels use sub-samples drawn from a sample of 16,782 men from
the SIPP-SSA data and uses a multiyear average of sons' earnings over 2003-2007 and parent earnings
over 1978-1986. Bootstrapped standard errors are in parentheses. Sample sizes are shown below the
standard errors.

Table 8: Regression decomposition of black-white mobility gaps
UTP leaving
bottom quintile
Percent
W-B gap
Explained

DTP leaving
top half
Percent
W-B gap
Explained

Unconditional

-0.271

--

0.253

--

Parent Covariates
Father's Education
Mother's Education
Single Mother

-0.242
-0.261
-0.279

0.107
0.036
-0.030

0.208
0.234
0.244

0.179
0.075
0.039

-0.251

0.075

0.198

0.221

-0.279
-0.160
-0.274
-0.258
-0.270
-0.279

-0.031
0.408
-0.010
0.046
0.004
-0.028

0.225
0.103
0.257
0.244
0.239
0.256

0.112
0.594
-0.015
0.037
0.057
-0.011

-0.226

0.165

0.153

0.397

All Parent covariates
Children Covariates
Education
AFQT Score
Self Esteem
Rotter Scale
Adult Physical Health
Adult Mental Health
All Children covariates

Figure 1: Stylized Example of Racial Differences in Intergenerational
Elasticities
18

LLog Income of Son

16

14

12

10

8

6
4

6

8

10

Log Income of Father

Whites

Blacks

12

14

16

Figure 2: Upward Transition Probabilities by Race
Using Cumulative Samples (tau=0)
1
0.9
08
0.8

Transition Probabiilities

0.7
06
0.6

Whites (NLSY)
Blacks (NLSY)

0.5

W ‐ B (NLSY)
Whites
(SIPP‐SSA)
Whit (SIPP
SSA)

04
0.4

Blacks (SIPP‐SSA)
0.3

W ‐ B (SIPP‐SSA)

0.2
0.1
0
1 to 10

1 to 20

1 to 30

1 to 40

Percentile Range of Parent Income

1 to 50

Figure 3: Downward Transition Probabilities by Race
Using Cumulative Samples (tau=0)
1
0.9
0.8
0.7

Transition Probabilities

0.6

Whites (NLSY)

0.5

Blacks (NLSY)

0.4

W ‐ B (NLSY)
03
0.3

Blacks
Bl k (SIPP‐SSA)
(SIPP SSA)

0.2

Whites (SIPP‐SSA)
W ‐ B (SIPP‐SSA)

0.1
0
‐0.1

91‐100

81‐100

71‐100

61‐100

‐0.2
‐0.3

Percentile Range of Parent Income

51‐100

Figure 4: Upward Rank Mobility by Race
Using Cumulative Samples (tau=0)
1
0.9
08
0.8

P
Probabilities

0.7
06
0.6

Whites (NLSY)
Blacks (NLSY)

0.5

W ‐ B (NLSY)
Whites
(SIPP‐SSA)
Whit (SIPP
SSA)

04
0.4

Blacks (SIPP‐SSA)
0.3

W ‐ B (SIPP‐SSA)

0.2
0.1
0
1 to 10

1 to 20

1 to 30

1 to 40

Percentile Range of Parent Income

1 to 50

Figure 5: Upward Rank Mobility by Race
Using Cumulative Samples (tau=0.2)
1
0.9
08
0.8

P
Probabilities

0.7
06
0.6

Whites (NLSY)
Blacks (NLSY)

0.5

W ‐ B (NLSY)
Whites
(SIPP‐SSA)
Whit (SIPP
SSA)

04
0.4

Blacks (SIPP‐SSA)
0.3

W ‐ B (SIPP‐SSA)

0.2
0.1
0
1 to 10

1 to 20

1 to 30

1 to 40

Percentile Range of Parent Income

1 to 50

Figure 6 : Downward Rank Mobility by Race
Using Cumulative Samples (tau=0)
1
0.9
0.8
0.7
0.6

Whites (NLSY)

Pro
obabilities

0.5

Blacks (NLSY)

0.4

W ‐ B (NLSY)
03
0.3

Whites
(SIPP‐SSA)
Whit (SIPP
SSA)

0.2

Blacks (SIPP‐SSA)
W ‐B (SIPP‐SSA)

0.1
0
‐0.1

91‐100

81‐100

71‐100

61‐100

‐0.2
‐0.3

Percentile Range of Parent Income

51‐100

Figure 7: Downward Rank Mobility by Race
Using Cumulative Samples (tau=0.2)
1
0.9
0.8
0.7
0.6

Whites (NLSY)

Probabilities

0.5

Blacks (NLSY)

0.4

W ‐ B (NLSY)
03
0.3

Whites
(SIPP‐SSA)
Whit (SIPP
SSA)

0.2

Blacks (SIPP‐SSA)
W ‐B (SIPP‐SSA)

0.1
0
‐0.1

91‐100

81‐100

71‐100

61‐100

‐0.2
‐0.3

Percentile Range of Parent Income

51‐100

Figure 8: Upward Mobility Estimates by Race
Using Intervalled Samples (tau=0)
1
0.9
08
0.8

........ ........

______ _

Transition Probabiilities

0.7

--

06
0.6

---

0.5
04
0.4

-

0.3
0.2
0.1
0
0 < s <=10

10 < s <=20

20 < s <=30

30 < s <=40

Percentile Range of Parent Income

40 < s <=50

Whites (UTP)
Blacks (UTP)
W ‐ B (UTP)
Whites
Whit (URM)
Blacks (URM)
W ‐ B (URM)

Figure 9: Upward and Downward Transition Probability Estimates Conditional on Covariates
1.2

A: Upward Transition Probability Out of Bottom Quintile
Conditional on Own Education

1
0.8

0.8

Transition Probability

Transition Probability

1

0.6
0.4
0.2

0.6
0.4
0.2
0

0

7
3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19

‐0.4

8

9

10

11

12

13

14

15

16

17

18

19

‐0.2

‐0.2

1.2

B: Downward Transition Probability Out of Top Half
Conditional on Own Education

‐0.4

Years of Schooling

C: Upward Transition Probability Out of Bottom Quintile
Conditional on Father's Education

1

Years of Schooling

D: Downward Transition Probability Out of Top Half
Conditional on Father's Education

1
0.8
0.6

Transition Probability

Transition Probability

0.8
0.6
0.4
0.2
0

0.4
0.2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
‐0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
02
‐0.2

‐0.4
‐0.4

Father's Years of Schooling

‐0.6

E: Upward Transition Probability Out of Bottom Quintile
Conditional on AFQT

1.2

1
0.9

1.0

F: Downward Transition Probability Out of Top Half
Conditional on AFQT

0.8
0.7

Transition Probability

0.8

Transition Probability

Father's Years of Schooling

0.6
0.4
0.2
0.0
1

11

21

31

41

51

61

71

81

91

0.6
0.5
0.4
0.3
0.2
0.1
0
‐0.1 1

11

21

31

41

51

61

71

81

‐0.2

‐0.2

‐0.3
‐0.4

Legend:

‐0.4

AFQT Percentile

AFQT Percentile

Whites

Blacks

W‐B

Whites, Unconditional

Blacks, Unconditional

W‐B, Unconditional

91

1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
‐0.1
‐0.2
‐0.3
‐0.4

G: Upward Transition Probability Out of Bottom Quintile
Conditional on Self Esteem

H: Downward Transition Probability Out of Top Half
Conditional on Self Esteem

1
0.9
0.8
0.7
0.6

Transition Probability

Transition Probability

Figure 9: Upward and Downward Transition Probability Estimates Conditional on Covariates

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0.5
0.4
0.3
0.2
0.1
0
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

‐0.1
‐0.2
‐0.3

Self Esteem

‐0.4

I: Upward Transition Probability Out of Bottom Quintile
Conditional on Rotter Scale

1.2
1.1

Self Esteem
J: Downward Transition Probability Out of Top Half
Conditional on Rotter Scale

1

1

0.8

0.9
0.7

Transition Probability

Transition Probability

0.8
0.6
0.5
0.4
0.3
0.2
0.1
0
‐0.1

1

2

3

4

5

6

7

8

9

10

11

12

0.6

0.4

0.2

0
1

13

2

3

4

5

6

7

8

9

10

11

12

13

‐0.2

‐0.2
‐0.3
‐0.4

1
0.9

‐0.4

Rotter Scale

Rotter Scale

1

K: Upward Transition Probability Out of Bottom Quintile
Conditional on Single Mother Status

0.9

L: Downward Transition Probability Out of Top Half
Conditional on Single Mother Status

0.8

0.8

0.7
0.6

Transition Probability

Transition Probability

0.7
0.6
0.5
0.4
0.3
0.2

0.5
0.4
0.3
0.2
0.1
0

0.1

‐0.1

0
‐0.1

Single Mother at 14

Two parents at 14

‐0.2

Two parents at 14

‐0.3
‐0.4

‐0.2

Legend:

Single Mother at 14

Whites

Blacks

W‐B

Whites, Unconditional

Blacks, Unconditional

W‐B, Unconditional

Figure 10: Upward Transition Probabliity Out of Bottom Quintile
Conditional on Childhood Family Structure, SIPP sample
1
0.9
0.8
0.7

Transition
n Probability

0.6
Whites, Unconditional
0.5

Blacks, Unconditional
W ‐ B, Unconditional

0.4

Whit
Whites
Blacks

0.3

W‐B
0.2
0.1
0
O Parent
One
P
E
Ever
‐0.1
‐0.2

T Parent
Two
P
Always
Al

Figure 11: Downward Transition Probabliity Out of Top Half
Conditional on Childhood Family Structure, SIPP sample
1
0.9
0.8
0.7

Transition
n Probability

0.6
05
0.5

Whites, Unconditional
Blacks, Unconditional

0.4

W ‐ B, Unconditional

0.3

Whit
Whites

0.2

Blacks
W‐B

0.1
0
One Parent Ever
‐0.1
‐0
0.2
2
‐0.3
‐0.4

Two Parent Always

Figure 12: Upward Transition Probabliity Out of Bottom Quintile
Conditional on Net Worth

Figure 13: Downward Transition Probabliity Out of Top Half
Conditional on Net Worth

Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
A Leverage-based Model of Speculative Bubbles
Gadi Barlevy

WP-08-01

Displacement, Asymmetric Information and Heterogeneous Human Capital
Luojia Hu and Christopher Taber

WP-08-02

BankCaR (Bank Capital-at-Risk): A credit risk model for US commercial bank charge-offs
Jon Frye and Eduard Pelz

WP-08-03

Bank Lending, Financing Constraints and SME Investment
Santiago Carbó-Valverde, Francisco Rodríguez-Fernández, and Gregory F. Udell

WP-08-04

Global Inflation
Matteo Ciccarelli and Benoît Mojon

WP-08-05

Scale and the Origins of Structural Change
Francisco J. Buera and Joseph P. Kaboski

WP-08-06

Inventories, Lumpy Trade, and Large Devaluations
George Alessandria, Joseph P. Kaboski, and Virgiliu Midrigan

WP-08-07

School Vouchers and Student Achievement: Recent Evidence, Remaining Questions
Cecilia Elena Rouse and Lisa Barrow

WP-08-08

Does It Pay to Read Your Junk Mail? Evidence of the Effect of Advertising on
Home Equity Credit Choices
Sumit Agarwal and Brent W. Ambrose

WP-08-09

The Choice between Arm’s-Length and Relationship Debt: Evidence from eLoans
Sumit Agarwal and Robert Hauswald

WP-08-10

Consumer Choice and Merchant Acceptance of Payment Media
Wilko Bolt and Sujit Chakravorti

WP-08-11

Investment Shocks and Business Cycles
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti

WP-08-12

New Vehicle Characteristics and the Cost of the
Corporate Average Fuel Economy Standard
Thomas Klier and Joshua Linn

WP-08-13

Realized Volatility
Torben G. Andersen and Luca Benzoni

WP-08-14

Revenue Bubbles and Structural Deficits: What’s a state to do?
Richard Mattoon and Leslie McGranahan

WP-08-15

1

Working Paper Series (continued)
The role of lenders in the home price boom
Richard J. Rosen

WP-08-16

Bank Crises and Investor Confidence
Una Okonkwo Osili and Anna Paulson

WP-08-17

Life Expectancy and Old Age Savings
Mariacristina De Nardi, Eric French, and John Bailey Jones

WP-08-18

Remittance Behavior among New U.S. Immigrants
Katherine Meckel

WP-08-19

Birth Cohort and the Black-White Achievement Gap:
The Roles of Access and Health Soon After Birth
Kenneth Y. Chay, Jonathan Guryan, and Bhashkar Mazumder

WP-08-20

Public Investment and Budget Rules for State vs. Local Governments
Marco Bassetto

WP-08-21

Why Has Home Ownership Fallen Among the Young?
Jonas D.M. Fisher and Martin Gervais

WP-09-01

Why do the Elderly Save? The Role of Medical Expenses
Mariacristina De Nardi, Eric French, and John Bailey Jones

WP-09-02

Using Stock Returns to Identify Government Spending Shocks
Jonas D.M. Fisher and Ryan Peters

WP-09-03

Stochastic Volatility
Torben G. Andersen and Luca Benzoni

WP-09-04

The Effect of Disability Insurance Receipt on Labor Supply
Eric French and Jae Song

WP-09-05

CEO Overconfidence and Dividend Policy
Sanjay Deshmukh, Anand M. Goel, and Keith M. Howe

WP-09-06

Do Financial Counseling Mandates Improve Mortgage Choice and Performance?
Evidence from a Legislative Experiment
Sumit Agarwal,Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff

WP-09-07

Perverse Incentives at the Banks? Evidence from a Natural Experiment
Sumit Agarwal and Faye H. Wang

WP-09-08

Pay for Percentile
Gadi Barlevy and Derek Neal

WP-09-09

The Life and Times of Nicolas Dutot
François R. Velde

WP-09-10

Regulating Two-Sided Markets: An Empirical Investigation
Santiago Carbó Valverde, Sujit Chakravorti, and Francisco Rodriguez Fernandez

WP-09-11

2

Working Paper Series (continued)
The Case of the Undying Debt
François R. Velde
Paying for Performance: The Education Impacts of a Community College Scholarship
Program for Low-income Adults
Lisa Barrow, Lashawn Richburg-Hayes, Cecilia Elena Rouse, and Thomas Brock
Establishments Dynamics, Vacancies and Unemployment: A Neoclassical Synthesis
Marcelo Veracierto

WP-09-12

WP-09-13

WP-09-14

The Price of Gasoline and the Demand for Fuel Economy:
Evidence from Monthly New Vehicles Sales Data
Thomas Klier and Joshua Linn

WP-09-15

Estimation of a Transformation Model with Truncation,
Interval Observation and Time-Varying Covariates
Bo E. Honoré and Luojia Hu

WP-09-16

Self-Enforcing Trade Agreements: Evidence from Antidumping Policy
Chad P. Bown and Meredith A. Crowley

WP-09-17

Too much right can make a wrong: Setting the stage for the financial crisis
Richard J. Rosen

WP-09-18

Can Structural Small Open Economy Models Account
for the Influence of Foreign Disturbances?
Alejandro Justiniano and Bruce Preston

WP-09-19

Liquidity Constraints of the Middle Class
Jeffrey R. Campbell and Zvi Hercowitz

WP-09-20

Monetary Policy and Uncertainty in an Empirical Small Open Economy Model
Alejandro Justiniano and Bruce Preston

WP-09-21

Firm boundaries and buyer-supplier match in market transaction:
IT system procurement of U.S. credit unions
Yukako Ono and Junichi Suzuki
Health and the Savings of Insured Versus Uninsured, Working-Age Households in the U.S.
Maude Toussaint-Comeau and Jonathan Hartley

WP-09-22

WP-09-23

The Economics of “Radiator Springs:” Industry Dynamics, Sunk Costs, and
Spatial Demand Shifts
Jeffrey R. Campbell and Thomas N. Hubbard

WP-09-24

On the Relationship between Mobility, Population Growth, and
Capital Spending in the United States
Marco Bassetto and Leslie McGranahan

WP-09-25

The Impact of Rosenwald Schools on Black Achievement
Daniel Aaronson and Bhashkar Mazumder

WP-09-26

3

Working Paper Series (continued)
Comment on “Letting Different Views about Business Cycles Compete”
Jonas D.M. Fisher

WP-10-01

Macroeconomic Implications of Agglomeration
Morris A. Davis, Jonas D.M. Fisher and Toni M. Whited

WP-10-02

Accounting for non-annuitization
Svetlana Pashchenko

WP-10-03

Robustness and Macroeconomic Policy
Gadi Barlevy

WP-10-04

Benefits of Relationship Banking: Evidence from Consumer Credit Markets
Sumit Agarwal, Souphala Chomsisengphet, Chunlin Liu, and Nicholas S. Souleles

WP-10-05

The Effect of Sales Tax Holidays on Household Consumption Patterns
Nathan Marwell and Leslie McGranahan

WP-10-06

Gathering Insights on the Forest from the Trees: A New Metric for Financial Conditions
Scott Brave and R. Andrew Butters

WP-10-07

Identification of Models of the Labor Market
Eric French and Christopher Taber

WP-10-08

Public Pensions and Labor Supply Over the Life Cycle
Eric French and John Jones

WP-10-09

Explaining Asset Pricing Puzzles Associated with the 1987 Market Crash
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein

WP-10-10

Prenatal Sex Selection and Girls’ Well‐Being: Evidence from India
Luojia Hu and Analía Schlosser

WP-10-11

Mortgage Choices and Housing Speculation
Gadi Barlevy and Jonas D.M. Fisher

WP-10-12

Did Adhering to the Gold Standard Reduce the Cost of Capital?
Ron Alquist and Benjamin Chabot

WP-10-13

Introduction to the Macroeconomic Dynamics:
Special issues on money, credit, and liquidity
Ed Nosal, Christopher Waller, and Randall Wright

WP-10-14

Summer Workshop on Money, Banking, Payments and Finance: An Overview
Ed Nosal and Randall Wright

WP-10-15

Cognitive Abilities and Household Financial Decision Making
Sumit Agarwal and Bhashkar Mazumder

WP-10-16

Complex Mortgages
Gene Amromin, Jennifer Huang, Clemens Sialm, and Edward Zhong

WP-10-17

4

Working Paper Series (continued)
The Role of Housing in Labor Reallocation
Morris Davis, Jonas Fisher, and Marcelo Veracierto

WP-10-18

Why Do Banks Reward their Customers to Use their Credit Cards?
Sumit Agarwal, Sujit Chakravorti, and Anna Lunn

WP-10-19

The impact of the originate-to-distribute model on banks
before and during the financial crisis
Richard J. Rosen

WP-10-20

Simple Markov-Perfect Industry Dynamics
Jaap H. Abbring, Jeffrey R. Campbell, and Nan Yang

WP-10-21

Commodity Money with Frequent Search
Ezra Oberfield and Nicholas Trachter

WP-10-22

Corporate Average Fuel Economy Standards and the Market for New Vehicles
Thomas Klier and Joshua Linn

WP-11-01

The Role of Securitization in Mortgage Renegotiation
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff

WP-11-02

Market-Based Loss Mitigation Practices for Troubled Mortgages
Following the Financial Crisis
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff

WP-11-03

Federal Reserve Policies and Financial Market Conditions During the Crisis
Scott A. Brave and Hesna Genay

WP-11-04

The Financial Labor Supply Accelerator
Jeffrey R. Campbell and Zvi Hercowitz

WP-11-05

Survival and long-run dynamics with heterogeneous beliefs under recursive preferences
Jaroslav Borovička

WP-11-06

A Leverage-based Model of Speculative Bubbles (Revised)
Gadi Barlevy

WP-11-07

Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation
Sule Alan, Bo E. Honoré, Luojia Hu, and Søren Leth–Petersen

WP-11-08

Fertility Transitions Along the Extensive and Intensive Margins
Daniel Aaronson, Fabian Lange, and Bhashkar Mazumder

WP-11-09

Black-White Differences in Intergenerational Economic Mobility in the US
Bhashkar Mazumder

WP-11-10

5