Where is the Land of Opportunity?

The Geography of Intergenerational Mobility in the United States

Raj Chetty, Harvard University and NBER
Nathaniel Hendren, Harvard University and NBER
Patrick Kline, UC-Berkeley and NBER
Emmanuel Saez, UC-Berkeley and NBER
June 2014

Abstract
We use administrative records on the incomes of more than 40 million children and their parents
to describe three features of intergenerational mobility in the United States. First, we characterize the joint distribution of parent and child income at the national level. The conditional
expectation of child income given parent income is linear in percentile ranks. On average, a
10 percentile increase in parent income is associated with a 3.4 percentile increase in a childs
income. Second, intergenerational mobility varies substantially across areas within the U.S. For
example, the probability that a child reaches the top quintile of the national income distribution starting from a family in the bottom quintile is 4.4% in Charlotte but 12.9% in San Jose.
Third, we explore the factors correlated with upward mobility. High mobility areas have (1)
less residential segregation, (2) less income inequality, (3) better primary schools, (4) greater
social capital, and (5) greater family stability. While our descriptive analysis does not identify the causal mechanisms that determine upward mobility, the publicly available statistics on
intergenerational mobility developed here can facilitate research on such mechanisms.

The opinions expressed in this paper are those of the authors alone and do not necessarily reflect the views of the
Internal Revenue Service or the U.S. Treasury Department. This work is a component of a larger project examining
the eects of tax expenditures on the budget deficit and economic activity. All results based on tax data in this
paper are constructed using statistics originally reported in the SOI Working Paper The Economic Impacts of Tax
Expenditures: Evidence from Spatial Variation across the U.S., approved under IRS contract TIRNO-12-P-00374
and presented at the National Tax Association meeting on November 22, 2013. We thank David Autor, Gary Becker,
David Card, David Dorn, John Friedman, James Heckman, Nathaniel Hilger, Richard Hornbeck, Lawrence Katz,
Sara Lalumia, Adam Looney, Pablo Mitnik, Jonathan Parker, Laszlo Sandor, Gary Solon, Danny Yagan, numerous
seminar participants, and four anonymous referees for helpful comments. Sarah Abraham, Alex Bell, Shelby Lin, Alex
Olssen, Evan Storms, Michael Stepner, and Wentao Xiong provided outstanding research assistance. This research
was funded by the National Science Foundation, the Lab for Economic Applications and Policy at Harvard, the
Center for Equitable Growth at UC-Berkeley, and Laura and John Arnold Foundation. Publicly available portions
of the data and code, including intergenerational mobility statistics by commuting zone and county, are available at
www.equality-of-opportunity.org.

Introduction

The United States is often hailed as the land of opportunity, a society in which a childs chances
of success depend little on his family background. Is this reputation warranted? We show that this
question does not have a clear answer because there is substantial variation in intergenerational
mobility across areas within the U.S. The U.S. is better described as a collection of societies, some
of which are lands of opportunity with high rates of mobility across generations, and others in
which few children escape poverty.
We characterize intergenerational mobility using information from de-identified federal income
tax records, which provide data on the incomes of more than 40 million children and their parents
between 1996 and 2012. We organize our analysis into three parts.
In the first part, we present new statistics on intergenerational mobility in the U.S. as a whole.
In our baseline analysis, we focus on U.S. citizens in the 1980-1982 birth cohorts the oldest
children in our data for whom we can reliably identify parents based on information on dependent
claiming. We measure these childrens income as mean total family income in 2011 and 2012, when
they are approximately 30 years old. We measure their parents income as mean family income
between 1996 and 2000, when the children are between the ages of 15 and 20.1
Following the prior literature (e.g., Solon 1999), we begin by estimating the intergenerational
elasticity of income (IGE) by regressing log child income on log parent income. Unfortunately, we
find that this canonical log-log specification yields very unstable estimates of mobility because the
relationship between log child income and log parent income is non-linear and the estimates are
sensitive to the treatment of children with zero or very small incomes. When restricting the sample
between the 10th and 90th percentile of the parent income distribution and excluding children with
zero income, we obtain an IGE estimate of 0.45. However, alternative specifications yield IGEs
ranging from 0.26 to 0.70, spanning most of the estimates in the prior literature.2
To obtain a more stable summary of intergenerational mobility, we use a rank-rank specification
similar to that used by Dahl and DeLeire (2008). We rank children based on their incomes relative
to other children in the same birth cohort. We rank parents of these children based on their incomes
relative to other parents with children in these birth cohorts. We characterize mobility based on the
1

We show that our baseline measures do not suer from significant lifecycle or attenuation bias (Solon 1992,
Zimmerman 1992, Mazumder 2005) by establishing that estimates of mobility stabilize by the time children reach
age 30 and are not very sensitive to the number of years used to measure parent income.
2
In an important recent study, Mitnik et al. (2014) propose a new dollar-weighted measure of the IGE and show
that it yields more stable estimates. We discuss the dierences between the new measure of mobility proposed by
Mitnik et al. and the canonical definition of the IGE in Section IV.A.

slope of this rank-rank relationship, which identifies the correlation between childrens and parents
positions in the income distribution.3
We find that the relationship between mean child ranks and parent ranks is almost perfectly
linear and highly robust to alternative specifications. A 10 percentile point increase in parent rank
is associated with a 3.41 percentile increase in a childs income rank on average. Childrens college
attendance and teenage birth rates are also linearly related to parent income ranks. A 10 percentile
point increase in parent income is associated with a 6.7 percentage point (pp) increase in college
attendance rates and a 3 pp reduction in teenage birth rates for women.
In the second part of the paper, we characterize variation in intergenerational mobility across
commuting zones (CZs). Commuting zones are geographical aggregations of counties that are
similar to metro areas but cover the entire U.S., including rural areas (Tolbert and Sizer 1996). We
assign children to commuting zones based on where they lived at age 16 i.e., where they grew
up irrespective of whether they left that CZ afterward. When analyzing CZs, we continue to
rank both children and parents based on their positions in the national income distribution, which
allows us to measure childrens absolute outcomes as we discuss below.
The relationship between mean child ranks and parent ranks is almost perfectly linear within
commuting zones, allowing us to summarize the conditional expectation of a childs rank given
his parents rank with just two parameters: a slope and intercept. The slope measures relative
mobility: the dierence in outcomes between children from top vs. bottom income families within
a CZ. The intercept measures the expected rank for children from families at the bottom of the
income distribution. Combining the intercept and slope for a CZ, we can calculate the expected
rank of children from families at any given percentile p of the national parent income distribution.
We term this measure absolute mobility at percentile p. Measuring absolute mobility is valuable
because increases in relative mobility have ambiguous normative implications, as they may be
driven by worse outcomes for the rich rather than better outcomes for the poor.
We find substantial variation in both relative and absolute mobility across CZs. Relative mobility is lowest for children who grew up in the Southeast and highest in the Mountain West and
the rural Midwest. Some CZs in the U.S. have relative mobility comparable to the highest mobility
countries in the world, such as Canada and Denmark, while others have lower levels of mobility
than any developed country for which data are available.
3
The rank-rank slope and IGE both measure the degree to which dierences in childrens incomes are determined
by their parents incomes. We discuss the conceptual dierences between the two measures in Section II.

We find similar geographical variation in absolute mobility. We focus much of our analysis on
absolute mobility at p = 25, which we term absolute upward mobility. This statistic measures
the mean income rank of children with parents in the bottom half of the income distribution given
linearity of the rank-rank relationship. Absolute upward mobility ranges from 35.8 in Charlotte
to 46.2 in Salt Lake City among the 50 largest CZs. A 1 standard deviation (SD) increase in
CZ-level upward mobility is associated with a 0.2 SD improvement in a childs expected rank given
parents at p = 25, 60% as large as the eect of a 1 SD increase in his own parents income. Other
measures of upward mobility exhibit similar spatial variation. For instance, the probability that a
child reaches the top fifth of the income distribution conditional on having parents in the bottom
fifth is 4.4% in Charlotte, compared with 10.8% in Salt Lake City and 12.9% in San Jose. The
CZ-level mobility statistics are robust to adjusting for dierences in the local cost-of-living, shocks
to local growth, and using alternative measures of income.
Absolute upward mobility is highly correlated with relative mobility: areas with high levels of
relative mobility (low rank-rank slopes) tend to have better outcomes for children from low-income
families. On average, children from families below percentile p = 85 have better outcomes when
relative mobility is greater; those above p = 85 have worse outcomes. Location matters more for
children growing up in low income families: the expected rank of children from low-income families
varies more across CZs than the expected rank of children from high income families.
The spatial patterns of the gradients of college attendance and teenage birth rates with respect
to parent income across CZs are very similar to the variation in intergenerational income mobility.
This suggests that the spatial dierences in mobility are driven by factors that aect children while
they are growing up rather than after they enter labor market.
In the final part of the paper, we explore such factors by correlating the spatial variation
in mobility with observable characteristics. To begin, we show that upward income mobility is
significantly lower in areas with larger African-American populations. However, white individuals
in areas with large African-American populations also have lower rates of upward mobility, implying
that racial shares matter at the community level.
We then identify five factors that are strongly correlated with the variation in upward mobility
across areas. The first is segregation: areas that are more residentially segregated by race and
income have lower levels of mobility. Second, areas with more inequality as measured by Gini coefficients have less mobility, consistent with the Great Gatsby curve documented across countries
(Krueger 2012, Corak 2013). Top 1% income shares are not highly correlated with intergenera3

tional mobility both across CZs within the U.S. and across countries, suggesting that the factors
that erode the middle class may hamper intergenerational mobility more than the factors that
lead to income growth in the upper tail. Third, proxies for the quality of the K-12 school system
are positively correlated with mobility. Fourth, social capital indices (Putnam 1995) which are
proxies for the strength of social networks and community involvement in an area are also positively correlated with mobility. Finally, mobility is significantly lower in areas with weaker family
structures, as measured e.g. by the fraction of single parents. As with race, parents marital status
does not matter purely through its eects at the individual level. Children of married parents also
have higher rates of upward mobility in communities with fewer single parents. Interestingly, we
find no correlation between racial shares and upward mobility once we control for the fraction of
single parents in an area.
We find modest correlations between upward mobility and local tax policies and no systematic
correlation between mobility and local labor market conditions, rates of migration, or access to
higher education. In a multivariable regression, the five key factors described above generally
remain statistically significant predictors of both relative and absolute upward mobility, even in
specifications with state fixed eects. However, we emphasize that these factors should not be
interpreted as causal determinants of mobility because all of these variables are endogenously
determined and our analysis does not control for numerous other unobserved dierences across
areas.
Our results build on an extensive literature on intergenerational mobility, reviewed by Solon
(1999) and Black and Devereux (2011). Our estimates of the level of mobility in the U.S. as
a whole are broadly consistent with prior results, with the exception of Mazumders (2005) and
Clarks (2014) IGE estimates, which imply much lower levels of intergenerational mobility. We
discuss why our findings may dier from their results in Online Appendices D and E. Our focus
on within-country comparisons oers two advantages over the cross-country comparisons that have
been the focus of prior comparative work (e.g., Bjorklund and Jantti 1997, Jantti et al. 2006,
Corak 2013). First, dierences in measurement and methods make it difficult to reach definitive
conclusions from cross-country comparisons (Solon 2002). The variables we analyze are measured
using the same data sources across all CZs. Second, and more importantly, we characterize both
relative and absolute mobility across CZs. The cross-country literature has focused exclusively
on dierences in relative mobility; much less is known about how the prospects of children from
low-income families vary across countries when measured on a common absolute scale (Ray 2010).
4

Our analysis also relates to the literature on neighborhood eects, reviewed by Jencks and
Mayer (1990) and Sampson, Moreno and Gannon-Rowley (2002). Unlike recent experimental work
on neighborhood eects (e.g., Katz, Kling and Liebman 2001, Oreopoulos 2003), our descriptive
analysis does not shed light on whether the dierences in outcomes across areas are due to the causal
eect of neighborhoods or dierences in the characteristics of people living in those neighborhoods.
However, in a followup paper, Chetty and Hendren (2014) show that a substantial portion of the
spatial variation documented here is driven by causal eects of place by studying families that move
across areas with children of dierent ages.
The paper is organized as follows. We begin in Section II by defining the measures of intergenerational mobility that we study and discussing their conceptual properties. Section III describes the
data. Section IV reports estimates of intergenerational mobility at the national level. In Section
V, we present estimates of absolute and relative mobility by commuting zone. Section VI reports
correlations of our mobility measures with observable characteristics of commuting zones. Section
VII concludes. Statistics on intergenerational mobility and related covariates are publicly available
by commuting zone, metropolitan statistical area, and county on the project website.

II

Measures of Intergenerational Mobility

At the most general level, studies of intergenerational mobility seek to measure the degree to which a
childs social and economic opportunities depend upon his parents income or social status. Because
opportunities are difficult to measure, virtually all empirical studies of mobility measure the extent
to which a childs income (or occupation) depends upon his parents income (or occupation).4
Following this approach, we aim to characterize the joint distribution of a childs lifetime pre-tax
family income (Yi ), and his parents lifetime pre-tax family income (Xi ).5
In large samples, one can characterize the joint distribution of (Yi , Xi ) non-parametrically, and
we provide such a characterization in the form of a 100 x 100 centile transition matrix below.
However, in order to provide a parsimonious summary of the degree of mobility and compare
rates of mobility across areas, it is useful to characterize the joint distribution using a small set
of statistics. We divide measures of mobility into two classes that capture dierent normative
4
This simplification is not innocuous, as a childs realized income may dier from his opportunities. For instance,
children of wealthy parents may choose not to work or may choose lower-paying jobs, which would reduce the
persistence of income across generations relative to the persistence of underlying opportunities.
5
If taxes and transfers do not generate rank-reversals (as is typically the case in practice), using post-tax income
instead of pre-tax income would have no impact on our preferred rank-based measures of mobility. See Mitnik et al.
(2014) for a comparison of pre-tax and post-tax measures of the intergenerational elasticity of income.

concepts: relative mobility and absolute mobility. In this section, we define a set of statistics that
we use to measure these two concepts empirically and compare their conceptual properties.
Relative Mobility. One way to study intergenerational mobility is to ask, What are the outcomes of children from low-income families relative to those of children from high-income families?
This question, which focuses on the relative outcomes of children from dierent parental backgrounds, has been the subject of most prior research on intergenerational mobility (Solon 1999,
Black et al. 2011).
The canonical measure of relative mobility is the elasticity of child income with respect to parent
Yi |Xi =x]
income ( dE[log
), commonly termed the intergenerational income elasticity (IGE). The most
d log x

common method of estimating the IGE is to regress log child income (logYi ) on log parent income
(logXi ), which yields a coefficient of
IGE = XY

SD(logYi )
,
SD(logXi )

(1)

where XY = Corr(logXi , logYi ) is the correlation between log child income and parent income and
SD() denotes the standard deviation. The IGE is a relative mobility measure because it measures
the dierence in (log) outcomes between children of high vs. low income parents.
An alternative measure of relative mobility is the correlation between child and parent ranks
(Dahl and Deleire 2008). Let Ri denote child is percentile rank in the income distribution of
children and Pi denote parent is percentile rank in the income distribution of parents. Regressing
the childs rank Ri on his parents rank Pi yields a regression coefficient P R = Corr(Pi , Ri ), which
we term the rank-rank slope.6 The rank-rank slope P R measures the association between a childs
position in the income distribution and his parents position in the distribution.
To understand the connection between the IGE and the rank-rank slope, note that the correlation of log incomes XY and the correlation of ranks P R are closely related scale-invariant
measures of the degree to which child income depends on parent income.7 Hence, (1) implies that
the IGE combines the dependence features captured by the rank-rank slope with the ratio of standard deviations of income across generations.8 The IGE diers from the rank-rank slope to the
extent that inequality changes across generations. Intuitively, a given increase in parents incomes
6

The regression coefficient equals the correlation coefficient because both child and parent ranks follow a Uniform
distribution by construction.
7
For example, if parent and child income follow a bivariate log Normal distribution, P R = 6ArcSin(XY /2)/
3XY / = 0.95XY when XY is small (Trivedi and Zimmer 2007).
8
More generally, the joint distribution of parent and child incomes can be decomposed into two components: the
joint distribution of parent and child percentile ranks (the copula) and the marginal distributions of parent and child
income. The rank-rank slope depends purely on the copula, while the IGE combines both components.

has a greater impact on the level of childrens incomes when inequality is greater among children
than parents.
We estimate both the IGE and the rank-rank slope to distinguish dierences in mobility from
dierences in inequality and to provide a comparison to the prior literature. However, we focus
primarily on rank-rank slopes because they prove to be much more robust across specifications and
are thus more suitable for comparisons across areas from a statistical perspective.
Absolute Mobility. A dierent way to measure intergenerational mobility is to ask, What are
the outcomes of children from families of a given income level in absolute terms? For example,
one may be interested in measuring the mean outcomes of children whose grow up in low-income
families. Absolute mobility may be of greater normative interest than relative mobility. Increases
in relative mobility (i.e., a lower IGE or rank-rank slope) could be undesirable if they are caused
by worse outcomes for the rich. In contrast, increases in absolute mobility at a given income
level, holding fixed absolute mobility at other income levels, unambiguously increase welfare if one
respects the Pareto principle (and if welfare depends purely on income).
We consider three statistical measures of absolute mobility. Our primary measure, which we
term absolute upward mobility, is the mean rank (in the national child income distribution) of
children whose parents are at the 25th percentile of the national parent income distribution.9 At
the national level, this statistic is mechanically related to the rank-rank slope and does not provide
any additional information about mobility.10 However, when we study small areas within the U.S.,
a childs rank in the national income distribution is eectively an absolute outcome because incomes
in a given area have little impact on the national distribution.
The second measure we analyze is the probability of rising from the bottom quintile to the top
quintile of the income distribution (Corak and Heisz 1999, Hertz 2006), which can be interpreted as
a measure of the fraction of children who achieve the American Dream. Again, when the quintiles
are defined in the national income distribution, these transition probabilities can be interpreted as
measures of absolute outcomes in small areas. Our third measure is the probability that a child has
family income above the poverty line conditional on having parents at the 25th percentile. Because
the poverty line is defined in absolute dollar terms in the U.S., this statistic measures the fraction
9

This measure is the analog of the rank-rank slope in terms of absolute mobility. The corresponding analog of
the IGE is the mean log income of children whose parents are at the 25th percentile. We do not study this statistic
because it is very sensitive to the treatment of zeros and small incomes.
10
We show below that the rank-rank relationship is approximately linear. Because child and parent ranks each
have a mean of 0.5 by construction in the national distribution, the mean rank of children with parents at percentile
p is simply 0.5 + P R (p 0.5). Conceptually, the slope is the only free parameter in the linear national rank-rank
relationship. Intuitively, if one child moves up in the income distribution in terms of ranks, another must come down.

of children who achieve a given absolute living standard.11

It is useful to analyze multiple measures of mobility because the appropriate measure of intergenerational mobility depends upon ones normative objective (Fields and Ok 1999). Fortunately,
we find that the patterns of spatial variation in absolute and relative mobility are very similar using alternative measures. In addition, we provide non-parametric transition matrices and marginal
distributions that allow readers to construct measures of mobility beyond those we consider here.

III

Data

We use data from federal income tax records spanning 1996-2012. The data include both income
tax returns (1040 forms) and third-party information returns (e.g., W-2 forms), which give us
information on the earnings of those who do not file tax returns. We provide a detailed description
of how we construct our analysis sample starting from the raw population data in Online Appendix
A. Here, we briefly summarize the key variable and sample definitions. Note that in what follows,
the year always refers to the tax year (i.e., the calendar year in which the income is earned).

III.A

Sample Definitions

Our base dataset of children consists of all individuals who (1) have a valid Social Security Number
or Individual Taxpayer Identification Number, (2) were born between 1980-1991, and (3) are U.S.
citizens as of 2013. We impose the citizenship requirement to exclude individuals who are likely to
have immigrated to the U.S. as adults, for whom we cannot measure parent income. We cannot
directly restrict the sample to individuals born in the U.S. because the database only records current
citizenship status.
We identify the parents of a child as the first tax filers (between 1996-2012) who claim the child
as a child dependent and were between the ages of 15 and 40 when the child was born. If the child is
first claimed by a single filer, the child is defined as having a single parent. For simplicity, we assign
each child a parent (or parents) permanently using this algorithm, regardless of any subsequent
changes in parents marital status or dependent claiming.12
11

Another intuitive measure of upward mobility is the fraction of children whose income exceeds that of their
parents. This statistic turns out to be problematic for our application because we measure parent and child income
at dierent ages and because it is very sensitive to dierences in local income distributions.
12
12% of children in our core sample are claimed as dependents by dierent individuals in subsequent years. To
ensure that this potential measurement error in linking children to parents does not aect our findings, we show that
we obtain similar estimates of mobility for the subset of children who are never claimed by other individuals (row 9
of Online Appendix Table VII).

If parents never file a tax return, we cannot link them to their child. Although some low-income
individuals do not file tax returns in a given year, almost all parents file a tax return at some point
between 1996 and 2012 to obtain a tax refund on their withheld taxes and the Earned Income
Tax Credit (Cilke 1998). We are therefore able to identify parents for approximately 95% of the
children in the 1980-1991 birth cohorts. The fraction of children linked to parents drops sharply
prior to the 1980 birth cohort because our data begin in 1996 and many children begin to the leave
the household starting at age 17 (Online Appendix Table I). This is why we limit our analysis to
children born during or after 1980.
Our primary analysis sample, which we refer to as the core sample, includes all children in the
base dataset who (1) are born in the 1980-82 birth cohorts, (2) for whom we are able to identify
parents, and (3) whose mean parent income between 1996-2000 is strictly positive (which excludes
1.2% of children).13 For some robustness checks, we use the extended sample, which imposes
the same restrictions as the core sample, but includes all birth cohorts from 1980-1991. There
are approximately 10 million children in the core sample and 44 million children in the extended
sample.
Statistics of Income Sample. Because we can only reliably link children to parents starting
with the 1980 birth cohort in the population tax data, we can only measure earnings of children
up to age 32 (in 2012) in the full sample. To evaluate whether estimates of intergenerational
mobility would change significantly if earnings were measured at later ages, we supplement our
analysis using annual cross-sections of tax returns maintained by the Statistics of Income (SOI)
division of the Internal Revenue Service prior to 1996. The SOI cross-sections provide identifiers for
dependents claimed on tax forms starting in 1987, allowing us to link parents to children back to
the 1971 birth cohort using an algorithm analogous to that described above (see Online Appendix
A for further details). The SOI cross-sections are stratified random samples of tax returns with
a sampling probability that rises with income; using sampling weights, we can calculate statistics
representative of the national distribution. After linking parents to children in the SOI sample,
we use population tax data to obtain data on income for children and parents, using the same
definitions as in the core sample. There are approximately 63,000 children in the 1971-79 birth
cohorts in the SOI sample (Online Appendix Table II).
13
We limit the sample to parents with positive income because parents who file a tax return (as required to link
them to a child) yet have zero income are unlikely to be representative of individuals with zero income and those
with negative income typically have large capital losses, which are a proxy for having significant wealth.

III.B

Variable Definitions and Summary Statistics

In this section, we define the key variables we use to measure intergenerational mobility. We
measure all monetary variables in 2012 dollars, adjusting for inflation using the consumer price
index (CPI-U).
Parent Income. Following Lee and Solon (2009), our primary measure of parent income is total
pre-tax income at the household level, which we label parent family income. More precisely, in years
where a parent files a tax return, we define family income as Adjusted Gross Income (as reported on
the 1040 tax return) plus tax-exempt interest income and the non-taxable portion of Social Security
and Disability benefits. In years where a parent does not file a tax return, we define family income
as the sum of wage earnings (reported on form W-2), unemployment benefits (reported on form
1099-G), and gross social security and disability benefits (reported on form SSA-1099) for both
parents.14 In years where parents have no tax return and no information returns, family income is
coded as zero.15
Our baseline income measure includes labor earnings and capital income as well as unemployment insurance, social security, and disability benefits. It excludes non-taxable cash transfers such
as TANF and SSI, in-kind benefits such as food stamps, all refundable tax credits such as the
EITC, non-taxable pension contributions (e.g., to 401(k)s), and any earned income not reported
to the IRS. Income is always measured prior to the deduction of individual income taxes and
employee-level payroll taxes.
In our baseline analysis, we average parents family income over the five years from 1996 to 2000
to obtain a proxy for parent lifetime income that is less aected by transitory fluctuations (Solon
1992). We use the earliest years in our sample to best reflect the economic resources of parents while
the children in our sample are growing up.16 We evaluate the robustness of our findings using data
14
The database does not record W-2s and other information returns prior to 1999, so non-filers income is coded
as 0 prior to 1999. Assigning non-filing parents 0 income has little impact on our estimates because only 2.9% of
parents in our core sample do not file in each year prior to 1999 and most non-filers have very low W-2 income. For
instance, in 2000, median W-2 income among non-filers was $29. Furthermore, we show below that defining parent
income based on data from 1999-2003 (when W-2 data are available) yields virtually identical estimates (Table I,
row 5). Note that we never observe self-employment income for non-filers and therefore code it as zero; given the
strong incentives for individuals with children to file created by the EITC, most non-filers likely have very low levels
of self-employment income as well.
15
Importantly, these observations are true zeros rather than missing data. Because the database covers all tax
records, we know that these individuals have 0 taxable income.
16
Formally, we define mean family income as the mothers family income plus the fathers family income in each
year from 1996 to 2000 divided by 10 (or divided by 5 if we only identify a single parent). For parents who do
not change marital status, this is simply mean family income over the 5 year period. For parents who are married
initially and then divorce, this measure tracks the mean family incomes of the two divorced parents over time. For
parents who are single initially and then get married, this measure tracks individual income prior to marriage and

10

from other years and using a measure of individual parent income instead of family income. We
define individual income as the sum of individual W-2 wage earnings, UI benefits, SSDI payments,
and half of household self-employment income (see Online Appendix A for details).
Child Income. We define child family income in exactly the same way as parent family income.
In our baseline analysis, we average child family income over the last two years in our data (2011
and 2012), when children are in their early 30s. We report results using alternative years to assess
the sensitivity of our findings. For children, we define household income based on current marital
status rather than marital status at a fixed point in time. Because family income varies with
marital status, we also report results using individual income measures for children, constructed in
the same way as for parents.
College Attendance. We define college attendance as an indicator for having one or more 1098-T
forms filed on ones behalf when the individual is aged 18-21. Title IV institutions all colleges and
universities as well as vocational schools and other post-secondary institutions eligible for federal
student aid are required to file 1098-T forms that report tuition payments or scholarships received
for every student. Because the 1098-T forms are filed directly by colleges independent of whether
an individual files a tax return, we have complete records on college attendance for all children.
The 1098-T data are available from 1999-2012. Comparisons to other data sources indicate that
1098-T forms capture college enrollment quite accurately overall (Chetty, Friedman, and Rocko
2014, Appendix B).17
College Quality. Using data from 1098-T forms, Chetty, Friedman, and Rocko (2014 forthcoming) construct an earnings-based index of college quality using the mean individual wage earnings
at age 31 of children born in 1979-80 based on the college they attended at age 20. Children who
do not attend college are included in a separate no college category in this index. We assign each
child in our sample a value of this college quality index based on the college in which they were
enrolled at age 20. We then convert this dollar index to percentile ranks within each birth cohort.
The children in the no-college group, who constitute roughly 54% of our core sample, all have the
same value of the college quality index. Breaking ties at the mean, we assign all of these children
total family income (including the new spouses income) after marriage. These household measures of income increase
with marriage and naturally do not account for cohabitation; to ensure that these features do not generate bias, we
assess the robustness of our results to using individual measures of income.
17
Colleges are not required to file 1098-T forms for students whose qualified tuition and related expenses are
waived or paid entirely with scholarships or grants. However, the forms are frequently available even for such cases,
presumably because of automated reporting to the IRS by universities. Approximately 6% of 1098-T forms are
missing from 2000-2003 because the database contains no 1098-T forms for some small colleges in these years. To
verify that this does not aect our results, we confirm that our estimates of college attendance by parent income
gradients are very similar for later birth cohorts (not reported).

11

a college quality rank of approximately 54/2 = 27.18

Teenage Birth. We define a woman as having a teenage birth if she ever claims a dependent
who was born while she was between the ages of 13 and 19. This measure is an imperfect proxy
for having a teenage birth because it only covers children who are claimed as dependents by their
mothers. Nevertheless, the aggregate level and spatial pattern of teenage births in our data are
closely aligned with estimates based on the American Community Survey.19
Summary Statistics. Online Appendix Table III reports summary statistics for the core sample.
Median parent family income is $60,129 (in 2012 dollars). Among the 30.6% of children matched to
single parents, 72.0% are matched to a female parent. Children in our core sample have a median
family income of $34,975 when they are approximately 30 years old. 6.1% of children have zero
income in both 2011 and 2012. 58.9% are enrolled in a college at some point between the ages of
18 and 21 and 15.8% of women have a teenage birth.
In Online Appendix B and Appendix Table IV, we show that the total cohort size, labor
force participation rate, distribution of child income, and other demographic characteristics of our
core sample line up closely with corresponding estimates in the Current Population Survey and
American Community Survey. This confirms that our sample covers roughly the same nationally
representative population as previous survey-based research.

IV

National Statistics

We begin our empirical analysis by characterizing the relationship between parent and child income
at the national level. We first present a set of baseline estimates of relative mobility and then
evaluate the robustness of our estimates to alternative sample and income definitions.20

IV.A

Baseline Estimates

In our baseline analysis, we use the core sample (1980-82 birth cohorts) and measure parent income
as mean family income from 1996-2000 and child income as mean family income in 2011-12, when
18

The exact value varies across cohorts. For example, in the 1980 birth cohort, 55.1% of children do not attend
college. We assign these children a rank of 55.1/2+0.02=27.7% because 0.2% of children in the 1980 birth cohort
attend colleges whose mean earnings are below the mean earnings of those not in college.
19
15.8% of women in our core sample have teenage births; the corresponding number is 14.6% in the 2003 ACS.
The unweighted correlation between state-level teenage birth rates in the tax data and the ACS is 0.80.
20
We do not present estimates of absolute mobility at the national level because absolute mobility in terms of
percentile ranks is mechanically related to relative mobility at the national level (see Section II). While one can
compute measures of absolute mobility at the national level based on mean incomes (e.g., the mean income of
children whose parents are at the 25th percentile), there is no natural benchmark for such a statistic as it has not
been computed in other countries or time periods.

12

children are approximately 30 years old. Figure Ia presents a binned scatter plot of the mean
family income of children versus the mean family income of their parents. To construct this figure,
we divide the horizontal axis into 100 equal-sized (percentile) bins and plot mean child income
vs. mean parent income in each bin.21 This binned scatter plot provides a non-parametric representation of the conditional expectation of child income given parent income, E[Yi |Xi = x]. The
regression coefficients and standard errors reported in this and all subsequent binned scatter plots
are estimated on the underlying microdata using OLS regressions.
The conditional expectation of childrens income given parents income is strongly concave.
Below the 90th percentile of parent income, a $1 increase in parent family income is associated
with a 33.5 cent increase in average child family income. In contrast, between the 90th and 99th
percentile, a $1 increase in parent income is associated with only a 7.6 cent increase in child income.
Log-Log Intergenerational Elasticity Estimates. Partly motivated by the non-linearity of the relationship in Figure Ia, the canonical approach to characterizing the joint distribution of child and
parent income is to regress the log of child income on the log of parent income (as discussed in Section II), excluding children with zero income. This regression yields an estimated intergenerational
elasticity (IGE) of 0.344, as shown in the first column of row 1 of Table I.
Unfortunately, this estimate turns out to be quite sensitive to changes in the regression specifications for two reasons, illustrated in Figure Ib. First, the relationship between log child income
and log parent income is highly non-linear, consistent with the findings of Corak and Heisz (1999)
in Canadian tax data. This is illustrated in the series in circles in Figure Ib, which plots mean log
child income vs. mean log family income by percentile bin, constructed using the same method as
Figure Ia. Because of this non-linearity, the IGE is sensitive to the point of measurement in the
income distribution. For example, restricting the sample to observations between the 10th and 90th
percentile of parent income (denoted by the vertical dashed lines in the graph) yields a considerably
higher IGE estimate of 0.452.
Second, the log-log specification discards observations with zero income. The series in triangles
in Figure Ib plots the fraction of children with zero income by parental income bin. This fraction
varies from 17% among the poorest families to 3% among the richest families. Dropping children
with zero income therefore overstates the degree of intergenerational mobility. The way in which
these zeros are treated can change the IGE dramatically. For instance, including the zeros by
21
For scaling purposes, we exclude the top bin (parents in the top 1%) in this figure only; mean parent income in
this bin is $1,408,760 and mean child income is $113,846.

13

assigning those with zero income an income of $1 (so that the log of their income is zero) raises
the estimated IGE to 0.618, as shown in row 2 of Table I. If instead we treat those with 0 income
as having an income of $1,000, the estimated IGE becomes 0.413. These exercises show that small
dierences in the way childrens income is measured at the bottom of the distribution can produce
substantial variation in IGE estimates.
Columns 2-7 in Table I replicate the baseline specification in Column 1 for alternative subsamples analyzed in the prior literature. Columns 2-5 split the sample by the childs gender and the
parents marital status in the year they first claim the child. Column 6 replicates Column 1 for
the extended sample of 1980-85 birth cohorts. Column 7 restricts the sample to children whose
mothers are between the ages of 24-28 and fathers are between 26-30 (a five year window around the
median age of birth). This column eliminates variation in parent income correlated with dierences
in parent age at child birth and restricts the sample to parents who are less than 50 years old when
we measure their incomes (for children born in 1980). Across these subsamples, the IGE estimates
range from 0.264 (for children of single parents, excluding children with zero income) to 0.697 (for
male children, recoding zeroes to $1).
The IGE is unstable because the income distribution is not well approximated by a bivariate
Log-Normal distribution, a result that was not apparent in smaller samples used in prior work.
This makes it difficult to obtain reliable comparisons of mobility across samples or geographical
areas using the IGE. For example, income measures in survey data are typically top-coded and
sometimes include transfers and other sources of income that increase incomes at the bottom of
the distribution, which may lead to larger IGE estimates than those obtained in administrative
datasets such as the one used here.
In a recent paper, Mitnik et al. (2014) propose a new measure of the IGE, the elasticity of
i |Xi =x]
expected child income with respect to parent income ( d log E[Y
), which they show is more
d log x

robust to the treatment of small incomes. In large samples, one can estimate this parameter by
regressing the log of mean child income in each percentile bin (plotted in Figure Ia) on the log of
mean parent income in each bin. In Online Appendix C, we show that Mitnik et al.s statistic can
be interpreted as a dollar-weighted average of elasticities (placing greater weight on high income
children), whereas the traditional IGE weights all individuals with positive income equally. These
two parameters need not coincide in general and the correct parameter depends upon the policy
question one seeks to answer. However, it turns out that in our data, the Mitnik et al. dollarweighted IGE estimate is 0.335, very similar to our baseline IGE estimate of 0.344 when excluding
14

children with zero income (Online Appendix Figure Ia).22

In another recent study, Clark (2014) argues that traditional estimates of the IGE understate
the persistence of status across generations because they are attenuated by fluctuations in realized
individual incomes across generations. To resolve this problem, Clark estimates the IGE based on
surname-level means of income in each generation and obtains a central IGE estimate of 0.8, much
larger than that in prior studies. In our data, estimates of mobility based on surname means are
similar to our baseline estimates based on individual income data (Online Appendix Table V). One
reason that Clark (2014) may obtain larger estimates of intergenerational persistence is that his
focus on distinctive surnames partly identifies the degree of convergence in income between racial
or ethnic groups (Borjas 1992) rather than across individuals (see Online Appendix D for further
details).23
Rank-Rank Estimates. Next, we present estimates of the rank-rank slope, the second measure
of relative mobility discussed in Section II. We measure the percentile rank of parents Pi based
on their positions in the distribution of parent incomes in the core sample. Similarly, we define
childrens percentile ranks Ri based on their positions in the distribution of child incomes within
their birth cohorts. Importantly, this definition allows us to include zeros in child income.24 Unless
otherwise noted, we hold the definition of these ranks fixed based on positions in the aggregate
distribution, even when analyzing subgroups.
Figure IIa presents a binned scatter plot of the mean percentile rank of children E[Ri |Pi = p]
vs. their parents percentile rank p. The conditional expectation of a childs rank given his parents
rank is almost perfectly linear. Using an OLS regression, we estimate that a one percentage point
(pp) increase in parent rank is associated with a 0.341 pp increase in the childs mean rank, as
reported in row 4 of Table I. The rank-rank slope estimates are generally quite similar across
subsamples, as shown in Columns 2-7 of Table I.
Figure IIb compares the rank-rank relationship in the U.S. with analogous estimates for Denmark constructed using data from Boserup, Kopczuk and Kreiner (2013) and estimates for Canada
22

Mitnik et al. (2014) find larger estimates of the dollar-weighted IGE in their sample of tax returns. A useful
direction for further work would be to understand why the two samples yield dierent IGE estimates.
23
For example, Clark (2014, page 60, Figure 3.10) compares the outcomes of individuals with the surname Katz
(a predominantly Jewish name) vs. Washington (a predominantly black name). This comparison generates an
implied IGE close to 1, which partly reflects the fact that the black-white income gap has changed very little over
the past few decades. Estimates of the IGE based on individual-level data (or pooling all surnames) are much lower
because there is much more social mobility within racial groups.
24
In the case of ties, we define the rank as the mean rank for the individuals in that group. For example, if 10%
of a birth cohort has zero income, all children with zero income would receive a percentile rank of 5.

15

constructed from the decile transition matrix reported by Corak and Heisz (1999).25 The relationship between child and parent ranks is nearly linear in Denmark and Canada as well, suggesting
that the rank-rank specification provides a good summary of mobility across diverse environments.
The rank-rank slope is 0.180 in Denmark and 0.174 in Canada, nearly half that in the U.S.
Importantly, the smaller rank-rank slopes in Denmark and Canada do not necessarily mean that
children from low-income families in these countries do better than those in the U.S. in absolute
terms. It could be that children of high-income parents in Denmark and Canada have worse
outcomes than children of high-income parents in the U.S. One cannot distinguish between these
possibilities because the ranks are defined within each country. One advantage of the withinU.S. CZ-level analysis implemented below is that it naturally allows us to study both relative and
absolute outcomes by analyzing childrens performance on a fixed national scale.
Transition Matrices. Table II presents a quintile transition matrix: the probability that a child
is in quintile m of the child income distribution conditional on his parent being in quintile n of the
parent income distribution. One statistic of particular interest in this matrix is the probability of
moving from the bottom quintile to the top quintile, a simple measure of success that we return to
below. This probability is 7.5% in the U.S., compared with 11.7% in Denmark (Boserup, Kopczuk
and Kreiner 2013) and 13.4% in Canada (Corak and Heisz 1999). In this sense, the chances of
achieving the American Dream are considerably higher for children in Denmark and Canada
than those in the U.S.
In Online Data Table I, we report a 100 x 100 percentile-level transition matrix for the U.S.
Using this matrix and the marginal distributions for child and parent income in Online Data Table
II, one can construct any mobility statistic of interest for the U.S. population.26

IV.B

Robustness of Baseline Estimates

We now evaluate the robustness of our estimates of intergenerational mobility to alternative specifications. We begin by evaluating two potential sources of bias emphasized in prior work: lifecycle
bias and attenuation bias.
25
Both the Danish and Canadian studies use administrative earnings information for large samples as we do here.
The Danish sample, which was constructed to match the analysis sample in this paper as closely as possible, consists
of children in the 1980-81 birth cohorts and measures child income based on mean income between 2009-11. Child
income in the Danish sample is measured at the individual level and parents income is the mean of the two biological
parents income from 1997-1999, irrespective of their marital status. The Canadian sample is less comparable to our
sample, as it consists of male children in the 1963-66 birth cohorts and studies the link between their mean earnings
from 1993-95 and their fathers mean earnings from 1978-82.
26
All of the online data tables are available at http://www.equality-of-opportunity.org/index.php/data.

16

Lifecycle Bias. Prior research has shown that measuring childrens income at early ages can
understate intergenerational persistence in lifetime income because children with high lifetime incomes have steeper earnings profiles when they are young (Haider and Solon, 2006, Grawe, 2006,
Solon 1999). To evaluate whether our baseline estimates suer from such lifecycle bias, Figure IIIa
plots estimates of the rank-rank slope by the age at which the childs income is measured. We
construct the series in circles by measuring childrens income as mean family income in 2011-2012
and parent income as mean family income between 1996-2000, as in our baseline analysis. We
then replicate the OLS regression of child income rank on parent income rank for each birth cohort
between 1980-1990. For children in the 1980 birth cohort, we measure earnings in 2011-12 at age
31-32 (denoted by 32 in the figure); for the 1990 cohort, we measure earnings at age 21-22.27 The
rank-rank slope rises very steeply in the early 20s as children enter the labor force, but stabilizes
around age 30. It increases by 2.1% from age 30 to 31 and 0.2% from age 31 to 32.
To obtain estimates beyond age 32, we use the SOI 0.1% random sample described in Section
III.A, which contains data back to the 1971 birth cohort. The series in triangles in Figure IIIa
replicates the analysis above within the SOI sample, using sampling weights to recover estimates
representative of the population. The estimates in the SOI sample are very similar to those in
the full population prior to age 32. After age 32, the estimates remain roughly constant. These
findings indicate that rank-rank correlations exhibit little lifecycle bias provided that child income
is measured after age 30, as in our baseline definition.
We also find that estimates of the IGE using the traditional log-log specification (limiting the
sample between the 10th and 90th percentiles of the parent income distribution) stabilize around
age 30, as shown in Online Appendix Figure IIa. In the population data, the IGE estimate is a
strictly concave function of age and rises by only 1.7% from age 31 to 32. The SOI 0.1% sample
exhibits a similar, albeit noisier, pattern.
An analogous lifecycle bias can arise if parent income is measured at very old or young ages. In
Online Appendix Figure IIb we plot the rank-rank slope using the core sample, varying the 5-year
window used to measure parent income from a starting year of 1996 (when mothers are 41 years
old on average) to 2010 (when mothers are 55 years old). The rank-rank estimates exhibit virtually
no variation with the age of parent income measurement within this range.
A closely related concern is that parent income at earlier ages might matter more for childrens
27
We obtain very similar results if we instead track a single cohort and vary age by measuring earnings in dierent
calendar years.

17

outcomes, e.g. if resources in early childhood are relevant for child development (e.g., Heckman
2006, Duncan, Ziol-Guest and Kalil 2010). While we cannot measure parent income before age 14
for children in our core sample, we can measure parent income at earlier ages for later birth cohorts.
In Chetty et al. (2014), we use data from the 1993 birth cohort and regress an indicator for college
attendance at age 19 on parent income rank in each year from 1996 to 2012. We reproduce the
coefficients from those regressions in Online Appendix Figure IIc. The relationship between college
attendance rates and parent income rank is virtually constant when children are between ages 3 and
19. Once again, this result indicates that the point at which parent income is measured (provided
parents are between ages 30-55) does not significantly aect intergenerational associations, at least
in administrative earnings records.28
Attenuation Bias. Income in a single year is a noisy measure of lifetime income, which attenuates estimates of intergenerational persistence (Solon (1992)). To evaluate whether our baseline
estimates suer from such attenuation bias, Figure IIIb plots estimates of the rank-rank slope,
varying the number of years used to calculate mean parent family income. In this figure, we plot
the slope from an OLS regression of child rank on parent rank (as in Row 4, Column 1 of Table
I), varying the number of years used to calculate mean parent income from one (1996 only) to 17
(1996-2012). The rank-rank slope based on five years of data (0.341) is 6.6% larger than the slope
based on one year of parent income (0.320). Solon (1992) finds a 33% increase in the IGE (from
0.3 to 0.4) when using a five-year average instead of one year of data in the PSID. We find less
attenuation bias for three reasons: (1) income is measured with less error in the tax data than in
the PSID, (2) we use family income measures rather than individual income, which fluctuates more
across years, and (3) we use a rank-rank specification rather than a log-log specification, which is
more sensitive to income fluctuations at the bottom of the distribution.
Mazumder (2005) reports that even five-year averages of parent income yield attenuated estimates of intergenerational persistence relative to longer time averages. Contrary to this result,
we find that the rank-rank slope is virtually unchanged by adding more years of data beyond five
years: the estimated slope using 15 years of data to measure parent income (0.350) is only 2.8%
larger than the baseline slope of 0.341 using 5 years of data. We believe our results dier because
we directly measure parent income, whereas Mazumder imputes parent income based on race and
28

While we cannot measure income before the year in which children turn 3, the fact that the college-income
gradient is not declining from ages 3-19 makes it unlikely that the gradient is significantly larger prior to age 2.
Parent income ranks in year t have a correlation of 0.91 with parent income ranks in year t + 1, 0.77 in year t + 5,
and 0.65 in year t + 15. The decay in this autocorrelation would generate a decreasing slope in the gradient in Online
Appendix Figure IIc if there were a discontinuous jump in the gradient prior to age 2.

18

education for up to 60% of the observations in his sample, with a higher imputation rate when
measuring parent income using more years (see Online Appendix E for further details). Such imputations are analogous to instrumenting for income with race and education, which is known to
yield upward-biased estimates of intergenerational persistence (Solon 1992).
We analyze the impact of varying the number of years used to measure the childs income in
Online Appendix Figure IId. The rank-rank slope increases very little when increasing the number
of years used to compute child family income, with no detectable change once one averages over
at least two years, as in our baseline measure. An ancillary implication of this result is that our
estimates of intergenerational mobility are not sensitive to the calendar year in which we measure
childrens incomes. This finding is consistent with the results of Chetty et al. (2014), who show that
estimates of intergenerational mobility do not vary significantly across birth cohorts when income
is measured at a fixed age.
Alternative Income Definitions. In rows 5-8 of Table I, we explore the robustness of the baseline
rank-rank estimate to alternative definitions of child and parent income. In row 5, we verify that the
missing W-2 data from 1996-1998 does not create significant bias by defining parent income as mean
income from 1999-2003. The rank-rank estimates are virtually unchanged with this redefinition.
In row 6, we define the parents rank based on the individual income of the parent with higher
mean income from 1999-2003.29 This specification eliminates the mechanical variation in family
income driven by the number of parents in the household, which could overstate the persistence of
income across generations if parent marital status has a direct eect of childrens outcomes. The
rank-rank correlation falls by approximately 10%, from 0.341 to 0.312 when we use top parent
income. The impact of using individual parent income instead of family income is modest because
(1) most of the variation in parent income across households is not due to dierences in marital
status and (2) the mean ranks of children with married parents are only 4.6 percentile points higher
than those with single parents.
Next, we consider alternative income definitions for the children. Here, one concern is that
children of higher income parents may be more likely to marry, again exaggerating the observed
persistence in family income relative to individual income. Using individual income to measure
the childs rank has dierential impacts by the childs gender, consistent with Chadwick and Solon
29

We use 1999-2003 income here because we cannot allocate earnings across spouses before 1999, as W-2 forms are
available starting only in 1999. Note that top income rank diers from family income rank even for single parents
because some individuals get married in subsequent years and because these individuals are ranked relative to the
population, not relative to other single individuals.

19

(2002). For male children, using individual income instead of family income reduces the rank-rank
correlation from 0.336 in the baseline specification to 0.317, a 6% reduction. For female children,
using individual income reduces the rank-rank correlation from 0.346 to 0.257, a 26% reduction.
The change may be larger for women because women from high income families tend to marry
high-income men and may choose not to work.
Finally, in row 8 of Table I, we define a measure of child income that excludes capital and
other non-labor income using the sum of individual wage earnings, UI benefits, SSDI benefits,
and Schedule C self-employment income. We divide self-employment income by two for married
individuals. This individual earnings measure also yields virtually identical estimates of the rankrank slope.

IV.C

Intermediate Outcomes: College Attendance and Teenage Birth

We supplement our analysis of intergenerational income mobility by studying the relationship

between parent income and two intermediate outcomes for children: college attendance and teenage
birth.
The series in circles in Figure IVa presents a binned scatter plot of the college attendance rate of
children vs. the percentile rank of parent family income using the core sample. College attendance
is defined as attending college in one or more years between the ages 18 and 21. The relationship
between college attendance rates and parental income rank is again virtually linear, with a slope
of 0.675. That is, moving from the lowest-income to highest-income parents increases the college
attendance rate by 67.5 percentage points, similar to the estimates reported by Bailey and Dynarski
(2011) using survey data.
The series in triangles in Figure IVa plots college quality ranks vs. parent ranks. We define a
childs college quality rank based on the mean earnings at age 30 of students who attended each
college at age 20. The 54% of children who do not attend college at age 20 are included in this
analysis and are assigned the mean rank for the non-college group, which is approximately 54/2 =
27 (see Section III.B for details). The relationship between college quality rank and parent income
rank is convex because most children from low-income families do not attend college and hence
increases in parent income have little impact on college quality rank at the bottom. To account for
this non-linearity, we regress college quality ranks on a quadratic function of parent income rank
and define the gradient in college quality as the dierence in the predicted college quality rank for
children with parents at the 75th percentile and children with parents at the 25th percentile. The

20

P25-75 gap in college quality ranks is 19.1 percentiles in our core sample.
Figure IVb plots teenage birth rates for female children vs. parent income ranks. Teenage birth
is defined (for females only) as having a child when the mother is aged 13-19. There is a 29.8
percentage point gap in teenage birth rates between children from the highest- and lowest-income
families.
These correlations between intermediate outcomes and parent income ranks do not vary significantly across subsamples or birth cohorts, as shown in rows 9-11 of Table I. The strength of
these correlations indicates that much of the divergence between children from low vs. high income
families emerges well before they enter the labor market, consistent with the findings of prior work
(e.g., Neal and Johnson 1996, Cameron and Heckman 2001, Bhattacharya and Mazumder 2011).

Spatial Variation in Mobility

We now turn to our central goal of characterizing the variation in intergenerational mobility across
areas within the U.S. We begin by defining measures of geographic location. We then present
estimates of relative and absolute mobility by area and assess the robustness of these estimates to
alternative specifications.

V.A

Geographical Units

To characterize the variation in childrens outcomes across areas, one must first partition the U.S.
into a set of geographical areas in which children grow up. One way to conceptualize the choice of
a geographical partition is using a hierarchical model in which childrens outcomes depend upon
conditions in their immediate neighborhood (e.g., peers or resources in their city block), local
community (e.g., the quality of schools in their county), and broader metro area (e.g., local labor
market conditions). To fully characterize the geography of intergenerational mobility, one would
ideally estimate all of the components of such a hierarchical model.
As a first step toward this goal, we characterize intergenerational mobility at the level of commuting zones (CZs). CZs are aggregations of counties based on commuting patterns in the 1990
Census constructed by Tolbert and Sizer (1996) and introduced to the economics literature by Dorn
(2009). Since CZs are designed to span the area in which people live and work, they provide a
natural starting point as the coarsest partition of areas. CZs are similar to metropolitan statistical
areas (MSA), but unlike MSAs, they cover the entire U.S., including rural areas. There are 741
CZs in the U.S.; on average, each CZ contains 4 counties and has a population of 380,000. See
21

Online Appendix Figure III for an illustration of the Boston CZ.

We focus on CZ-level variation because mobility statistics in very small neighborhoods are
likely to be heavily aected by sorting. Because property prices are typically homogeneous within
narrow areas and home values are highly correlated with parent income, comparisons within a
small neighborhood eectively condition on a proxy for parent income. As a result, the variation
in parent income across individuals in a small area (such as a city block) must be correlated with
other latent factors that could aect childrens outcomes directly, making it difficult to interpret
the resulting mobility estimates.30 Nevertheless, to obtain some insight into within-CZ variation,
we also report statistics on intergenerational mobility by county in Online Data Table III. There
is almost as much variance in intergenerational mobility across counties within a CZ as there is
across CZs, suggesting that the total amount of geographical variation may be even greater than
that documented below.31
We permanently assign each child to a single CZ based on the ZIP code from which his or his
parent filed their tax return in the first year the child was claimed as a dependent. We interpret
this CZ as the area where a child grew up. Because our data begin in 1996, location is measured
in 1996 for 95.9% of children in our core sample.32 For children in our core sample of 1980-82 birth
cohorts, we therefore typically measure location when children were approximately 15 years old.
For the children in the more recent birth cohorts in our extended sample, location is measured at
earlier ages. Using these more recent cohorts, we find that 83.5% of children live in the same CZ
at age 16 as they did at age 5. Furthermore, we verify that the spatial patterns for the outcomes
we can measure at earlier ages (college attendance and teenage birth) are similar if we define CZs
based on location at age 5 instead of age 16.
The CZ where a child grew up does not necessarily correspond to the CZ he lives in as an adult
when we measure his income (at age 30) in 2011-12. In our core sample, 38% of children live in a
dierent CZ in 2012 relative to where they grew up.
30

For example, it would be difficult to estimate the degree of intergenerational mobility on Park Avenue in Manhattan because any families with low observed income in such a high-property-value area would have to be latently
wealthy to be able to aord to live there.
31
We also report statistics by MSA in Online Data Table IV. For CZs that intersect MSAs, correlations between
CZ-level and MSA-level mobility statistics exceed 0.9.
32
Location is measured after 1996 for approximately 3% of children because they were linked to parents based on
tax returns filed after 1996. We have no information on location for the remaining 1% of children in the national
sample because the ZIP code listed on the parents tax returns is invalid or missing (see Online Appendix Table I);
these children are excluded from the analysis in the remainder of the paper.

22

V.B

Measures of Relative and Absolute Mobility

In our baseline analysis, we measure mobility at the CZ level using the core sample (1980-82 birth
cohorts) and the definitions of parent and child family income described in III.B. Importantly,
we continue to rank both children and parents based on their positions in the national income
distribution (rather than the distribution within their CZ).
We begin by examining the rank-rank relationship in selected CZs. Figure Va presents a binned
scatter plot of the mean child rank vs. parent rank for children who grew up in the Salt Lake City,
UT (circles) or Charlotte, NC (triangles) commuting zones. The rank-rank relationship is virtually
linear in both of these CZs. The linearity of the rank-rank relationship is a remarkably robust
property across CZs, as illustrated for the 20 largest CZs in Online Appendix Figure IV.
Exploiting this approximate linearity, we summarize the conditional expectation of a childs
rank given his parents rank in each CZ using two parameters: a slope and an intercept. Let Ric
denote the national income rank (among children in his birth cohort) of child i who grew up in
CZ c. Similarly, let Pic denote his parents rank in the income distribution of parents in the core
sample. We estimate the slope and intercept of the rank-rank relationship in CZ c by regressing
child rank on parent rank:
Ric = c +

c Pic

+ "ic

(2)

The slope of the rank-rank relationship ( c ) in (2) measures degree of relative mobility in CZ c, as
defined in Section II. In Salt Lake City,

= 0.264.33 The dierence between the expected ranks of

children born to parents at the top and bottom of the income distribution is r100,c r0,c = 100

26.4 in Salt Lake City. There is much less relative mobility (i.e., much greater persistence of income
across generations) in Charlotte, where r100

r0 = 39.7.

Following the discussion in Section II, we define absolute mobility at percentile p in CZ c as the
expected rank of a child who grew up in CZ c with parents who have a national income rank of p:
rpc = c +

c p.

(3)

We focus much of our analysis on average absolute mobility for children from families with belowmedian parent income in the national distribution (E [Ric |Pic < 50]), which we term absolute upward
mobility.34 Because the rank-rank relationship is linear, the average rank of children with below33

We always measure percentile ranks on a 0-100 scale and slopes on a 0-1 scale, so c ranges from 0-100 and c
ranges from 0 to 1 in (3).
34
We integrate over the national parent income distribution rather than the local distribution when defining
E [Ric |Pic < 50] to ensure that our cross-CZ comparisons are not aected by dierences in local income distributions.

23

median parent income equals the average rank of children with parents at the 25th percentile in
the national distribution (
r25,c = c + 25 c ), illustrated by the dashed vertical line in Figure Va.
Absolute upward mobility is r25 = 46.2 in Salt Lake City, compared with r25 = 35.8 in Charlotte.
That is, among families earning $28,800 the 25th percentile of the national parent family income
distribution children who grew up in Salt Lake City are on average 10 percentile points higher in
their birth cohorts income distribution at age 30 than children who grew up in Charlotte.
Absolute mobility is higher in Salt Lake City not just for below-median families, but at all
percentiles p of the parent income distribution. The gap in absolute outcomes is largest at the
bottom of the income distribution and nearly zero at the top. Hence, the greater relative mobility
in this particular comparison comes purely from better absolute outcomes at the bottom of the
distribution rather than worse outcomes at the top. Of course, this is not always the case. Figure Vb
shows that San Francisco has substantially higher relative mobility than Chicago: r100
in San Francisco vs. r100

r0 = 25.0

r0 = 39.3 in Chicago. But part of the greater relative mobility in

San Francisco comes from worse outcomes for children from high-income families. Below the 60th
percentile, children in San Francisco have better outcomes than those in Chicago; above the 60th
percentile, the reverse is true.
The comparisons in Figure V illustrate the importance of measuring both relative and absolute
mobility. Any social welfare function based on mean income ranks that respects the Pareto principle
would rate Salt Lake City above Charlotte. But normative comparisons of San Francisco and
Chicago depend on the weight one puts on relative vs. absolute mobility (or, equivalently, on the
weights one places on absolute mobility at each percentile p).

V.C

Baseline Estimates by CZ

We estimate (2) using OLS to calculate absolute upward mobility (

r25,c = c + 25 c ) and relative
mobility ( c ) by CZ. The estimates for each CZ are reported in Online Data Table V.
Absolute Upward Mobility. Figure VIa presents a heat map of absolute upward mobility. We
construct this map by dividing CZs into deciles based on their estimated value of r25,c . Lighter
colors represent deciles with higher levels of r25,c .35 Upward mobility varies significantly across
We focus on the absolute outcomes of children from low-income families both because the outcomes of disadvantaged
youth are a central focus of policy interest and because there is more variation across areas in the outcomes of
children from low-income families than those from high-income families, as we show in Figure VII below. However,
the CZ-level statistics in Online Data Tables V and VI can be used to analyze spatial variation in the outcomes of
children from high-income families.
35
We cannot estimate mobility for 32 CZs in which we have fewer than 250 children in the core sample, shown by
the cross-hatched areas in the maps in Figure VI. These CZs account for less than 0.05% of the U.S. population in

24

areas. CZs in the top decile have r25,c > 52.0, while those in the bottom decile have r25,c < 37.4.
Note that the 37th percentile of the family income distribution for children at age 30 is $22,900,
while the 52nd percentile is $35,500; hence, the dierence in upward mobility across areas translates
to substantial dierences in childrens incomes.
Pooling all CZs, the unweighted standard deviation (SD) of r25,c is 5.68; the population-weighted
SD is 3.34. The unconditional SD of childrens income ranks (which have a Uniform distribution) is
p
100/ 12 = 28.9. Hence, a 1 SD improvement in CZ quality as measured by its level of absolute
upward mobility r25,c is associated with a 5.68/28.9 = 0.20 SD increase in the expected income
rank of children whose parents are at the 25th percentile.36 For comparison, a 1 SD increase in
parent income rank is associated with a 0.34 SD increase in a childs income rank (Figure IIa).
Hence, a 1 SD improvement in CZ quality is associated with 60% as large an increase in a childs
income as a 1 SD increase in his own parents income.
There are three broad spatial patterns in upward mobility evident in Figure VIa. First, upward
mobility varies substantially at the regional level. Upward mobility is lowest in the Southeast and
highest in the Great Plains. The West Coast and Northeast also have high rates of upward mobility,
though not as high as the Great Plains.
Second, there is substantial within-region variation as well. Using unweighted CZ-level regressions of the upward mobility estimates on Census division and state fixed eects, we estimate that
53% of the cross-CZ variance in absolute upward mobility is within the nine Census divisions and
36% is within states. For example, many parts of Texas exhibit relatively high rates of upward
mobility, unlike much of the rest of the South. Ohio exhibits much lower rates of upward mobility
than nearby Pennsylvania. The statistics also pick up much more granular variation in upward
mobility. For example, South Dakota generally exhibits very high levels of upward mobility, with
the exception of a few areas in the Southwest corner of the state. These areas are some of the
largest Native American reservations in the U.S. and are well known to suer from very high rates
of persistent poverty.
the 2000 Census. In Online Appendix Figure V, we present a version of this map in which we use data from the
1980-85 cohorts to estimate mobility for the CZs that have fewer than 250 observations in the core (1980-82) sample.
The estimates of mobility in the CZs with missing data are quite similar to those in neighboring CZs, consistent with
the spatial autocorrelation evident in the rest of the map.
36
An analogous calculation using the estimates of college attendance gradients by CZ in Section IV.C below implies
that a 1 SD increase in CZ quality is associated with a 0.19 SD (9.3 percentage point) increase in college attendance
rates for children with parents at the 25th percentile. Using data from the PSID, Solon, Page and Duncan (2002, p390)
estimate that a 1 SD increase in neighborhood quality is associated with a 0.32 SD increase in years of education.
We find less variation in outcomes across neighborhoods presumably because commuting zones are much larger than
the PSID sampling clusters analyzed by Solon, Page, and Duncan.

25

The third generic pattern is that urban areas tend to exhibit lower levels of intergenerational
mobility than rural areas on average. For instance, children from low-income families who grow
up in the Chicago area have significantly lower incomes at age 30 than those who grow up in rural
areas in Illinois. On average, urban areas which we define as CZs that intersect MSAs have
upward mobility of r25,c = 41.7, while rural areas have r25,c = 45.8. In interpreting this comparison,
it is important to recall that our definition of geography is based on where children grew up, not
where they live as adults. 44.6% of children who grow up in rural areas live in urban areas at age
30. Among those who rose from the bottom quintile of the national income distribution to the top
quintile, 55.2% of children who grew up in rural areas live in urban areas at age 30.
Table III shows statistics on intergenerational mobility for the 50 largest CZs by population.
Among these cities, absolute upward mobility ranges from 46.2 in the Salt Lake City area to 35.8
in Charlotte (Column 4). There is considerable variation even between nearby cities: Pittsburgh
is ranked second in terms of upward mobility among large metro areas, while Cleveland approximately 100 miles away is ranked in the bottom 10. Upward mobility is especially low in certain
cities in the Rust Belt such as Indianapolis and Columbus and cities in the Southeast such as
Atlanta and Raleigh. The fact that children who grow up in low-income families in Atlanta and
Raleigh fare poorly is especially noteworthy because these cities are generally considered to be
booming cities in the South with relatively high rates of job growth.
In Column 5 of Table III, we consider an alternative measure of upward mobility: the probability
that a child born to a family in the bottom quintile of the national income distribution reaches the
top quintile of the national income distribution.37 To improve precision in smaller CZs, we estimate
this probability pooling the 1980-1985 birth cohorts.38 The ranking of areas based on this statistic
is similar to that based on the mean rank measure of upward mobility. The probability that a
child from the lowest quintile of parental income rises to the top quintile is 10.8% in Salt Lake
City, compared with 4.4% in Charlotte. The city with the highest probability of moving from the
bottom fifth to the top fifth is San Jose, where the probability (12.9%) is nearly three times that
37

In principle, dierences in local income distributions within the bottom quintile could generate dierences in
this probability. In an earlier version of this analysis (v1.0 available on the project website), we accounted for these
dierences by calculating the chance of reaching the top quintile separately for each percentile and computed the
unweighted mean across the percentiles, eectively integrating over the national parent income distribution. The
adjusted CZ-level transition probabilities obtained using this approach were virtually identical to the raw transition
probabilities we report in this paper.
38
We verify that including more recent cohorts does not generate significant bias by showing that the national
transition matrix based on the 1980-85 cohorts (Online Appendix Table VI) is virtually identical to the matrix based
on the 1980-82 cohorts in Table II. We report the quintile transition matrix for each CZ in Online Data Table VI and
provide statistics on the marginal distributions of parent and child income by CZ in Online Data Table VII.

26

in Charlotte. The chances of rising from the bottom fifth to the top fifth for children growing up in
San Jose are comparable to those in Denmark and Canada (see Section IV.A). Note that if parent
income played no role in determining childrens outcomes, all the quintile transition probabilities
would be 20%. Hence, the variation in rates of upward mobility across areas is large relative to the
maximum plausible range of 0 to 20%.
In Column 6 of Table III, we consider another measure of absolute upward mobility: the probability that a child has family income above the poverty line conditional on having parents at the
25th percentile (see Online Appendix F for details on the construction of this measure). This statistic also generates very similar rankings across CZs, confirming that our results are not sensitive to
the way in which we measure upward mobility.
Relative Mobility. Figure VIb presents a heat map of relative mobility. This map is constructed
in the same way as Panel A, dividing CZs into deciles based on the rank-rank slope
lighter areas denote areas with greater relative mobility (lower

c ).

c.

In this map,

Relative mobility also varies

substantially across areas. The expected rank of children from the richest vs. poorest families diers
by more than 40.2 percentiles in CZs in the bottom decile of relative mobility. The corresponding
gap is less than 23.5 percentiles for CZs in the top decile.
The geographical patterns in relative mobility in Panel B are similar to those for absolute
upward mobility in Panel A. The unweighted correlation across CZs between the two measures is
-0.68; the population-weighted correlation is -0.61. This indicates that areas with greater relative
mobility tend to have better absolute outcomes for children from low-income families.
To investigate the connection between absolute and relative mobility more systematically, let
pc = E [Ric |Pic = p] denote a childs expected rank given a parent rank of p in CZ c. We estimate
pc in each CZ non-parametrically as the mean value of Ric for children in each percentile bin of
the parent income distribution p = 0, ..., 99.39 For each of the 100 values of p, we estimate an
unweighted OLS regression of pc on relative mobility
pc = a +
In this equation,

p c

with one observation per CZ:

+ pc .

measures the association across CZs between a 1 unit increase in

39

(i.e., greater

The expected value pc diers from rpc defined above because pc is estimated non-parametrically using only
data in percentile bin p, whereas rpc is calculated based on the linear approximation to the rank-rank relationship in
(3). In practice, the two estimates are extremely similar. For instance, in the 100 largest CZs, where pc is estimated
with very little error, the correlation between pc and rpc exceeds 0.99. We use the linear approximation rpc in most
of our analysis to obtain more precise estimates of absolute mobility in smaller CZs. However, because the goal of
the exercise here is to evaluate the relationship between relative mobility c and absolute mobility at each percentile
non-parametrically, we use pc here.

27

intergenerational persistence) and the mean rank of children with parents at the pth percentile of
the national income distribution. A negative coefficient (p < 0) implies that CZs with greater
relative mobility generate better mean outcomes for children with parents at percentile p.
Figure VIIa plots the coefficients p at each parent income percentile p along with a linear fit to
the coefficients. The coefficients p are increasing with p: CZs with greater relative mobility (lower
c)

produce better outcomes for children from lower income families. The best linear fit crosses 0

at p = 85.1. Hence, increases in relative mobility are associated with better outcomes for children
who grow up in families below the 85th percentile on average. For families at the 85th percentile,
dierences in relative mobility across CZs are uncorrelated with a childs mean rank. For families
in the top 15%, living in a CZ with greater relative mobility is associated with worse outcomes on
average for children. Observe that

reaches only 0.2 for the richest families but is nearly -0.8 for

the poorest families. This shows that dierences in relative mobility across CZs are associated with
much larger dierences in absolute mobility for children from low-income families than high-income
families.40
Figure VIIb presents a schematic that illustrates the intuition underlying the preceding results.
This figure plots hypothetical rank-rank relationships in two representative CZs, one of which has
more relative mobility than the other. Figure VIIa implies that in such a pairwise comparison, the
rank-rank relationship pivots at the 85th percentile on average. This is why the spatial patterns
of absolute mobility at p = 25 and relative mobility in Figure VI look similar.
Because the pivot point is high in the income distribution, dierences in relative mobility have a
smaller eect on childrens percentile ranks in high-income families than low-income families.41 This
may be because the rich are able to insulate themselves from dierences in the local environment.
If the dierences in relative mobility across areas are caused by dierences in local policies, this
result suggests that policies that improve relative mobility may be able to improve the outcomes
of children from poor families without hurting children from high income families significantly.
40

If the rank-rank relationship were perfectly linear, the relationship plotted in Figure VIIa would be perfectly
linear and 100
0 = 1 mechanically. The slight deviation from linearity at the bottom of the distribution evident
in Figure V generates the slight deviation of 100
0 from 1.
41
It bears emphasis that this result applies to percentile ranks rather than mean income levels. Because the income
distribution has a thick upper tail, a given dierence in percentile ranks translates to a much larger dierence in
mean incomes in the upper tail of the income distribution. The probability that children of auent parents become
very high income superstars may therefore dier significantly across areas.

28

V.D

Robustness of Spatial Patterns

We assess the robustness of the spatial patterns in mobility along several dimensions. The results
of this robustness analysis are reported in Online Appendix F and Appendix Table VII; we present
a brief summary here.
We begin by considering changes in sample definitions: limiting the sample to male vs. female
children, married vs. single parents, and later birth cohorts (for which we measure childrens
location at earlier ages). Measures of both absolute and relative mobility across areas in these
subsamples generally have a correlation of more than 0.9 with the corresponding baseline measures
reported above. Restricting the sample to hold the parents ages at the birth of child fixed, limiting
the sample to children who stay in the CZ where they grew up as adults, and limiting the sample to
children linked to only one parent in all years yield very similar estimates of mobility across areas.
We also find that the spatial patterns are highly robust to using alternative measures of income
used in Table I. For example, using individual income instead of family income or wage earnings
instead of total income yields very spatial patterns.
We evaluate whether adjusting for dierences in cost-of-living across areas aects our estimates
by dividing parents income by a local price index (based on the ACCRA survey) for the CZ where
their child grew up and the childs income by the price index for the CZ where he lives in 2012 to
obtain real income measures. Measures of intergenerational mobility based on real incomes are very
highly correlated with our baseline measures. The degree of upward mobility i.e., the dierence
between the childs rank and the parents rank is essentially unaected by adjusting for local
prices because few children move to areas with very dierent levels of cost of living relative to their
parents (see Appendix F for details).
Because we measure parent income before 2000 and child income in 2011-12, part of the variation
in upward mobility across areas could be driven by shocks to local economic growth. While growth
shocks e.g., from the discovery of a natural resource such as oil are a real source of upward
mobility, one may be interested in isolating variation in mobility attributable to more stable factors
that can be manipulated by policy. We assess the extent to which economic growth is responsible
for the spatial variation in upward mobility in two ways. First, we define parent income as mean
family income in 2011-12, the same years in which we measure child income. Insofar as local
economic growth raises the incomes of both parents and children, this measure nets out the eects
of growth on mobility. Second, we regress upward mobility on the CZ-level growth rate from 2000-

29

2010 and calculate residuals. Both of these growth-adjusted mobility measures have a correlation
of more than 0.8 with our baseline measures, indicating that most of the spatial variation in upward
mobility is not driven by dierences in growth rates.
Finally, we consider a set of alternative statistics for relative and absolute mobility. Estimating
relative mobility based on parent and child ranks in the local income distribution yields estimates
that are very highly correlated with our baseline estimates based on national ranks. We also show
that the two alternative measures of upward mobility analyzed in Table III the probability of rising
from the bottom fifth to the top fifth and the probability of having income above the poverty line
conditional on having parents at the 25th percentile also generate very similar spatial patterns,
with correlations above 0.9 with our baseline mean rank measure of upward mobility (Online
Appendix Figure VI).

V.E

Intermediate Outcomes: College Attendance and Teenage Birth

To better understand the sources of the spatial variation in intergenerational income mobility, we
characterize spatial variation in the three intermediate outcomes analyzed in Figure IV: college
attendance rates, college quality rank, and teenage birth rates. We first regress each of these
outcomes on parent national income rank in each CZ c using specifications analogous to (2). We
then characterize spatial variation in two measures of mobility for each outcome using the regression
estimates: the slope coefficient, which is analogous to our measure of relative mobility above, and
the predicted outcome for children with parents at the 25th percentile, which is analogous to our
measure of absolute mobility.42
We present heat maps for the relative and absolute mobility measures for the three intermediate
outcomes in Online Appendix Figures VII-IX; the CZ-level data underlying these maps are reported
in Online Data Table V. There is substantial spatial variation in all three intermediate outcomes
and the variation is highly correlated with the variation in the intergenerational income mobility.
For example, college attendance rates for children with parents at the 25th percentile vary from less
than 32.4% in bottom decile of CZs to more than 55.6% in the top decile of CZs. The unweighted
correlation between college attendance rates at the 25th percentile and mean income ranks at the
25th percentile (absolute upward mobility) across CZs is 0.71 (Online Appendix Table VII, row
23). Similarly, teenage birth rates for female children whose parents are at the 25th percentile vary
42

Because the relationship between college quality rank and parent rank is not linear, we regress college quality
ranks on a quadratic function of parent income rank and define the relative mobility measure for college quality as
the dierence in the predicted college quality rank for children with parents at the 75th percentile and children with
parents at the 25th percentile, as in Figure IVa.

30

from less than 15.4% in bottom-decile of CZs to more than 29.4% in the top decile. The correlation
between teen birth rates and absolute upward mobility is -0.61.
An important implication of these results is that much of the dierence in intergenerational
mobility across areas emerges while children are teenagers, well before they enter the labor market
as adults.43 This suggests that the spatial variation in income mobility is driven by factors that
either directly aect children at early ages (such as the quality of schools or social structure) or
anticipatory behavioral responses to subsequent dierences (such as returns to education in the
local labor market). We explore mechanisms that have such properties in the next section.

VI

Correlates of Intergenerational Mobility

Why do some areas of the U.S. exhibit much higher rates of upward mobility than others? As a first
step toward answering this question, we correlate our measures of intergenerational mobility with
local area characteristics. Naturally, such correlations cannot be interpreted as causal mechanisms.
Our goal is merely to document a set of stylized facts to guide the search for causal determinants
and the development of new models of intergenerational mobility.
We correlate our mobility statistics with various factors that have been discussed in the sociology
and economics literature, such as segregation and inequality. Because most of these factors are slowmoving and we have estimates of intergenerational income mobility for essentially one birth cohort,
we focus on cross-sectional correlations rather than changes over time. For most covariates, we use
data from the 2000 Census and other publicly available datasets because many variables cannot be
consistently measured in earlier years. See Online Appendix G for details on the construction of
the covariates analyzed in this section and Online Data Table VIII for CZ-level data on each of the
covariates.
Figure VIII presents a summary of our correlational results. It plots the unweighted univariate
correlation between absolute upward mobility and various CZ-level characteristics, using all CZs
with available data for the relevant variable. We consider several proxies for each broad factor (segregation, inequality, etc.). The dots show the point estimate of the correlation and the horizontal
lines show a 95% confidence interval, based on standard errors clustered at the state level. The sign
of the correlation is shown in parentheses next to each variable. In Online Appendix Table VIII, we
report these correlations as well as estimates from several alternative specifications: including state
43
Further supporting this claim, we find a strong positive correlation of 0.63 between teenage labor force participation rates (between the ages of 14 and 16) and upward mobility (see Figure VIII and Online Appendix H).

31

fixed eects, weighting CZs by population, restricting to urban areas, and controlling for dierences
in racial demographics and income growth (see Online Appendix H for details). These alternative
specifications generally yield very similar results to the baseline estimates shown in Figure VIII.
Most importantly, the correlations discussed below hold even in specifications with state fixed effects, showing that the results are not just driven by broad regional dierences across the South
vs. other parts of the country. We also show in Online Appendix Table VIII that the factors that
are positively associated with absolute upward mobility are generally positively associated with
relative mobility (i.e., are negatively correlated with rank-rank slopes).
In the remainder of this section, we discuss correlations of mobility with the categories in Figure
VIII that have the strongest relationship with mobility: racial demographics, segregation, income
inequality, school quality, social capital, and family structure. We discuss results for four other
broad categories for which we find weaker correlations local tax policies, higher education, labor
market conditions, and migration in Online Appendix H.

VI.A

Race

Perhaps the most obvious pattern from the maps in Figure VI is that intergenerational mobility
is lower in areas with larger African-American populations, such as the Southeast. Indeed, the
unweighted correlation between upward mobility and the fraction of black residents in the CZ
(based on the 2000 Census) is -0.580, as shown in the first row of Figure VIII.
This correlation could be driven by two very dierent channels. One channel is an individuallevel race eect: black children may have lower incomes than white children conditional on parent
income, and hence areas with a larger black population may have lower upward mobility. An
alternative possibility is a place-level race eect: areas with large black populations might have
lower rates of upward mobility for children of all races.
To distinguish between these two channels, we would ideally control for race at the individual
level, essentially asking whether whites have lower rates of upward mobility in areas with a larger
black population. Unfortunately, we do not observe each individuals race in our data. As an
alternative, we predict race based on the parents 5-digit ZIP code (in the year they first claim
their child as a dependent). We use data from the 2000 Census to measure racial shares by
ZIP code. Figure IXa replicates the map of absolute upward mobility (
r25,c ) by CZ, restricting
the sample to ZIP codes within each CZ in which at least 80% of the residents are non-hispanic

32

whites.44 In this subsample, 91% of individuals are white. The spatial pattern in Figure IXa is
very similar to that in the original map for the full sample in Figure VIa. Most notably, even in
this predominantly white sample, rates of upward mobility remain low in the Southeast and are
much higher in the West. Among the 604 CZs for which we are able to compute upward mobility
measures for predominantly white individuals, the unweighted correlation between upward mobility
for the predominantly white sample and the full sample is 0.91.
In Figure IXb, we generalize this approach to assess how the spatial pattern of upward mobility
changes as we restrict the sample to be increasingly white. To construct this figure, we first
compute upward mobility in each CZ, restricting the sample to individuals living in ZIP codes that
w . We then regress r
w
are more than w% white, which we denote by r25,c
25,c
on r25,c , our baseline

estimates of upward mobility based on the full sample, using an unweighted OLS regression with
one observation per CZ with available data. We vary w from 0% to 95% in increments of 5%
and plot the resulting regression coefficients in Figure IXb against the fraction of white individuals
in each of the subsamples. When w = 0, the regression coefficient is 1 by construction because
w=0 . Since 68% of the U.S. population is white, the first point on the figure is (0.68,
r25,c = r25,c

1). The point generated by the w = 80% threshold is (0.91, 0.84), consistent with the map in
Figure IXa. The dotted lines show a 95% confidence interval for the regression coefficients based
on standard errors clustered at the state level.
If the variation in upward mobility across areas were entirely driven by heterogeneity in outcomes
across race at the individual level, the coefficient in Figure IXb would fall to zero as the fraction
white in the sample converged to 1, as illustrated by the dashed line. Intuitively, if all of the spatial
variation in Figure VIa were driven by individual-level dierences in race, there would be no spatial
variation left in a purely white sample. The data reject this hypothesis: even in the subsample
with more than 95% white individuals, the regression coefficient remains at 0.89.
The main lesson of this analysis is that both blacks and whites living in areas with large AfricanAmerican populations have lower rates of upward income mobility.45 There are many potential
mechanisms for such a correlation, including dierences in the institutions and industries that
developed in areas with large African-American populations. We are unable to distinguish between
44

We continue to estimate r25,c at the CZ level in this map, but we only include ZIP-5s within each CZ in which
80% or more of the residents are white. To facilitate comparison to Figure VI, we color the entire CZ based on this
statistic, including ZIP-5s whose own white share is below 80%. CZs that have fewer than 250 children who grew
up in ZIP codes where more than 80% of the residents are white are omitted (and shown with cross-hatch shading).
45
To be clear, this result does not imply that race does not matter for childrens outcomes at the individual level,
as shown e.g. by Mazumder (2011). Our finding is simply that there is spatial heterogeneity in upward mobility even
conditional on race.

33

these mechanisms in our data; instead, we next turn to one such mechanism that has received the
greatest attention in prior work: segregation. The U.S. has a historical legacy of greater segregation
in areas with more blacks. Such segregation could potentially aect both low-income whites and
blacks, as racial segregation is often associated with income segregation.

VI.B

Segregation

Prior work has argued that segregation has harmful eects on disadvantaged individuals through
various channels: reducing exposure to successful peers and role models, decreasing funding for local
public goods such as schools, or hampering access to nearby jobs (Wilson 1987, Massey and Denton
1993, Cutler and Glaeser 1997). In this subsection, we evaluate these hypotheses by exploring the
correlation between intergenerational mobility and various measures of segregation (shown in the
second panel of Figure VIII and Online Appendix Table VIII).
We begin by measuring racial segregation using a Theil (1972) index, constructed using data
from the 2000 Census as in Iceland (2004). Let

denote the fraction of individuals of race r in a

given CZ, with four racial groups: whites, blacks, hispanics, and others. We measure the level of
P
1
1
racial diversity in the CZ by an entropy index: E =
r log2 r , with r log2 r = 0 when r = 0.
Letting j = 1, ..., N index census tracts in the CZ, we analogously measure racial diversity within
P
1
each tract as Ej =
rj log2 rj where rj denotes the fraction of individuals of race r in tract j.
We define the degree of racial segregation in the CZ as
H=

X
j

popj E Ej
]
poptotal E

(4)

where popj denotes the total population of tract j and poptotal denotes the total population of
the CZ. Intuitively, H measures the extent to which the racial distribution in each Census tract
deviates from the overall racial distribution in the CZ. The segregation index H is maximized at
H = 1 when there is no racial heterogeneity within census tracts, in which case Ej = 0 in all tracts.
It is minimized at H(p) = 0 when all tracts have racial composition identical to the CZ as a whole,
so that Ej = E.
Column 1 of Table IV reports the coefficient estimate from an unweighted OLS regression of
absolute upward mobility r25,c on the racial segregation index, with one observation per CZ. In this
and all subsequent regressions, we standardize the dependent variable and all independent variables
to have mean 0 and standard deviation 1 within the estimation sample. Hence, the coefficients in the
univariate regressions can be interpreted as correlation coefficients. Standard errors are clustered
34

by state to account for spatial correlation across CZs.

More racially segregated areas have less upward mobility. The unweighted correlation between
upward mobility and the racial segregation index in Column 1 is -0.361.46 Column 2 shows that
the correlation remains at -0.360 in urban areas, i.e. CZs that overlap with metropolitan statistical
areas (MSAs).
Next, we turn to the relationship between income segregation and upward mobility. Following
Reardon and Firebaugh (2002) and Reardon (2011), we begin by measuring the degree to which
individuals below the pth percentile of the local household income distribution are segregated from
individuals above the pth percentile in each CZ using a two-group Theil index H(p). Here, entropy
in a given area is E(p) = p log2 p1 + (1

p) log2

1
1 p

and the index H(p) is defined using the formula

in (4). Building on this measure, Reardon (2011) defines the overall level of income segregation in
a given CZ as
income segregation = 2log(2)

p E(p)H(p)dp.

(5)

This measure is simply a weighted average of segregation at each percentile p, with greater weight
placed on percentiles in the middle of the income distribution, where entropy E(p) is maximized.
We implement (5) using data from the 2000 Census, which reports income binned in 16 categories.
Following Reardon (2011, Appendix 3), we measure H(p) at each of these cutos and take a
weighted sum of these values to calculate income segregation.
In Column 3 of Table IV, we regress absolute upward mobility on the income segregation index;
see Online Appendix Figure Xb for the corresponding non-parametric binned scatter plot. The
correlation between income segregation and upward mobility is -0.393, consistent with the findings
of Graham and Sharkey (2013) using survey data. Interestingly, areas with a larger black population
exhibit greater income segregation: the correlation between the fraction of black individuals in a
CZ and the income segregation index is 0.264 (s.e. 0.082). Hence, the negative relationship between
income segregation and upward mobility could partly explain why low-income white children fare
more poorly in areas with large African-American populations.
In Column 4, we decompose the eects of segregation in dierent parts of the income distribution. Following Reardon and Bischo (2011), we define the segregation of poverty as H(p = 25),
i.e. the extent to which individuals in the bottom quartile are segregated from those above the 25th
percentile. We analogously define the segregation of auence as H(p = 75). Column 4 regresses
46

Online Appendix Figure Xa presents a non-parametric binned scatter plot corresponding to this regression; see
Online Appendix H for details on the construction of this figure.

35

upward mobility on both segregation of poverty and auence. Segregation of poverty has a strong
negative association with upward mobility, whereas segregation of auence does not. Column 5
shows that the same pattern holds when restricting the sample to urban areas. These results suggest that the isolation of low-income families (rather than the isolation of the rich) may be most
detrimental for low income childrens prospects of moving up in the income distribution.
Another mechanism by which segregation may diminish upward mobility is through spatial
mismatch in access to jobs (Kain 1968, Kasarda 1989, Wilson 1996). We explore this mechanism in
Column 6 by correlating upward mobility with the fraction of individuals who commute less than
15 minutes to work in the CZ, based on data from the 2000 Census. Areas with less sprawl (shorter
commutes) have significantly higher rates of upward mobility; the correlation between commute
times and upward mobility is 0.605. Column 7 shows that commute times remain a significant
predictor of upward mobility in a multivariable regression but income segregation does not.
These results are consistent with the view that the negative impacts of segregation may operate
by making it more difficult to reach jobs or other resources that facilitate upward mobility. But any
such spatial mismatch explanation must explain why the gradients emerge before children enter
the labor market, as shown in Section V.E. A lack of access to nearby jobs cannot directly explain
why children from low-income families are also more likely to have teenage births and less likely to
attend college in cities with low levels of upward mobility. However, spatial mismatch could produce
such patterns if it changes childrens behavior because they have fewer successful role models or
reduces their perceived returns to education.

VI.C

Income Levels and Inequality

In this subsection, we explore the correlation between properties of the local income distribution
mean income levels and inequality and intergenerational mobility.
Mean Income Levels. The third section of Figure VIII shows that the mean level of household
income in a CZ (as measured in the 2000 Census) is essentially uncorrelated with upward mobility
(see Online Appendix Figure XIa for the corresponding non-parametric binned scatter plot). Children in low-income families who grow up in the highest-income CZs (with mean incomes of $47,600
per year) reach almost exactly the same percentile of the national income distribution on average
as those who grow up in the lowest-income areas (with mean incomes of $21,900).
Income Inequality. Prior work has documented a negative correlation between income inequality and intergenerational mobility across countries (e.g., Corak 2013). This Great Gatsby curve

36

(Krueger 2012) has attracted attention because it suggests that greater inequality within a generation could reduce social mobility. We explore whether there is an analogous relationship across
areas within the U.S. by correlating upward mobility with the Gini coefficient of parent income
within each CZ. We compute the Gini coefficient for parents in our core sample within each CZ as
Gini =

2
c Cov(Xic , Pic ),
X

c is the mean family income (from 1996-2000) of parents in CZ c

where X

and Cov(Xic , Pic ) is the covariance between the income level (Xic ) and the percentile rank (Pic ) of
parents in CZ c. The correlation between the Gini coefficient and upward mobility is -0.578 (see
also Online Appendix Figure XIb).
An alternative measure of inequality is the portion of income within a CZ that accrues to the
richest households, e.g. those in the top 1%. This measure is of particular interest because the rise
in inequality in the U.S. over the past three decades was driven primarily by an increase in top
income shares (Piketty and Saez 2003). We calculate top 1% income shares using the distribution
of parent family income within each CZ. The correlation between upward mobility and the top 1%
income share is only -0.190 (see also Online Appendix Figure XIc), much weaker than that with
the Gini coefficient.
We investigate why the Gini coefficient and top 1% share produce dierent results in Table V,
which is constructed in the same way as Table IV. Column 1 replicates the regression corresponding
to the raw correlation between the Gini coefficient and upward mobility as a reference. We decompose the Gini coefficient into inequality coming from the upper tail and the rest of the income
distribution by defining the bottom 99% Gini as the Gini coefficient minus the top 1% income
share. The bottom 99% Gini can be interpreted as the deviation of the Lorenz curve from perfect
equality amongst households in the bottom 99%. Column 2 of Table V shows that a 1 SD increase
in the bottom 99% Gini is associated with a 0.634 SD reduction in upward mobility. In contrast, a
1 SD increase in the top 1% share is associated with only a 0.123 SD reduction in upward mobility.
Column 3 shows that in urban areas (CZs that overlap with MSAs), the pattern is even more stark:
upper tail inequality is uncorrelated with upward mobility, whereas the Gini coefficient within the
bottom 99% remains very highly strongly correlated with upward mobility.
Another measure of inequality within the bottom 99% is the size of the middle class in the CZ,
which we define as the fraction of parents in the CZ who have family incomes between the 25th
and 75th percentiles of the national parent income distribution. Column 4 of Table V shows that
upward mobility is strongly positively correlated with the size of the middle class.
Finally, Column 5 of Table V replicates Column 2 using relative mobility
37

as the dependent

variable. The bottom 99% Gini coefficient is strongly positively associated with this measure. That
is, greater inequality in the bottom 99% is negatively related to relative mobility.47 But once again,
the top 1% share is uncorrelated with relative mobility.
Comparison to Cross-Country Evidence. Next, we explore whether the size of the middle class
is more strongly correlated with intergenerational mobility than upper tail inequality in the crosscountry data as well. In Column 6 of Table V, we replicate Coraks (2013, Figure 1) result that
there is a strong positive correlation between the Gini coefficient (as measured in survey data on
income in 1985) and the intergenerational elasticity (IGE) using data from 13 developed countries
compiled by Corak (2013).48 In Column 7, we include the top 1% income share in each country,
based on statistics from the World Top Incomes Database. As in the within-U.S. analysis, there is
little correlation between the top 1% income share and intergenerational mobility across countries.
Column 8 shows that results are similar if one uses inequality measures from 2005 instead of 1985.
We conclude that there is a robust negative correlation between inequality within the current
generation of adults and mobility across generations. However, intergenerational mobility is primarily correlated with inequality among the bottom 99% and not the extreme upper tail inequality
of the form that has increased dramatically in recent decades. Interestingly, this pattern parallels
the results we obtained for segregation above: segregation of auence is not significantly correlated
with intergenerational mobility, while segregation of poverty is negatively associated with mobility.

VI.D

School Quality

In the fourth panel of Figure VIII, we study the correlation between mobility and various proxies
for school quality. We first consider two proxies for inputs into school quality: mean public school
expenditures per student and mean class sizes based on data from the National Center for Education
Statistics (NCES) for the 1996-97 school year. We find a positive correlation between public school
expenditures and upward mobility, but the correlation is not as strong or robust as with measures
of inequality or segregation. There is a strong negative correlation between class size and upward
mobility (Columns 1 and 2 of Online Appendix Table VIII) when pooling all CZs. However, there
is no correlation between upward mobility and class size in more urban areas (Columns 3 and 4).
One shortcoming of input-based measures of school quality is that they may capture relatively
47

Because parent and child ranks are measured in the national income distribution, there is no mechanical relationship between the level of inequality within the CZs income distribution and the rank-rank slope.
48
We obtain estimates of the Gini coefficient by country from the OECD Income Distribution Database. We
interpret these estimates as applying to the bottom 99% because surveys typically do not capture the thickness of
the top tail due to top-coding.

38

little of the variation in school quality (Hanushek 2003). To address this problem, we construct
output-based proxies for school quality based on test scores and dropout rates adjusted for dierences in parent income. We obtain data on mean grade 3-8 math and English test scores by CZ from
the Global Report Card. The Global Report Card converts school-district-level scores on statewide
tests to a single national scale by benchmarking statewide test scores to scores on the National
Assessment of Educational Progress (NAEP) tests. We obtain data on high school dropout rates
from the NCES for the 2000-01 school year, restricting the sample to CZs in which at least 75% of
school districts have non-missing data. We regress test scores on mean parent family income (from
1996-2000) in the core sample and compute residuals to obtain an income-adjusted measure of test
score gains. We construct an income-adjusted measure of dropout rates analogously.
The income-adjusted test score and dropout rates are very highly correlated with upward mobility across all specifications, as shown in the fourth panel of Figure VIII. In the baseline specification,
the magnitude of the correlation between both measures and upward mobility is nearly 0.6. These
results are consistent with the hypothesis that the quality of schools as judged by outputs rather
than inputs plays a role in upward mobility. At a minimum, they strengthen the view that
much of the dierence in intergenerational income mobility across areas emerges while children are
relatively young.

VI.E

Social Capital

Several studies have emphasized the importance of social capital the strength of social networks
and engagement in community organizations in local areas for social and economic outcomes
(e.g., Coleman 1988, Borjas 1992, Putnam 1995). We explore the relationship between mobility
and measures of social capital used in prior work in the fifth panel of Figure VIII.
Our primary proxy for social capital is the social capital index constructed by Rupasingha and
Goetz (2008), which we aggregate to the CZ level using population-weighted means. This index is
comprised of voter turnout rates, the fraction of people who return their census forms, and various
measures of participation in community organizations. The correlation between upward mobility
and social capital is 0.641 in our baseline specification, an estimate that is quite robust across
alternative specifications. Interestingly, one of the original measures proposed by Putnam (1995)
the number of bowling alleys in an area has an unweighted correlation of 0.562 with our measures
of absolute upward mobility.
We also consider two other proxies for social capital: the fraction of religious individuals (based

39

on data from the Association of Religion Data Archives) and the rate of violent crime (using data
from the Uniform Crime Report). Religiosity is very strongly positively correlated with upward
mobility, while crime rates are negatively correlated with mobility.

VI.F

Family Structure

Many have argued that family stability plays a key role in childrens outcomes (see e.g., Becker
1991, Murray 1984, Murray 2012). To evaluate this hypothesis, we use three measures of family
structure in the CZ based on data from the 2000 Census: (1) the fraction of children living in
single-parent households, (2) the fraction of adults who are divorced, and (3) the fraction of adults
who are married. All three of these measures are very highly correlated with upward mobility, as
shown in the sixth panel of Figure VIII.
The fraction of children living in single-parent households is the single strongest correlate of
upward income mobility among all the variables we explored, with a raw unweighted correlation of
-0.76 (see Online Appendix Figure XIIa for the corresponding non-parametric binned scatter plot).
One natural explanation for this spatial correlation is an individual-level eect: children raised by a
single parent may have worse outcomes than those raised by two parents (e.g., Thomas and Sawhill
2002, Lamb 2004). To test whether this individual-level eect drives the spatial correlation, we
calculate upward mobility in each CZ based only on the subsample of children whose own parents
are married. The correlation between upward mobility and the fraction of single parents in their
CZ remains at -0.66 even in this subgroup (Online Appendix Figure XIIb). Hence, family structure
correlates with upward mobility not just at the individual level but also at the community level,
perhaps because the stability of the social environment aects childrens outcomes more broadly.
The association between mobility and family structure at the community level echoes our findings
in Section VI.A on the community-level eects of racial shares.

VI.G

Comparison of Alternative Explanations

In Table VI, we assess which of the five factors identified above segregation, inequality, school
quality, social capital, and family structure are the strongest predictors of upward mobility in
multivariable regressions that control for race and other covariates. Based on the analysis above, we
first identify the proxy that has the strongest and most robust univariate correlation with upward
mobility in each category: the fraction of working individuals who commute less than 15 minutes to
work (segregation), the bottom 99% Gini coefficient (inequality), high school dropout rates adjusted

40

for income dierences (school quality), the social capital index, and the fraction of children with
single parents (family structure).49 As in preceding regression specifications, we normalize all the
dependent and independent variables to have a standard deviation of 1 in the estimation sample
for each regression in Table VI.50
We begin in Column 1 with an unweighted OLS regression of absolute upward mobility r25,c
on the five factors, pooling all CZs. All of the factors except the Gini coefficient are significant
predictors of the variation in absolute upward mobility in this specification. Together, the five
factors explain 76% of the variance in upward mobility across areas. Column 2 shows that the
coefficients remain similar when state fixed eects are included. Column 3 shows that the estimates
are roughly similar when restricting the sample to urban areas (CZs that intersect MSAs). Across
all the specifications, the strongest and most robust predictor is the fraction of children with single
parents.
In Column 4, we use relative mobility

as the dependent variable instead of absolute upward

mobility. The fraction of single-parents and commute times are strong predictors of dierences in
relative mobility across areas, but the other factors are not statistically significant. To understand
why this is the case, in Column 5 we replicate Column 4 but exclude the fraction of children with
single parents. In this specification, all four of the remaining factors including the Gini coefficient
are strong predictors of the variation in relative mobility across CZs. Column 6 replicates the
specification in Column 5 using absolute upward mobility as the dependent variable. Once again, all
four factors are strong predictors of upward mobility when the fraction of single parents is excluded.
These results suggest that the fraction of single parents may capture some of the variation in the
other factors, most notably the level of income inequality.
In the last two columns of Table VI, we explore the role of racial demographics vs. the other
explanatory factors. Column 7 shows that when we regress absolute upward mobility on both
the fraction of single-parent families in the CZ and the share of black residents, black shares are
no longer significantly correlated with upward mobility. Column 8 shows that the correlation of
upward mobility with black shares is slightly positive and statistically significant when we include
controls for all five explanatory factors. These results support the view that the strong correlation
49

We obtain similar results if we combine the various proxies into a single index for each factor using weights from
an OLS regression of absolute upward mobility on the proxies within each category.
50
We code the high school dropout rate as 0 for 126 CZs in which dropout rate data are missing for more than
25% of the districts in the CZ and include an indicator for having a missing high school dropout rate. We do the
same for 16 CZs that have missing data on social capital. We normalize these variables to have mean 0 and standard
deviation 1 among the CZs with non-missing data.

41

of upward mobility with race operates through channels beyond the direct eect of race on mobility.
Overall, the results in Table VI indicate that the dierences in upward mobility across areas
are better explained by a combination of the factors identified above rather than any single factor.
However, the regression coefficients should be interpreted with caution for two reasons. First, the
regression may place greater weight on factors that are measured with less error rather than those
that are truly the strongest determinants of mobility. Second, all of the independent variables are
endogenously determined. These limitations make it difficult to identify which of the factors is the
most important determinant of upward mobility.

VII

Conclusion

This paper has used population data to present a new portrait of intergenerational income mobility
in the United States. Intergenerational mobility varies substantially across areas. For example, the
probability that a child reaches the top quintile of the national income distribution starting from
a family in the bottom quintile is 4.4% in Charlotte but 12.9% in San Jose. The spatial variation
in intergenerational mobility is strongly correlated with five factors: (1) residential segregation, (2)
income inequality, (3) school quality, (4) social capital, and (5) family structure.
In this paper, we have presented a cross-sectional snapshot of intergenerational mobility for
a single set of birth cohorts. In a companion paper (Chetty et al. 2014), we study trends in
mobility over time. We find that the level of intergenerational mobility (national rank-rank slope)
has remained stable for the 1971-1993 birth cohorts in the U.S., especially in comparison to the
degree of variation across areas. A natural question given the results of the two papers is whether
the cross-sectional correlations documented here are consistent with the time trends in mobility.
To answer this question, we predict the trend in the rank-rank slope implied by changes in the
five key correlates over time (see Online Appendix I and Appendix Figure XIII). The predicted
changes are quite small because the factors move in opposing directions. For example, the increase
in inequality and single parenthood rates in recent decades predict a small decline in mobility in
recent decades. In contrast, the decline in racial segregation and high school dropout rates predict
an increase in mobility of similar magnitude. Overall, the cross-sectional correlations documented
here are consistent with the lack of a substantial time trend in mobility in recent decades.
The main lesson of our analysis is that intergenerational mobility is a local problem, one that
could potentially be tackled using place-based policies (Kline and Moretti 2014). Going forward,
a key question is why some areas of the U.S. generate higher rates of mobility than others. We
42

hope that future research will be able to shed light on this question by using the mobility statistics
constructed here (available online at the county by birth cohort level) to study the impacts of local
policy changes.

43

ONLINE APPENDICES
A. Data Construction
Core and Extended Samples. We begin with the universe of individuals in the Death Master
(also known as the Data Master-1) file produced by the Social Security Administration. This file
includes information on year of birth and gender for all persons in the United States with a Social
Security Number or Individual Taxpayer Identification Number. We restrict this sample to all
individuals who are current US citizens as of March 2013. The Data Master-1 file does not contain
historical citizenship status, and thus we can only restrict to a sample who are currently US citizens
as of the time at which we access the data. We further restrict to individuals who are alive through
the end of 2012. The resulting dataset contains 47.8 million children across all cohorts 1980-1991
(Appendix Table I). We measure parent and child income, location, college attendance, and all
other variables using data from the IRS Databank, a balanced panel covering all individuals in the
United States who appear on any tax form between 1996-2012.
For each child, we define the parent(s) as the first person(s) who claim the child as a dependent
on a 1040 tax form. If parents are married but filing separately, we assign the child both parents.
To eliminate dependent claiming by siblings or grandparents, in the case of a potential match to
married parents or single mothers, we require the mother to be age 15-40 at the birth of the child.51
In the case of a match to a single father, we require the father to be age 15-40 at the birth of the
child. If no such eligible match occurs in 1996, the first year of our data, we search subsequent
years (through 2011) until a valid match is found.
Once we match a child to parent(s), we hold this definition of parents fixed regardless of subsequent dependent claims or changes in marital status. For example, a child matched to married
parents in 1996 who divorce in 1997 will always be matched to the two original parents. Conversely,
a child matched to a single parent in 1996 that marries in 1997 will be considered matched to a
single parent, though spouse income will be included in our definition of parent income because we
measure parent income at the family level in our baseline analysis.
To reduce the eects of outliers and measurement error in the upper tail of the income distribution, we use data from the IRS Statistics of Income (SOI) manually perfected cross-sectional
files spanning 1996-2011 (see below for details on these files). If an individuals adjusted gross
income exceeds $10 million, we look for the individual in the SOI sample; if present, we use the
SOI measure of adjusted gross income and wage income as reported on a F1040 return. If not, we
replace the adjusted gross income with the total wages reported on the filed F1040 contained in the
databank. Because the IRS Databank includes tax year 2012 whereas the SOI sample does not, we
top code income at $100 million for all individuals in 2012. These adjustments in the upper tail
aect 0.017% of parents in our core sample (or, equivalently, 1.7% of parents in the top 1% of the
income distribution).
For most of our analysis, we measure parent income at the household level. For certain robustness checks, we measure individual parent income as follows. For married parents, we define each
parents individual earnings as the sum of wage earnings from form W-2, unemployment benefits
from form 1099-G, and Social Security and Disability benefits from form SSA-1099 for that individual. Individual earnings excludes capital and other non-labor income. To incorporate these sources
51

Children can be claimed as a dependent only if they are aged less than 19 at the end of the year (less than 24 if
enrolled as a student) or are disabled. A dependent child is a biological child, step child, adopted child, foster child,
brother or sister, or a descendant of one of these (for example, a grandchild or nephew). Children must be claimed by
their custodial parent, i.e. the parent with whom they live for over half the year. Furthermore, the custodial parent
must provide more than 50% of the support to the child. Hence, working children who support themselves for more
than 50% cannot be claimed as dependents. See IRS Publication 501 for further details.

44

of income, we add half of family non-labor income defined as total family income minus total
family earnings reported on form 1040 to each parents individual earnings. We divide non-labor
earnings equally between spouses because we cannot identify which spouse earns non-labor income
from the 1040 tax return. For single parents, individual income is the same as family income.
Statistics of Income Sample. Starting in 1987, the IRS Statistics of Income cross sections
which are stratified random samples of tax returns contain dependent information, allowing us
to link children to parents. We use the 1987-2011 SOI cross-sections to construct a sample of
children born in the 1971-1991 birth cohorts and correct for errors in the upper tail of the income
distribution as described above. For each SOI cross-section from 1987 to 2007, we first identify
all dependent children between the ages of 12 and 16 who are alive at age 30. We then pool all
the SOI cross-sections that give us information for a given birth cohort. For example, the 1971
cohort is represented by children claimed at age 16 in 1987, while the 1991 cohort is comprised by
children claimed at ages 12-16 in 2003-2007. Using the sampling weights for the SOI cross-sections
(see Internal Revenue Service (2013) for details), each cohort-level dataset is representative of the
population of children claimed on tax returns between the ages of 12 and 16 in that birth cohort.
Unlike in the population-based samples, we do not limit the SOI sample to children who are
currently citizens because citizenship data are not fully populated for birth cohorts prior to 1980 and
because we begin from a sample of children claimed by parents rather than the universe of children
who currently appear in the population data (which includes later immigrants). In the years where
the SOI and population-based samples overlap, we obtain very similar estimates in both samples.
The citizenship restriction has a minor impact because the vast majority of children claimed as
dependents between the ages of 12-16 are U.S. citizens as adults. We also do not impose any age
restrictions on the parents in the SOI sample. In the population-based sample, some children are
claimed by dierent adults across years and the age restriction is useful to discriminate between
these potential parents. In the SOI sample, each child can only be linked to the parents who claim
him in the cross-section file, so the age restriction would not play such a role. In practice, this
restriction has little impact, as the age distribution of parents in the SOI sample is very similar to
that in the core sample using the population data.
Children whose parents are sampled in multiple SOI cross-sections appear multiple times in the
SOI sample. There are 228,295 unique children in the SOI sample and 523,700 total observations.
The SOI sample grows from 4,383 unique children in 1971 to 21,231 unique children in 1991 because
we have more cross-sections to link parents to children in more recent cohorts and because the size
of the SOI cross-sections has increased over time (Appendix Table II). To be consistent with the
core sample definition of parent income, we define parent income as the 5-year average of parent
family income from 1996-2000 in the IRS Databank.
We provide additional information on the SOI sample in Chetty et al. (2014). Using sampling
weights, we show that the SOI sample represents roughly 85% of children in each birth cohort (based
on vital statistics counts) from 1971-1979, the cohorts we use to obtain estimates of intergenerational
mobility after age 32 in Figure IIIa. We also show that summary statistics for the SOI sample are
very similar to the core sample for the 1980-82 birth cohorts reported in Appendix Table III of this
paper. Note that Chetty et al. (2014) compute parent income using the income of the parents in
the single year of the parent-child match there, whereas we compute parent income as the five-year
average over 1996-2000 here for consistency with results from the population data. Because we
restrict to parents with positive income, this leads to a small dierence in the SOI sample used
across the two papers. For example, we have 4,383 children in the 1971 cohort, compared with
4,331 children in the sample used by Chetty et al. (2014).
Assignment of Children to Commuting Zones. Children are assigned ZIP codes of residence
based on their parents ZIP code on the form 1040 in which the parent is matched to the child. In
45

the few cases where a parent files a F1040 claiming the child but does not report a valid ZIP code,
we search information returns (such as W-2 and 1099-G forms) for a valid ZIP code in that year.
We map these ZIP codes to counties based on the 1999 Census crosswalk between ZIP codes
and counties. We then aggregate counties into Commuting Zones using David Dorns county-to-CZ
crosswalk (download file E6). The counties in the U.S. Census Bureau crosswalk and in Dorns
crosswalk are not identical because they correspond to county definitions at dierent points in
time; in particular the U.S. Census Bureau crosswalk includes changes between 1990 and 1999. We
make manual adjustments for changes that aected 200 or more people. Using this procedure, we
identify the CZ of 38,839 ZIP codes. To track individuals residing in ZIP codes that have been
created since 1999, we add an additional 477 ZIP codes not valid in 1999 but appearing in the more
up-to-date 2011 HUD-USPS crosswalk. For example, in 2007, Manhattans ZIP code 10021 was
split into three separate ZIP codes, resulting in the creation of new ZIP codes 10065 and 10075.
Of 9,864,965 children with non-missing ZIP codes in our core sample, 9,778,071 were assigned a
childhood CZ using ZIP codes that existed in 1999; an additional 2,718 were assigned a CZ based
on a ZIP code that existed in 2011 but not in 1999. For simplicity, we use the same crosswalk for all
years of matching ZIP codes to CZs. We have verified that using year-specific crosswalks from ZIP
codes to counties has a negligible eect on CZ assignments. All of the crosswalks we constructed
are available on our project website.
Some of our specifications require tracking childrens locations into adulthood using the ZIP
code where they live as adults when we measure their income (e.g., for cost-of-living adjustments).
We define a childs adult location using the latest non-missing ZIP code. We first search for a ZIP
code in their 1040 form in 2012, followed by their information returns in 2012. We then repeat
this procedure for 2011 if we do not find a zipcode in 2012. This yields 9,834,975 non-missing child
ZIP codes in adulthood. Of these, we match 9,537,283 to a CZ from a ZIP code using the 1999
crosswalk (i.e. this ZIP code was in use in 1999) and an additional 198,317 using the later crosswalk
because the ZIP code was created after 1999.
Construction of ZIP-Level Racial Shares. To construct Figure IXa and IXb, which condition
on racial shares at the ZIP level, we need data on racial shares by ZIP code. The 2000 Census
includes summary tables by ZIP code tabulation areas (ZCTAs) instead of ZIP code. ZCTAs are
a U.S. Census Bureau geographical unit that in most cases correspond closely to ZIP codes, but
sometimes do not. We use a ZCTA to ZIP Crosswalk from the John Snow Institute to assign each
ZIP code a racial share based on Census 2000 ZCTA-level data from table P008.
CZ-Level Price Index. To measure real incomes, we first construct a CZ-level ACCRA price
index using the 2010 ACCRA composite cost of living index (table 728) for urbanized areas
in 2010, which we crosswalk to CZs as follows. First, we use the 2012Q1-2013Q1 correspondence
(downloaded on 11/21/2013) to assign 298 out of the 325 urbanized areas to MSAs. Each county in
an MSA was assigned the same value of the index. We then merge counties to CZs and calculate an
unweighted mean of the index among non-missing values within the CZ. Some CZs had no counties
within an MSA and were therefore assigned a missing value of the ACCRA index.
To construct a price index that covers all CZs, we regress the CZ-level ACCRA index on a
quadratic in log population density (from the 2000 Census), a quadratic in log median housing
values, the latitude and longitude of the CZ centroid, and state fixed eects. Housing values are
the population-weighted mean of tract median housing values for owner-occupied units in the 1990
Census short form. Latitude and longitude are the mean latitude and longitude across counties
within each CZ, obtained from the Census 2000 Gazetteer county-level data. The predicted values
from this regression constitute our final price index that covers all CZs.

B. Comparison to Survey Datasets

46

In Appendix Table IV, we compare selected moments of income distributions and other variables
in the tax data to data from two nationally representative surveys that have been used in prior
work on the income distribution: the 2011-12 CPS and the 2011-12 ACS. We restrict the ACS and
CPS samples to citizens in the same birth cohorts as our core sample (1980-82). To the extent
possible, we define all income variables to match the concepts in the tax data.
To assess whether our method of linking children to parents based on dependent claiming creates
selection bias, we compute statistics in the tax data both on the full sample of all children in the
1980-82 birth cohorts who are current U.S. citizens and the core sample of children linked to parents.
Because most children are linked to parents, the dierences between these two samples are small,
though children who lack valid parent matches have slightly lower earnings on average.
Overall, the tax data are very similar to the CPS and ACS. The sum of the sampling weights
in our survey-based samples provide estimates of the size of the target population being sampled.
This population is very similar in the tax data and the two surveys. The mean and median earnings
levels are very similar, as are the fractions with non-zero income. Perhaps more surprisingly, the
interquartile range (P75-P25) of earnings is also similar across the three data sources. If survey
data were reported with classical measurement error, we would expect the interquartile range to be
larger in survey sources. However, survey reports of income exhibit mean reverting measurement
error which has the eect of reducing variability (Bound and Krueger 1991, Bound, Brown and
Mathiowetz 2001). Moreover, survey non-response tends to follow a U-shaped pattern (Kline and
Santos 2013), with very high and low earning individuals being least likely to provide earnings
responses, which can further reduce variability. The quantiles of family income also line up well
across the three data sources, with the tax-based moments strongly resembling those from the ACS,
perhaps because the ACS has a higher response rate for earnings than the CPS.

C. Comparison to Mitnik et al. (2014)

Mitnik et al. (2014) propose a new measure of the intergenerational elasticity that is more
robust to the treatment of small incomes. In this appendix, we compare the traditional definition
of the IGE (Solon 1999, Black and Devereux 2011) to the new measure proposed by Mitnik et al.
We first show that the traditional IGE can be interpreted as the average elasticity of child income
with respect to parent income in a model with heterogeneous elasticities, while Mitnik et al.s new
measure is a dollar-weighted (i.e., child-income-weighted) average of the same elasticity. We then
compare estimates of the dollar-weighted IGE to estimates of the traditional IGE in our data and
to the estimates of Mitnik et al.
Setup. Let Yi denote the level of child income and Xi denote the level of parent income. Let
FY |X=x (y) denote the conditional distribution of Y given X, which we assume is dierentiable with
respect to x at all (y, x) > 0. Define the conditional quantile function (CQF) as the inverse of the
CDF:
1
q(x, ) = FY |X=x
( )

for 2 [0, 1].52 The CQF gives the quantiles of the conditional distribution of Yi given Xi ; for
example, q (x, .5) is the median of Yi when Xi = x.
We can use the CQF to represent Yi as:
Yi = q (Xi , Ui ) ,
where Ui |Xi Uniform (0, 1). Hence, the conditional mean of child income given parent income
52

At mass points, we define q(x, ) inf y : FY |X=x (y)

47

can be written as a function of the CQF:

E [Yi |Xi = x] = E [q (Xi , Ui ) |Xi = x] =

q (x, ) d.

Define the elasticity of a given quantile of the childs income distribution with respect to parent
income around a parent income level x as
(x, )

dq (x, ) x
qx (x, )x
=
.
dx q (x, )
q(x, )

In general, the elasticity will vary across quantiles .53 We now show that traditional estimates of
the intergenerational elasticity (e.g., Solon 1992) and the new estimator proposed by Mitnik et al.
(2014) can be interpreted as dierent averages of the elasticities (x, ).
Traditional IGE. The intergenerational elasticity at a given parent income level x, which we
denote byIGE(x), is defined as the impact of an increase in log parent income (starting from x)
on expected log child income:

IGE(x) =

dE [logYi |Xi = x]
dlogx

=
=

d
dlogx
1

logq (x, ) d

d
logq (x, ) d
dlogx

(x, ) d

= (x)
where (x) E [ (Xi , Ui ) |Xi = x]. If we interpret the IGE as the average of IGE(x) across levels
of parent income x, we obtain
IGE = E [ (x)] =

1
1

(x, ) d dFX (x) ,

where FX (.) is the marginal distribution of Xi . Hence, the traditional IGE can be interpreted as
the average elasticity of child income with respect to parent income across quantiles and parent
income levels.
Mitnik et al. IGE. Mitnik et al. (2014) propose an alternative approach to estimating the IGE
that switches the order of the log and the expectation relative to the traditional approach. They
define the IGE as the impact of an increase in log parent income (starting from x) on the log of
expected child income:
dlogE [Yi |Xi = x]
IGEW (x)
.
dlogx
53

Naturally, this elasticity is only defined for quantiles where q(x, ) > 0; the standard empirical practice in the
prior literature (e.g., Solon 1992) has been to exclude children with zero income for this reason.

48

To see how their estimand relates to the traditional IGE, observe that
1
d
IGEW (x) =
log
q (x, ) d
dlogx
0
1
qx (x, ) xd
= 0 1
0 q (x, ) d
1
q (x, ) (x, ) d
= 0 1
0 q (x, ) d
= E [! (Xi , Ui ) (Xi , Ui ) |Xi = x]
q(Xi ,Ui )
where ! (Xi , Ui ) E[q(X
is a set of quantile specific weights which sum to one for each
i ,Ui )|Xi ]
value of Xi . Averaging IGEW (x) across levels of parent income x, Mitnik et al.s statistic can be
written as IGEW = E [IGEW (x)]. The parameter IGEW (x) is a weighted average of the elasticity
(x, ) across quantiles , with weights that are an increasing function of the childs income. Higher
quantiles get larger weights, in proportion to their dollar value; the weights approach zero as the
childs income approaches 0. In this sense, the IGEW statistic defined by Mitnik et al. is a
dollar-weighted mean of the IGE across quantiles.
The traditional IGE and the dollar-weighted IGEW proposed by Mitnik et al. are two dierent
parameters. The correct parameter depends on the question one seeks to answer. If ones goal
is to estimate IGEW , then the traditional IGE estimate will in general yield a biased estimate of
IGEW . Conversely, if ones target is to estimate the traditional IGE (e.g., for comparison to prior
estimates in the literature), then IGEW will in general be biased.
As Mitnik et al. note, one statistical benefit of the dollar-weighted IGE is that it is not sensitive
small changes in incomes at the bottom of the distribution, such as recoding zero income as $1.
Intuitively, dollar-weighted elasticities are not sensitive to the impacts of parent income on childrens
income at the bottom of the distribution. In contrast, person-weighted estimates are very sensitive
to changes in incomes at the bottom of the distribution, because such changes can aect elasticities
at the lowest quantiles substantially. The traditional IGE is unstable because the elasticity of child
income with respect to parent income is ill-defined at quantiles with zero income.
Empirical Estimates. In large samples, we can estimate E [Yi |Xi = x] non-parametrically as
shown in Figure Ia. It is therefore straightforward to estimate IGEW simply by regressing the
non-parametric estimates of logE [Yi |Xi = x] on logx.54 The series in circles in Appendix Figure Ia
plots logE [Yi |Xi = x] vs. logx simply by taking logs of the data points shown in Figure Ia.55 As
a reference, we also replicate the non-parametric plot of E [logYi |Xi = x] vs. logx from Figure Ib
(excluding children with zero income) in the series in triangles.
i |Xi =x]
The two series are very similar, implying that nonparametric estimates of dlogE[Y
and
dlogx
dE[logYi |Xi =x]
dlogx

are very similar for most values of x. The dollar-weighted IGE estimate (including
children with zero income) is IGEW = 0.335, virtually identical to the traditional IGE estimate
of IGE = 0.344 obtained when we exclude children with zero income. Between the 10th and 90
percentiles, the dollar-weighted IGE is 0.414, while the traditional IGE is 0.452.
In Appendix Figure Ib, we report dollar-weighted IGE estimates by the age of the child to assess
the extent of lifecycle bias in the dollar-weighted IGE estimates. We find that the dollar-weighted
IGE also stabilizes around age 30: the estimated IGEW is 2.1% higher at age 32 than age 31 (0.343
54

Mitnik et al. use a Poisson pseudo-maximum-likelihood (PPML) estimator to estimate IGEW in survey data,
which approximates logE [Yi |Xi = x] in large samples.
55
Unlike in Figure Ia, we include the top bin (the top 1% of parents) in this figure.

49

vs. 0.336).
Mitnik et al. (2014) obtain larger estimates of the dollar-weighted IGE (around 0.5) in their
SOI sample. Although both studies use similar data from tax records, there are several small
methodological dierences between Mitnik et al.s approach and our approach. A useful direction
for future work would be to investigate which of these dierences in responsible for the dierences
in the IGE estimates.

D. Comparison to Clark (2014)

Clark (2014) presents estimates of mobility across generations using surname averages of income,
representation in elite professions, and other related outcomes. He obtains implied IGE estimates
around 0.8, well above the estimates of intergenerational persistence obtained in our analysis and
the prior literature (e.g., Solon 1999). In this appendix, we first show that in our data, estimates of
mobility based on surname means are generally quite similar to our baseline individual-level estimates. We then present a simple hypothesis that may explain why Clarks focus on rare surnames
leads to a much higher estimated IGE.
Surname-Based Estimates. In Chetty et al. (2014, Appendix B), we construct estimates of
intergenerational mobility across surnames as follows. We begin with all the children in our core
sample and restrict attention to those whose surnames in 2012 are the same as their parents
surnames.56 We then obtain a de-identified table of surname-level means of percentile ranks (using
the baseline income definition) for both parents and children. Finally, we regress the surname-level
mean ranks for children on surname-level mean ranks for parents (as suggested by Clark 2014,
Appendix 2), weighting by the number of individuals with each surname, to obtain a surname-level
rank-rank slope. We construct surname-level estimates of the log-log IGE analogously, computing
surname level means of log income (excluding zeroes) for children and parents.
Appendix Table V reports the results of this analysis. Each row of the table shows the estimates
for dierent subsets of names. The first row considers all names. Rows 2-4 restrict to rare surnames,
i.e. names held by fewer that 25, 50, or 100 children. Rows 5-8 conversely limit the sample to
common surnames, i.e. names held by more than 100, 1000, 10000, or 20000 people. In each row,
we report the number of children in the sample (Column 1), the number of unique surnames in the
sample (Column 2), surname-based estimates of the rank-rank slope (Column 3), individual-level
estimates of the rank-rank slope (Column 4), surname-based estimates of the log-log IGE (Column
5), and individual-level estimates of the log-log IGE (Column 6).
Appendix Table V shows that surname-based averages of income generally do not imply much
greater intergenerational persistence than individual-level regressions unless one uses specific subsets of names for the analysis. For example, when including all names (row 1), the individual-level
rank-rank slope is 0.30, compared with a surname-level rank-rank slope of 0.39. If we restrict to
the rarest names (shared by fewer than 25 people), the individual-level rank-rank slope is 0.27,
compared with a surname-based rank-rank slope of 0.30. The IGE estimates at the individual level
are also slightly smaller than those based on surname averages.
The only case in which the surname averages yield much larger implied IGEs and rank-rank
slopes is in the last row of the table, where we restrict to the 7 most common names in the U.S.
population. Here, the surname-based IGE is 0.81, compared with an individual-level IGE of 0.36.
This implies that the rate of convergence in income across generations across these broad name
groups which likely capture broad dierences in ethnicities or race is much smaller than the
56

As Clark (2014, Appendix 2) notes, surname-based analyses will yield attenuated estimates of the IGE if they
include parents and children who do not actually have the same surname. Consistent with this hypothesis, we find
smaller estimates of rank-rank correlations and IGEs when we use the full core sample, without limiting to children
who have the same surname as their parents.

50

rate of convergence within the groups, a point we return to below.

Interpretation of Clark (2014) Estimates. Why does Clark obtain much larger estimates of
intergenerational persistence than we find in Appendix Table V? There are many methodological
dierences between Clarks analysis and our approach above. For example, Clark analyzes multiple
generations and uses other proxies for status (such as professional occupation) rather than income.
While a comprehensive analysis of the source of the dierence is outside the scope of this study,
we believe that one key dierence is Clarks focus on distinctive surnames. For instance, one
comparison Clark (2014, page 60, Figure 3.10) gives is of the surname Katz vs. Washington.
As he notes, Katz is a common Jewish surname, while Washington is a common black surname. The
comparison of intergenerational convergence in income between these two names is thus analogous
to using an indicator for race as an instrument in a traditional individual-level IGE regression.57
As is well known from prior work, using race to instrument for income yields much larger IGE
estimates, presumably because race has direct eects on childrens income independent of its impact
on parent income, as shown e.g., by Borjas (1992). If one uses an indicator for being black as an
instrument, the IGE estimate is equivalent to the proportional reduction in the black-white income
gap across generations. In 1980, blacks median earnings were 78.8% that of whites on average
(Bureau of Labor Statistics 2011, Table 14, page 41). In 2010, blacks median earnings were 79.9%
that of whites. Hence, the implied between-group IGE is 78.8/79.9 = 0.986, consistent with Clarks
larger estimates. Importantly, even though there is very little convergence across racial groups
during this time period, there is considerable social mobility within racial groups. This is why our
estimates of the IGE based on individual-level data (or pooling all surnames) over the same period
are much lower.
In sum, we believe that Clarks approach eectively identifies a parameter analogous to the
degree of convergence in income across generations between racial or ethnic groups rather than
across individuals. This is an interesting parameter, but one that diers from standard studies
of intergenerational mobility that seek to measure the extent to which an individuals status is
determined by his parents idiosyncratic circumstances.58 A useful direction for future research
would be to investigate why the rate of income convergence across certain ethnic groups is small
even though intergenerational mobility within these groups is much higher.

E. Comparison to Mazumder (2005)

Mazumder (2005) reports that IGEs estimated using even 5-year averages of parent earnings
exhibit substantial attenuation bias because of long-lasting transitory shocks to income. This
appendix provides further details on why we find much less attenuation bias than Mazumder.
Mazumder (2005, Table 4, row 1, page 246) obtains IGE estimates as high as 0.6 when using
15-year averages of parent income matched SIPP-SSA administrative data, 54% larger than his 4year pooled estimate of 0.388. In contrast, we find little dierence between IGEs based on five-year
vs. fifteen-year averages of parent income both using our preferred rank-rank specification (Figure
IIIb) and using a log-log IGE specification similar to that estimated by Mazumder. For example,
we obtain a log-log IGE of 0.366 using a 15-year average of parent family income, 6% larger than
the estimate using a 5 year average reported in row 1 of Table I.59
57

Clark reports many other surname comparisons that do not map as directly to racial or ethnic groups. However,
it is possible that similar group-level persistence eects are picked up by other unique surname contrasts as well.
58
This interpretation diers from that put forth by Clark, who argues that individual-level estimates do not capture
latent status as well as surname-based averages. Our analysis of surname means suggests that the dierences in
the results are driven by dierences in the rate of income convergence within vs. between ethnic groups rather than
a downward bias in measures of intergenerational persistence based on individual data.
59
When computing long time averages, we measure earnings of parents at older ages than Mazumder (2005) because

51

We believe our results dier from Mazumders findings because we directly observe income for
all individuals in our data, whereas Mazumder imputes parent income based on race and education
for up to 60% of the observations in his sample to account for top-coding in social security records.60
These imputations are analogous to instrumenting for parent income using race and education, an
approach known to yield higher estimates of the IGE, perhaps because parents education directly
aects childrens earnings (Solon 1992). Because the SSA earnings limit is lower in the early years
of his sample, Mazumder imputes income for a larger fraction of observations when he averages
parent income over more years (Mazumder 2005, Figure 3). As a result, Mazumders estimates
eectively converge toward IV estimates as he uses more years to calculate mean parent income,
explaining why his estimates rise so sharply with the number of years used to measure parent
income. Consistent with this explanation, when he drops imputed observations, his IGE estimates
increase much less with the number of years used to measure parent income (Mazumder 2005, Table
6).
Mazumder also reports simulations of earnings processes showing that attenuation bias in the
IGE should be substantial even when using five-year averages. However, he calibrates the parameters of the earnings process in his simulation based on estimates from survey data and his SIPP-SSA
sample, both of which may have more noise than the population data we use here, which cover all
workers and are not top-coded. If one replicates Mazumders simulations using a smaller variance
share for transitory shocks, one obtains results similar to ours in Figure IIIb, with little attenuation
bias in estimates based on five-year averages.
To be clear, Mazumder acknowledges the potential bias due to imputation, as he recommends
in his conclusion that future research should attempt to verify the results here using long-term
measures of permanent earnings from other sources that do not require the kind of imputations
that were necessary in this study. We simply follows this recommendation.

F. Robustness of Spatial Patterns

In Appendix Table VII, we assess the robustness of the spatial patterns in mobility documented
in Section V along four dimensions: (1) changes in sample definitions, (2) changes in income
measures, (3) adjustments for dierences in the cost-of-living and growth rates across areas, and
(4) the use of alternative statistics to measure relative and upward mobility. The first number
in each cell of this table reports the correlation across CZs of a baseline mobility measure (using
child family income rank and parent family income rank in the core sample) with an alternative
mobility measure described in each row. The second number in each cell reports the ratio of the
standard deviation of the alternative measure to the baseline measure. Note that we do not report
the ratio of standard deviations for statistics that are measured in dierent units relative to the
corresponding baseline measure.
Column 1 reports the unweighted correlation (and SD ratio) across CZs between our baseline
measure of absolute upward mobility (
r25,c ) and the corresponding alternative measure of r25,c .
Column 2 replicates Column 1 for relative mobility ( c ). Columns 3 and 4 replicate Columns 1 and
2 weighting CZs by their population in the 2000 Census.
Sample Definitions. In the first section of Appendix Table VII, we assess the robustness of the
of the structure of our data. However, Appendix Figure IIb shows that our estimates of mobility are not sensitive to
varying the age in which parent income is measured over the range observed in our dataset. Hence, the dierences
between the findings of the two papers cannot be explained by dierences in the age at which parent income is
measured.
60
There are also other dierences in Mazumders specification, such as the imputation of income for children whose
earnings are not covered by SSA. However, it is less obvious why these dierences would produce sharp changes in
the estimated IGE when using longer time averages of parent income.

52

spatial patterns to changes in the sample definition, as we did at the national level in Table I. Rows
1 and 2 restrict the sample to male and female children, respectively. Rows 3 and 4 consider the
subsamples of married parents and single parents. The correlations of both absolute and relative
mobility in these subsamples with the corresponding baseline measures is typically above 0.9.
In row 5, we replicate the baseline specifications using the 1983-85 birth cohorts (whose incomes
are measured at age 27 on average in 2011-12). In row 6, we consider the 1986-88 birth cohorts
instead. The intergenerational mobility estimates across CZs for these later birth cohorts are
very highly correlated with the baseline estimates. This result has three implications. First, it
demonstrates that the reliability of CZ-level estimates is quite high across cohorts; in particular,
sampling error or cohort-specific shocks do not lead to much fluctuation in the CZ-level estimates.
Second, because the later cohorts are linked to parents at earlier ages (as early as age 8), we
conclude that the spatial patterns in intergenerational mobility are not sensitive to the precise age
at which we link children to parents or measure their geographical location. Finally, because the
earnings of later cohorts are measured at earlier ages, we conclude that one can detect the spatial
dierences in mobility even when measuring earnings quite early in childrens careers.
In row 7, we restrict the sample based on the age of parents at the birth of the child. We limit
the sample to children whose mothers are between the ages of 24-28 and fathers are between 26-30
(a five year window around the median age of birth). The intergenerational mobility estimates in
this subsample are very highly correlated with the baseline estimates, indicating that the cross-area
dierences in income mobility are not biased by dierences in the age of child birth for low income
individuals.
In row 8, we assess the extent to which the variation in intergenerational mobility comes from
children who succeed and move out of the CZ as adults vs. children who stay within the CZ. To
do so, we restrict the sample to the 62% of children who live in the same CZ in 2012 as where
they grew up. Despite the fact that this sample is endogenously selected on an ex-post outcome,
the mobility estimates remain very highly correlated with those in the full sample. Apparently,
areas such as Salt Lake City that generate high levels of upward income mobility do so not just
by sending successful children to other CZs as adults but also by helping children move up in the
income distribution within the area.
In row 9, we restrict the sample to the 88% of children in the core sample who are not claimed
as dependents by other individuals in subsequent years after they are linked to the parents we
identify. We obtain very similar estimates for this unique parent subsample, indicating that the
spatial pattern of our mobility estimates is not distorted by measurement error in linking children
to their parents.
Income Definitions. In the second section of Appendix Table VII, we evaluate the sensitivity of
the spatial patterns to alternative definitions of income. The definitions we consider match those
in the robustness analysis in Table I; see Section IV.B for details on these definitions. In row 10 of
Appendix Table VII, we define parent income as the income of the higher earner rather than total
family income to evaluate potential biases from dierences in parent marital status across areas. In
row 11, we measure the childs income using individual income instead of family income to assess the
eects of dierences in the childs marital status. In row 12, we use the childs individual earnings
(excluding capital and other non-labor income). In row 13, we replicate the specification in row
11 for male children, using individual income for the child and family income for the parent. Row
14 replicates row 13, but defines parent income as the income of the higher earner instead. In row
15, we define parent income using data from 1999-2003 (when we have data from W-2s) instead
of 1996-2000. All of these definitions produce very similar spatial patterns in intergenerational
mobility: correlations with the baseline measures exceed 0.9 in most cases.
Adjustments for Cost-of-Living and Growth Rates. The third section of Appendix Table VII
53

considers a set of other factors that could bias comparisons of intergenerational mobility across
areas. One natural concern is that our estimates of upward mobility may be aected by dierences
in prices across areas. To evaluate the importance of dierences in cost of living, we construct a
CZ-level price index using the American Chamber of Commerce Research Association (ACCRA)
price index for urban areas combined with information on housing values, population density, and
CZ location (see Appendix A for details). We then divide parents income by the price index for
the CZ where their child grew up and the childs income by the price index for the CZ where he
lives as an adult (in 2012) to obtain real income measures.
Row 16 of Appendix Table VII shows that the measures of intergenerational mobility based on
real incomes are very highly correlated with our baseline measures (see also Appendix Figure VIa).
The reason that cost-of-living adjustments have little eect is that prices aect both the parent and
the child. Intuitively, in high-priced areas such as New York City, adjusting for prices reduces the
childs absolute rank in the national real income distribution. But adjusting for prices also lowers
the real income rank of parents living in New York City. As a result, the degree of upward mobility
i.e., the dierence between the childs rank and the parents rank is essentially unaected by
adjusting for local prices.
The preceding logic assumes that children always live in the same cities as their parents. In
practice, some children move to areas with higher prices (e.g. from rural Iowa to New York City).
Our measures of upward mobility are aected by the cost of living adjustment in such cases, but
they are not sufficiently frequent to have a large impact on our estimates. The correlation between
the cost of living in the childs CZ at age 30 and the parents CZ is 0.77, and the correlation between
a childs nominal percentile rank and the local price index is only 0.10. As a result, cost of living
adjustments end up having a minor impact on the dierence between child and parent income and
thus have little eect on our mobility statistics.
Next, we assess the extent to which economic growth is responsible for the spatial variation
in upward mobility. In row 17, we define parent income as mean family income in 2011-12, the
same years in which we measure child income. Insofar as local economic growth raises the incomes
of both parents and children, this measure nets out the eects of growth on mobility. Both the
upward and relative mobility measures remain very highly correlated with the baseline measures,
suggesting that dierences in local economic growth drive relatively little of the spatial variation
in mobility.
As an alternative approach to accounting for growth shocks, we regress our measures of mobility on the CZ-level growth rate from 2000-2010 and calculate residuals.61 Row 18 of Appendix
Table VII shows that the correlation of the growth-adjusted relative mobility measures with the
baseline measures exceeds 0.9; the correlations for absolute mobility exceed 0.8. Note that these
growth-adjusted measures over-control for exogenous growth shocks insofar as growth is partly a
consequence of factors that generate upward income mobility in an area. Hence, the finding that
even controlling for growth rates directly does not significantly change the spatial pattern of intergenerational mobility supports the view that most of the variation in mobility across areas is not
due to exogenous growth shocks in the 2000s.62
61

We measure income in 2000 using the Census and in 2008 using the 5-year American Community Survey, averaged
over 2006-2010. We calculate household income per working age adult as aggregate income in a CZ divided by the
number of individuals aged 16-64 in that CZ. Annualized income growth is calculated as the annual growth rate
implied by the change in income over the 8 year period; we use 8 years because 2008 is the midpoint of 2006-2010.
62
The fact that college and teenage birth gradients are similar to income mobility gradients provides further evidence
that growth shocks in the 2000s do not generate the dierences in mobility across areas, as college and teenage birth
are measured around 2000. These results also show that the spatial patterns are unlikely to be driven by dierences
in reporting of taxable income.

54

Alternative Statistics for Mobility. One potential concern with our approach is that using
national ranks may misrepresent the degree of relative mobility within the local income distribution,
which may better reflect a childs opportunities. To address this concern, in row 19 of Appendix
Table VII, we measure relative mobility using local ranks. We rank parents relative to other
parents living in the same CZ and children relative to other children who grew up in the same
CZ (no matter where they live as adults). We define relative mobility as the slope of the local
rank-rank relationship.63 Relative mobility based on local ranks is very highly correlated with
relative mobility based on national ranks. This is because local ranks are approximately a linear
transformation of national ranks.
Finally, we consider two alternative measures of absolute upward mobility. In row 20, we
measure absolute upward mobility based on the probability that the child rises from the bottom
quintile of parent income to the top quintile of child income, as in Column 5 of Table III. In row 21,
we measure absolute upward mobility as the probability that a child has family income above the
poverty line conditional on having parents at the 25th percentile. To construct this statistic, we
first regress an indicator for having family income above the federal poverty line in 2012 on parent
rank in the national income distribution in each CZ.64 We then calculate the predicted fraction of
children above the poverty line for parents at the 25th percentile based on the slope and intercept
in each CZ. The spatial patterns in both of these measures which are also shown in the maps
in Appendix Figure VI are very similar to those in our mean-rank based measure of upward
mobility, with correlations across CZs above 0.9 in both cases.

G. Construction of CZ-Level Covariates

This appendix provides definitions and sources for the CZ-level covariates used in Section VO.
Online Data Table IX contains detailed descriptions of each covariate and briefly describes the
source of data for each variable. Here, we provide additional details on each data source along with
links to original sources. As a reference, we provide Stata code on our website that constructs the
final CZ-level covariates (data available in Online Data Table VIII) from the raw data downloaded
from the links below.
Our source data are primarily at the ZIP code and county level. We map ZIP codes and
counties to CZs using the procedure described in Appendix A. We compute CZ-level means of the
ZIP- and county-level data using population-weighted averages, with population counts from the
2000 Census.
Racial Demographics. Racial shares are calculated from the 2000 census short form (SF1) table
P008. Note that all Census data can be obtained by searching for the relevant census table on the
U.S. Census Bureaus American FactFinder. The black share is defined as the number of people
in a CZ who are black alone divided by the CZ population; the white share is calculated similarly.
For the Hispanic share, the numerator is the number of people of any race who are Hispanic. We
also calculate a residual category where the numerator is the number of people that are neither
black alone nor white alone nor Hispanic.
Segregation. We measure racial and income segregation using Theil indices as described in
the text.65 We compute the racial segregation index using the census tract level data on racial
63

We cannot study absolute mobility with local ranks because both child and parent ranks have a mean of 50 by
definition: if one child moves up in the local distribution, another must move down.
64
We define household size as the maximum household size in 2010-11, where household size is defined as 1 plus
an indicator for being married plus the number of dependents claimed. The poverty line threshold is defined as
$11, 170+(household size - 1)$3, 960.
65
As Iceland (2004) argues, the Theil index is an attractive measure conceptually because it captures segregation
across multiple racial groups. However, we obtain similar results using alternative two-group measures of black-white

55

shares from table P008 from the 2000 Census.66 For segregation of auence and poverty, we use
the sample data from the 2000 census long form (SF3) on the income distribution of households
in 1999 by census tract contained in table P052. Our formulas for the three income segregation
measures are taken directly from Reardon (2011). We compute H(pk ) for each of the 16 income
groups given in table P052. We then estimate H(p25 ) and H(p75 ) in each CZ using the 4th order
polynomial version of the weighted linear regression in equation 12 on page 23 of Reardon (2011).
The overall segregation of income index is Reardons rank-order index, which we compute from
equation 13, where the vector is given in Appendix A4 of Reardon (2011).
To compute the commute time variable, we divide the number of workers that commute for less
than 15 minutes by the total number of workers. The sample for both of these counts is restricted
to workers that are at least 16 years old and do not work from home. Travel time data is from the
2000 census table P031.
Income Distributions. We compute mean income per working age adult by dividing aggregate
household income in a CZ by the total number of people aged 16-64 in that CZ. These data come
from the 2000 census table P054 and P008. The Gini coefficient, fraction middle class, and top 1%
income share are computed using our sample of parents and the family income definitions used for
the main analysis in this paper, but with family income top coded at $100 million in all years.
K-12 Education. We use the National Center for Education Statistics Common Core of Data
data for public schools for several of our K-12 covariates. School expenditures per student is taken
from school-district data for the 1996-1997 fiscal year. We drop 8 CZs that are in the top 1% of the
distribution of expenditures per student to reduce the influence of outliers. While we would ideally
measure school spending in the 1980s and early 1990s, when the students in our core sample were
in school, such data are not readily available for earlier years. However, the correlation in school
spending per capita across states in 1982 and 1992 is 0.86, suggesting that using earlier data would
not substantially aect our findings.
We use school-level data on student-teacher ratios for the 1996-1997 school year. We drop
the top 0.1% of observations, which have student-teacher ratios that exceed 100. We also drop
approximately 10% of schools whose student-teacher ratios are recorded as being 0.
High school dropout rates are obtained from school-district data for the 2000-2001 school year.
We code the dropout rate as missing in CZs in which more than 25% of school districts have missing
data on dropout rates. We construct an income-adjusted measure of dropout rates using residuals
from a CZ-level regression of the dropout rate on mean parent family income (from 1996-2000) in
the core sample.
We obtain a standardized measure of grade 3-8 test scores from the National Math Percentile
and National Reading Percentile series in the Global Report Card. We calculate the studentweighted mean of the math and reading rankings over 2004, 2005, and 2007 in each CZ to arrive
at our measure of mean test scores. We then construct a measure of income-adjusted test scores
using the residual from a CZ-level regression of mean test scores on mean parent family income
(from 1996-2000) in the core sample.
segregation such as isolation indices or dissimilarity indices because alternative measures of segregation are highly
correlated at the level of metro areas (Cutler, Glaeser and Vigdor 1999). The segregation patterns are sufficiently
stark that one can directly see the dierences in segregation between the least and most upwardly mobile cities using
the color-coded dot maps produced by Cable (2013) using Census data. For instance, compare Atlanta one of the
most segregated cities and one of the lowest-mobility cities in our data to Sacramento one of the most integrated
and highest-mobility cities.
66
We also replicated the analysis using measures of segregation from the 1990 Census and find very similar results.
For example, the correlation between upward mobility and the Theil racial segregation index measured using the
1990 Census is -0.357, compared with -0.361 when measured using the 2000 Census. The correlation between upward
mobility and income segregation is -0.393 using both the 1990 and 2000 Census.

56

We construct enrollment-weighted means at the ZIP code level of all the school and school
district level variables using the school and district ZIP codes provided in each of the data sources.
We then take enrollment-weighted means across ZIP codes to construct CZ-level estimates using
the ZIP to CZ crosswalk discussed in Appendix A.
Social Capital. For social capital, we use the 1990 county-level social capital index from Rupasingha and Goetz (2008). For religious affiliation, we use data on the self-reported number of
religious adherents from the Association of Religion Data Archives at Pennsylvania State University. Data on crime rates are from the FBIs Uniform Crime Reporting program. We downloaded
county-level data from the ICPSR and use the number of arrests for serious (part 1 index) violent
crimes divided by the total covered population.
Family Structure. We define the share of single mothers in each county as the number of
households with female heads (and no husband present) with own children present divided by the
total number of households with own children present. These data from from the 2000 census long
form (SF3) in table P018. We calculate the fraction married and fraction divorced in each county
using the number of people that are married or divorced (in the sample of people that are 15 years
and older) using data from the 2000 census in table P018.
Taxes and Government Expenditures. We estimate local tax rates using data on tax revenue
by county from the U.S. Census Bureaus 1992 Census of Government county-level summaries,
which we downloaded from the ICPSR. In particular, Part 2 of the ICPSR download contains
the county-level summaries. We define the tax rate in each CZ as follows. First, we calculate
county tax revenue divided by the county population estimate for each county in the CZ. We
then take a population-weighted mean across these counties to obtain a CZ-level mean per-person
taxes. Finally, we divide mean per-person taxes by the Census 1990 estimate of nominal income
per household, which we downloaded from the National Historical Geographic Information System
(NHGIS). We code the tax rate as missing for one CZ (Barrow, Alaska), which has a calculated
tax rate of 90%.
We compute total government spending per capita in each county using Census data on government expenditures by aggregating all county-level total expenditure categories and dividing by the
1992 county population estimates. We then construct a CZ-level measure by taking populationweighted means of expenditures per capita in the counties in each CZ. We code local government
expenditures as missing for two CZs (Barrow, Alaska and Kotzebue, Alaska), which have unusually
high expenditures per capita that exceed 50% of per capita income.
We measure state income tax progressivity as the dierence between the top state income tax
rate and the state income tax rate for individuals with taxable income of $20,000 in 2008 based
on data from the Tax Foundation. We obtain data on State EITC rates by year from Hotz and
Scholz (2003). We calculate mean EITC rate for the years 1980-2001, setting the rate to zero for
state-year pairs where there was no state EITC. Note that Wisconsins state EITC rate depends
on the number of children in a household; we use the rate for households with two children.
Higher Education. We use the Integrated Postsecondary Education Data System (IPEDS) to
construct our three measures of college access and quality. We restrict the sample to Title IV
institutions that have undergraduate students, and are degree oering. The number of colleges per
capita in each CZ is the number of institutions in the 2000 IPEDS in each CZ divided by the CZ
population. We define college tuition as the mean in-state tuition and fees for first-time, full-time
undergraduates for the institutions in each CZ. We define the enrollment-weighted mean graduation
rate based on the 150% of normal time college graduation rate from IPEDS 2009, the first year for
which this data is available. We construct a measure of income-adjusted graduation rates using the
residual from a CZ-level regression of graduation rates on mean parent income in the core sample.
Local Labor Market Conditions. The labor force participation rate is defined as the number of
57

people in the labor force by the total population in the sample of people that are at least 16 years
old. These data are from the 2000 Census long form (SF3) in table P043. We compute the share
of workers in manufacturing from the 2000 census in table P049; we divide the number of people
working in manufacturing by the total number of workers.
The exposure to Chinese trade variable is the percentage change in imports per worker from
China between 1990 and 2000. It is measured as the growth in imports allocated to a CZ, divided
by the CZ work force in 1990 (with the growth rate defined as 10 times the annualized change).
This variable was constructed by Autor et al. (2013) and provided to us by David Dorn.
The teenage labor force participation rate is defined in each CZ as the share of individuals who
received one or more W-2s between the ages of 14 and 16. We calculate the teenage LFP rate
using W-2 data for the 1985-1987 birth cohorts, the earliest cohorts for which we have W-2 data
at age 14.
Migration Rates. For inflow and outflow migration data, we use the county-to-county migration
data from the Internal Revenue Services Statistics of Income for 2004-2005. Inflow migration is the
number of people moving into a CZ from counties in other CZs divided by the total CZ population;
outflow migration is calculated similarly. We compute the share of each CZs population that is
foreign born using sample data from the 2000 census (table P021) on the number of foreign born
inhabitants divided by total CZ population. In both cases, total CZ population is the sum of county
populations from the 2000 Census (table P008) over counties in the CZ.

H. Correlates of Intergenerational Mobility: Other Factors

In this appendix, we first discuss correlations between absolute upward mobility and the four
factors in Figure VIII that were not discussed in Section VI: local tax policies, higher education,
labor market conditions, and migration. We then summarize the methodology used to estimate the
correlations in Appendix Table VIII and the binned scatter plots in Appendix Figures X-XII.
Local Public Goods and Tax Policies. We assess correlations between local tax and expenditure
policies and intergenerational mobility in the seventh panel of Figure VIII and Appendix Table
VIII. We begin by correlating upward mobility with local tax rates. We measure the average local
tax rate in each CZ as total tax revenue collected at the county or lower level in the CZ (based
on the 1992 Census of Governments) divided by total household income in the CZ based on the
1990 Census.67 Note that 75% of local tax revenue comes from property taxes; hence, this measure
largely captures variation in property tax rates. In the baseline unweighted specification pooling all
CZs, the correlation between absolute upward mobility and the average local tax rates is 0.33. We
find a robust positive correlation between tax rates and upward mobility across the specifications
in Appendix Table VIII.
An alternative measure of local public good provision is local government expenditure. Tax
revenue diers from local government expenditure because of inter-governmental transfers. We
define local government expenditure as mean local govt. expenditure per capita at the county
or lower level in the CZ (based on the 1992 Census of Governments). The correlation between
government expenditure and upward mobility is also positive, but it is smaller than that between
local tax rates and upward mobility. This could potentially be because local tax rates are used
67

Government expenditures in the neighborhoods where low-income families live within the CZ (rather than average
government expenditures) may be more relevant for upward mobility. To evaluate this possibility, we reconstructed
each of the measures of public goods and school quality analyzed in this and the next subsection, weighting by the
number of below-median income families living in each county or school district. The correlations between upward
mobility and these measures of public goods for low-income individuals are very similar to those reported in Appendix
Table VIII because expenditures in low-income areas are very highly correlated with mean expenditures at the CZ
level.

58

primarily to finance schools, which may have a larger impact on upward mobility than expenditures
funded by other sources of revenue.
Next, we evaluate whether areas that provide more transfers to low-income families through the
tax system exhibit greater upward mobility. We use two state-level proxies for the progressivity of
local tax policy. The first is the size of the state Earned Income Tax Credit. State EITC programs
are the largest state-level cash transfer for low income earners. Because state EITC policies changed
significantly over the period when children in our sample were growing up, we define a measure
of mean exposure to the state EITC as the mean state EITC rate between 1981 and 2001, when
the children in our sample were between the ages of 0 and 20.68 The mean state EITC rate is
positively correlated with upward mobility, with a correlation of approximately 0.25 that is fairly
robust across specifications. Our second proxy for the progressivity of the local tax code is the
dierence between the top state income tax rate and the state income tax rate for individuals with
taxable income of $20,000 in 2008 based on data from the Tax Foundation. There is a weak positive
correlation between local tax progressivity and upward mobility across the various specifications in
Appendix Table VIII, but the correlation is not statistically significant.
In summary, we find that areas that provide more local public goods and larger tax credits
for low income families tend to have higher levels of upward mobility. However, factors such
as segregation and inequality are much stronger and more robust predictors of the variation in
intergenerational mobility than dierences in local tax and expenditure policies.
Access to Higher Education. We construct three measures of local access to higher education
using data from the Integrated Postsecondary Education Data System (IPEDS). The first measure
is the number of Title IV, degree-granting colleges per capita in the CZ in 2000, which is similar to
the distance-based instrument used by Card (1995). The second measure is the mean (enrollmentweighted) tuition sticker price for in-state, full-time undergraduates for colleges in the CZ, which
reflects the aordability of local higher education. The third measure is the residual from an OLS
regression of the mean (enrollment-weighted) graduation rate from colleges in the CZ on mean
parent family income in the CZ, a rough proxy for the output of local higher education.
The correlations between all three of these measures shown in the eighth panel of Figure VIII
and Appendix Table VIII are small and typically statistically insignificant. We also evaluated
several additional measures of access to higher education, including the mean value of institutional
grants to students enrolled in colleges in the CZ, the number of low-cost (below the national median)
colleges per capita in the CZ, and the mean distance to the nearest low-cost college. We found
no significant relationship between any of these measures and our measures of intergenerational
mobility (not reported).
We conclude that very little of the spatial variation in intergenerational mobility is explained by
dierences in local access to higher education. Of course, this finding does not imply that college
does not play a role in upward mobility. Indeed, areas with greater upward mobility tend to have
high college attendance rates for children from low-income families (Appendix Figure VIIIa), suggesting that attending college is an important pathway for moving up in the income distribution.
The point here is simply that the characteristics of local colleges are not a strong predictor of childrens success, perhaps because the marginal impact of improving local access to higher education
on college attendance and later outcomes is small.
Labor Market Structure. Some analysts have suggested that the availability of certain types of
jobs (e.g., manufacturing) may provide ladders for lower-skilled workers to move up in the income
distribution (e.g., Wilson 1996). To explore this possibility, we measure various characteristics of
68

We assign state-years without a state EITC a rate of 0 when computing this mean. See Appendix G for further
details on the computation of state EITC rates.

59

the local labor market: (1) the overall employment rate in the local labor market in 2000, (2)
the fraction of workers employed in the manufacturing industry, and (3) a measure of exposure
to import competition based on the growth in Chinese imports per worker from Autor, Dorn and
Hanson (2013). As shown in the ninth panel of Figure VIII and Appendix Table VIII, all of these
characteristics are weakly correlated with the variation in upward mobility, with little evidence of
a clear, robust relationship across specifications. We also find no significant correlation with other
indicators such as the fraction of workers employed in management or professional occupations or
industry establishment shares (not reported).
One labor market indicator that is strongly correlated with upward mobility is the teenage labor
force participation rate. We measure the teenage labor force participation rate as the fraction of
children who have a W-2 between the ages of 14-16 in the 1985-87 birth cohorts, the earliest cohorts
for which W-2 data are available at age 14 in the tax data. The unweighted correlation between
the teenage labor force participation rate and absolute upward mobility is 0.631. This could be
because formal jobs help disadvantaged teenagers directly or because areas with good schools and
other characteristics tend to have more teenagers who work. In either case, this finding mirrors the
general pattern documented above: the strongest predictors of upward mobility are factors that
aect children before they enter the labor force as adults.
Migration Rates. We evaluate whether there is a correlation between migration rates and
intergenerational mobility using three measures: (1) the migration inflow rate, defined as the
number of people who move into the CZ between 2004 and 2005 based on IRS Statistics of Income
migration data divided by the CZ population in 2000 based on Census data, (2) the migration
outflow rate, defined as the number of people who move out of the CZ between 2004 and 2005
divided by population in 2000, and (3) the fraction of foreign-born individuals living in the CZ
based on the 2000 Census.
The correlations between all three of these measures shown in the last panel of Figure VIII and
Appendix Table VIII are generally quite low and statistically insignificant. In the first two specifications, migration rates are negatively correlated with upward mobility, but in the populationweighted and urban-area specifications, there are no significant relationships.
Empirical Methodology: Appendix Table VIII. Appendix Table VIII reports each of the correlations corresponding to Figure VIII in Column 1. The remaining columns evaluate the robustness
of these estimates to alternative specifications. In Column 2, we report estimates based on withinstate variation by including state fixed eects in a regression specification analogous to that in
Column 1 of Table IV. Column 3 replicates Column 1, weighting each CZ by its population as
recorded in the 2000 Census.69 Column 4 restricts the sample to urban areas (CZs that intersect
MSAs) and replicates Column 1. Column 5 replicates Column 1, controlling for the fraction of
black individuals in the CZ and the local income growth rate from 2000-2010 (calculated as in
Appendix G) using regression specifications of the form used in Table IV. Finally, in Column 6, we
correlate each covariate with relative mobility c .
Empirical Methodology: Appendix Figures X-XII. Appendix Figures X-XII present binned scatter plots of absolute upward mobility (
r25,c ) in each CZ vs. various characteristics. Each figure
is constructed using one observation for each CZ in which we have more than 250 parent-child
pairs. To construct the binned scatter plots, we divide the variable plotted on the x-axis into 20
equally sized bins (vingtiles) and plot the mean value of the variable plotted on the y-axis (absolute upward mobility) vs. the mean value of the x variable within each bin. We also report
the unweighted correlation between the x and y variables (estimated using the underlying CZ-level
69

We normalize all variables by their weighted standard deviations in this and all other specifications that use
weights, so that univariate regression coefficients can be interpreted as weighted correlations.

60

data), with standard errors clustered at the state level to correct for spatial correlation across CZs.
To facilitate comparisons across figures that plot the relationship between upward mobility and
dierent factors, we always use a fixed y scale ranging from 35 to 55, approximately the 5th to 95th
percentile of the distribution of r25,c across CZs.

I. Construction of Predicted Time Trends

This appendix describes the construction of Appendix Figure XIII. The series in circles is taken
directly from Chetty et al. (2014, Figure 2). The solid circles show estimates of national rank-rank
slopes by birth cohort using the SOI 0.1% sample. The open circles show forecasts of the rank-rank
slope based on income measured at age 26 and the college attendance rates using the population
data. The remaining series in the figure show predicted changes in relative mobility based on trends
in the five factors that are most strongly correlated with the variation in intergenerational mobility
across CZs (see Section VI). We choose proxies for the five factors that are strongly correlated with
mobility in the cross section and are consistently measured over time.
We begin by describing how we construct the prediction based on changes in racial segregation,
shown by the series in solid triangles. This series is constructed in four steps. (1) We regress
the rank-rank slope on the Theil index of racial segregation, with one observation per CZ. This
regression corresponds to the correlation reported in Row 2, Column 6 of Appendix Table VIII,
except that we do not use normalized variables in this regression. (2) Using Census data from the
NHGIS, we compute the Theil index of racial segregation across census tracts in each CZ in 1980,
1990, and 2000, following the method described in Appendix G. We then compute the predicted
value from the regression in step (1) using the population-weighted national mean of the racial
segregation index in 1980, 1990, and 2000.70 (3) We assign each birth cohort the predicted value
when they were age 10, the mid-point of their childhood. For instance, the 1990 birth cohort is
assigned the fitted value based on racial segregation in 2000. (4) We add a constant to the series
to make the mean predicted values in 1970, 1980, and 1990 match the mean observed rank-rank
slope (from Chetty et al. 2014) between 1971-1990. This final step normalizes the levels of the
fitted values and allows us to focus on the predicted time trends.
The remaining series are constructed similarly; however, due to limitations in historical data
availability, we cannot always use the same data source as the one used to estimate cross-sectional
correlations. For the bottom 99% Gini coefficient, we follow Chetty et al. (2014) and use the U.S.
Census Bureaus time series (Table F-4) on the Gini coefficient for families, which we interpret as
a measure of the bottom 99% Gini because of top-coding in survey data.71 For the religious share,
we use a time series compiled by the Association of Religion Data Archives using data from the
General Social Survey. We define the religious share as the share of people that attend a religious
service at least once per month, the closest analog of the CZ-level definition of religious adherents
that we use for the cross-sectional correlations. For the share of single mothers, we use data for
the 1980, 1990, and 2000 Censuses obtained from the NHGIS. For all three of these variables, we
assign each birth cohort predicted values at age 10, as for racial segregation.
For the high school dropout rate, we use the same CCD data that we use for the CZ-level
cross-sectional correlations. We assign each birth cohort the predicted value corresponding to the
national high school dropout rate when they were 17. For simplicity, we do not residualize the HS
dropout rate by income both in the cross-sectional regression and the prediction. For example, the
1997 high school dropout rate is assigned to the 1980 birth cohort. Analogous high school dropout
70

Tract-level data on racial shares are not available for all Census tracts in 1980; we compute the national mean
using the tracts for which data are available.
71
Chetty et al. (2014) note that there is a break in this series in 1993. We address this issue in the same manner
as that paper by subtracting 0.021 from the Gini coefficient from 1993 onward.

61

rate data are unavailable in 1987, and hence we have no prediction for the 1970 birth cohort.
The predicted changes in the rank-rank slope from the 1970 to 1990 birth cohorts based on
each of these factors are -0.024 (racial segregation), +0.026 (Gini), +0.003 (religious share), and
+0.038 (fraction single mothers). The predicted change from the 1980 to 1990 birth cohort based
on high school dropout rates is -0.010. Using a multivariable cross-sectional regression specification
combining all five factors yields a predicted increase in the rank-rank slope from 1980 to 1990 of
0.010, or 0.001 per year. An analogous prediction for the change from 1970 to 1980 based on four
factors (excluding the high school dropout rate) yields a predicted increase from 1970 to 1980 of
approximately 0.014.

62

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67

TABLE I
Intergenerational Mobility Estimates at the National Level
Sample
Core
sample
(1)

Male
children
(2)

Female
children
(3)

Married
parents
(4)

Single
parents
(5)

1980-1985
cohorts
(6)

Fixed Age at
Child Birth
(7)

Log family income

0.344
(0.0004)

0.349
(0.0006)

0.342
(0.0005)

0.303
(0.0005)

0.264
(0.0008)

0.316
(0.0003)

0.361
(0.0008)

2. Log family income

(recoding zeros to $1)

Log family income

0.618
(0.0009)

0.697
(0.0013)

0.540
(0.0011)

0.509
(0.0011)

0.528
(0.0020)

0.580
(0.0006)

0.642
(0.0018)

3. Log family income

(recoding zeros to $1000)

Log family income

0.413
(0.0004)

0.435
(0.0007)

0.392
(0.0006)

0.358
(0.0006)

0.322
(0.0009)

0.380
(0.0003)

0.434
(0.0009)

4. Family income rank

Family income rank

0.341
(0.0003)

0.336
(0.0004)

0.346
(0.0004)

0.289
(0.0004)

0.311
(0.0007)

0.323
(0.0002)

0.359
(0.0006)

5. Family income rank

Family income rank

(1999-2003)

0.339
(0.0003)

0.333
(0.0004)

0.344
(0.0004)

0.287
(0.0004)

0.294
(0.0007)

0.323
(0.0002)

0.357
(0.0006)

6. Family income rank

Top par. income rank

0.312
(0.0003)

0.307
(0.0004)

0.317
(0.0004)

0.256
(0.0004)

0.253
(0.0006)

0.296
(0.0002)

0.327
(0.0006)

7. Individual income rank

Family income rank

0.287
(0.0003)

0.317
(0.0004)

0.257
(0.0004)

0.265
(0.0004)

0.279
(0.0007)

0.286
(0.0002)

0.292
(0.0006)

8. Individual earnings rank

Family income rank

0.282
(0.0003)

0.313
(0.0004)

0.249
(0.0004)

0.259
(0.0004)

0.272
(0.0007)

0.283
(0.0002)

0.287
(0.0006)

9. College attendance

Family income rank

0.675
(0.0005)

0.708
(0.0007)

0.644
(0.0007)

0.641
(0.0006)

0.663
(0.0013)

0.678
(0.0003)

0.661
(0.0010)

10. College quality rank

(P75-P25 gradient)

Family income rank

0.191
(0.0010)

0.188
(0.0014)

0.195
(0.0015)

0.174
(0.0014)

0.172
(0.0020)

0.198
(0.0007)

0.189
(0.0022)

11. Teenage birth

(females only)

Family income rank

-0.298
(0.0006)

-0.231
(0.0007)

-0.322
(0.0016)

-0.285
(0.0004)

-0.290
(0.0011)

6,854,588

3,013,148

20,520,588

Child's outcome

Parent's Income Def.

1. Log family income

(excluding zeros)

Number of observations

9,867,736

4,935,804

4,931,066

2,250,380

Notes: Each cell in this table reports the coefficient from a univariate OLS regression of an outcome for children on a measure of their parents' incomes with
standard errors in parentheses. All rows report estimates of slope coefficients from linear regressions of the child outcome on the parent income measure
except row 10, in which we regress college quality rank on a quadratic in parent income rank (as in Figure IVa). In this row, we report the difference between
the fitted values for children with parents at the 75th percentile and parents at the 25th percentile using the quadratic specification. Column 1 uses the core
sample of children, which includes all current U.S. citizens with a valid SSN or ITIN who are (1) born in birth cohorts 1980-82, (2) for whom we are able to
identify parents based on dependent claiming, and (3) whose mean parent income over the years 1996-2000 is strictly positive. Columns 2 and 3 limit the
sample used in column 1 to males or females. Columns 4 and 5 limit the sample to children whose parents were married or unmarried in the year the child was
linked to the parent. Column 6 uses all children in the 1980-85 birth cohorts. Column 7 restricts the core sample to children whose parents both fall within a 5
year window of median parent age at time of child birth (age 26-30 for fathers; 24-28 for mothers); we impose only one of these restrictions for single parents.
Child family income is the mean of 2011-12 family income, while parent family income is the mean from 1996-2000. Parent top earner income is the mean
income of the higher-earning spouse between 1999-2003 (when W-2 data are available). Child's individual income is the sum of W-2 wage earnings, UI
benefits, and SSDI benefits, and half of any remaining income reported on the 1040 form. Individual earnings includes W-2 wage earnings, UI benefits, SSDI
income, and self-employment income. College attendance is defined as ever attending college from age 18 to 21, where attending college is defined as
presence of a 1098-T form. College quality rank is defined as the percentile rank of the college that the child attends at age 20 based on the mean earnings at
age 31 of children who attended the same college (children who do not attend college are included in a separate no college group); see Section III.B for
further details. Teenage birth is defined as having a child while between age 13 and 19. In Columns 1-5 and 7, income percentile ranks are constructed by
ranking all children relative to others in their birth cohort based on the relevant income definition and ranking all parents relative to other parents in the core
sample. Ranks are always defined on the full sample of all children; that is, they are not re-defined within the subsamples in Columns 2-5 or 7. In Column 6,
parents are ranked relative to other parents with children in the 1980-85 birth cohorts. The number of observations corresponds to the specification in row 4.
The number of observations is approximately 7% lower in row 1 because we exclude children with zero income. The number of observations is approximately
50% lower in row 11 because we restrict to the sample of female children. There are 866 children in the core sample with unknown sex, which is why the
number of observations in the core sample is not equal to the sum of the observations in the male and female samples.

TABLE II
National Quintile Transition Matrix

1
2
Child
3
Quintile
4
5

Parent Quintile
3

33.7%
28.0%
18.4%
12.3%
7.5%

24.2%
24.2%
21.7%
17.6%
12.3%

17.8%
19.8%
22.1%
22.0%
18.3%

13.4%
16.0%
20.9%
24.4%
25.4%

10.9%
11.9%
17.0%
23.6%
36.5%

Notes. Each cell reports the percentage of children with family income in
the quintile given by the row conditional on having parents with family
income in the quintile given by the column for the 9,867,736 children in the
core sample (1980-82 birth cohorts). See notes to Table I for income and
sample definitions. See Online Appendix Table VI for an analogous
transition matrix constructed using the 1980-85 cohorts.

TABLE III
Intergenerational Mobility in the 50 Largest Commuting Zones
Upward
Mob. Rank
(1)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50

CZ Name
(2)
Salt Lake City, Utah
Pittsburgh, Pennsylvania
San Jose, California
Boston, Massachusetts
San Francisco, California
San Diego, California
Manchester, New Hampshire
Minneapolis, Minnesota
Newark, New Jersey
New York, New York
Los Angeles, California
Providence, Rhode Island
Washington DC
Seattle, Washington
Houston, Texas
Sacramento, California
Bridgeport, Connecticut
Fort Worth, Texas
Denver, Colorado
Buffalo, New York
Miami, Florida
Fresno, California
Portland, Oregon
San Antonio, Texas
Philadelphia, Pennsylvania
Austin, Texas
Dallas, Texas
Phoenix, Arizona
Grand Rapids, Michigan
Kansas City, Missouri
Las Vegas, Nevada
Chicago, Illinois
Milwaukee, Wisconsin
Tampa, Florida
Orlando, Florida
Port St. Lucie, Florida
Baltimore, Maryland
St. Louis, Missouri
Dayton, Ohio
Cleveland, Ohio
Nashville, Tennessee
New Orleans, Louisiana
Cincinnati, Ohio
Columbus, Ohio
Jacksonville, Florida
Detroit, Michigan
Indianapolis, Indiana
Raleigh, North Carolina
Atlanta, Georgia
Charlotte, North Carolina

Population
(3)
1,426,729
2,561,364
2,393,183
4,974,945
4,642,561
2,813,833
1,193,391
2,904,389
5,822,286
11,781,395
16,393,360
1,582,997
4,632,415
3,775,744
4,504,013
2,570,609
3,405,565
1,804,370
2,449,044
2,369,699
3,955,969
1,419,998
1,842,889
1,724,863
5,602,247
1,298,076
3,405,666
3,303,211
1,286,045
1,762,873
1,568,418
8,183,799
1,660,659
2,395,997
1,697,906
1,533,306
2,512,431
2,325,609
1,179,009
2,661,167
1,246,338
1,381,652
1,954,800
1,663,807
1,176,696
5,327,827
1,507,346
1,412,127
3,798,017
1,423,942

Absolute
Upward Mobility

P(Child in Q5 |
Parent in Q1)

Pct. Above
Poverty Line

Relative Mobility
Rank-Rank Slope

(4)

(5)

(6)

(7)

46.2
45.2
44.7
44.6
44.4
44.3
44.2
44.2
44.1
43.8
43.4
43.4
43.2
43.2
42.8
42.7
42.4
42.3
42.2
42.0
41.5
41.3
41.3
41.1
40.8
40.4
40.4
40.3
40.1
40.1
40.0
39.4
39.3
39.1
39.1
39.0
38.8
38.4
38.3
38.2
38.2
38.2
37.9
37.7
37.5
37.3
37.2
36.9
36.0
35.8

10.8
9.5
12.9
10.5
12.2
10.4
10.0
8.5
10.2
10.5
9.6
8.2
11.0
10.9
9.3
9.7
7.9
9.1
8.7
6.7
7.3
7.5
9.3
6.4
7.4
6.9
7.1
7.5
6.4
7.0
8.0
6.5
4.5
6.0
5.8
6.2
6.4
5.1
4.9
5.1
5.7
5.1
5.1
4.9
4.9
5.5
4.9
5.0
4.5
4.4

77.3
74.9
73.5
73.7
72.5
74.3
75.0
75.2
73.7
72.2
73.8
73.6
72.2
72.0
74.7
71.3
72.4
73.6
73.3
73.1
76.3
71.3
70.5
74.3
69.6
71.9
72.6
70.6
71.3
70.4
71.1
70.8
70.3
71.3
71.5
71.2
67.7
69.0
68.2
68.7
67.9
69.5
66.4
67.1
68.9
68.5
67.5
67.3
69.4
67.0

0.264
0.359
0.235
0.322
0.250
0.237
0.296
0.338
0.350
0.330
0.231
0.333
0.330
0.273
0.325
0.257
0.359
0.320
0.294
0.368
0.267
0.295
0.277
0.320
0.393
0.323
0.347
0.294
0.378
0.365
0.259
0.393
0.424
0.335
0.326
0.303
0.412
0.413
0.397
0.405
0.357
0.397
0.429
0.406
0.361
0.358
0.398
0.389
0.366
0.397

Notes: This table reports estimates of intergenerational mobility for the 50 largest commuting zones (CZs) according to their populations in the 2000
Census. The CZs are sorted in descending order by absolute upward mobility (Column 4). The mobility measures are calculated using the core
sample (1980-82 birth cohorts) and the baseline family income definitions described in Table I (except for Column 5, which uses the 1980-85 birth
cohorts). The measures in Columns 4 and 7 are both derived from within-CZ OLS regressions of child income rank against parent income rank.
Column 7 reports the slope coefficient from this regression, which is equal to the difference in mean child income rank between children with parents
in the 100th percentile and children with parents in the 0th percentile (divided by 100). Column 4 reports the predicted value at parent income rank
equal to 25. Column 5 reports the percentage of children whose family income is in the top quintile of the national distribution of child family income
conditional on having parent family income in the bottom quintile of the parental national income distribution. These probabilities are taken directly
from Online Data Table VII. Column 6 reports the fitted values at parent rank 25 from a regression of an indicator for child family income being above
the poverty line on parent income rank (see Appendix F for details). . See Online Data Table V for estimates for all CZs as well as estimates using
alternative samples and income definitions.

TABLE IV
Segregation and Intergenerational Mobility
Dep. Var.:
Racial Segregation

(1)

(2)

-0.361
(0.045)

-0.360
(0.068)

Income Segregation

Absolute Upward Mobility

(3)
(4)
(5)

-0.393
(0.065)
-0.508
(0.155)

-0.408
(0.166)

Segregation of Affluence (>p75)

0.108
(0.140)

0.216
(0.171)

Share with Commute < 15 Mins

Urban Areas Only

Observations

(7)

-0.058
(0.090)

Segregation of Poverty (<p25)

R-Squared

(6)

0.605
(0.126)

0.571
(0.165)

0.131

0.130

0.154

0.167

0.052

0.366

0.368

709

325

709

709

325

709

709

Notes: Each column reports coefficients from an OLS regression with standard errors clustered at the state level reported
in parentheses. All independent and dependent variables are normalized (in the relevant estimation sample) to have mean
0 and standard deviation 1, so univariate regression coefficients equal correlation coefficients. The regressions are run
using data for the 709 CZs with at least 250 children in the core sample. The dependent variable in all columns is our
baseline measure of absolute upward mobility, the expected rank of children whose parents are at the 25th national
percentile. Column 2 and 5 restrict to the sample of CZs that intersect an MSA. Racial segregation is measured by the
Theil index defined in Section VI.B using racial shares at the census tract level. Income segregation is measured by a
weighted average of two-group Theil indices, as in Reardon (2011). Segregation of poverty is a two-group Theil index,
where the groups are defined as being above vs. below the 25th percentile of the local household income distribution.
Segregation of affluence is defined analogously at the 75th percentile. Share with commute <15 minutes is the fraction of
working individuals in each CZ who commute less than 15 minutes to work. See Appendix G for details on the definitions
of the independent variables.

TABLE V
Income Inequality and Intergenerational Mobility: The "Great Gatsby" Curve
Across CZs within the U.S.
Dep. Var.:

Relative
Mobility

Absolute Upward Mobility

(1)

(2)

(3)

Gini Bottom 99%

-0.634
(0.090)

-0.624
(0.113)

0.476
(0.088)

Top 1% Income Share

-0.123
(0.035)

0.029
(0.039)

-0.032
(0.032)

Gini Coefficient

0.72
(0.21)

0.62
(0.27)

0.78
(0.27)

0.17
(0.27)

-0.11
(0.28)

0.679
(0.111)

Urban Areas Only

Observations

(5)

-0.578
(0.093)

Frac. Between p25 and p75

R-Squared

(4)

Across Countries
Log-Log
Log-Log
Elasticity
Elasticity
1985 Inequality
2005 Inequality
(6)
(7)
(8)

x
0.334

0.433

0.380

0.462

0.224

0.518

0.536

0.531

709

709

325

709

709

13

13

12

Notes: Each column reports regression coefficients from an OLS regression with all variables normalized to have mean 0 and standard
deviation 1 in the estimation sample, so univariate regression coefficients are equal to correlation coefficients. Columns 1-5 are estimated
using data for the 709 CZs with at least 250 children in the core sample. The dependent variable in Columns 1-4 is our baseline CZ-level
measure of absolute upward mobility, the expected rank of children whose parents are at the 25th national percentile in the core sample. In
Column 5, the dependent variable is relative mobility, the rank-rank slope within each CZ. In Column 3, we restrict to CZs that intersect
MSAs. In Columns 1-5, the Gini coefficient is defined as the Gini coefficient of family income for parents in the core sample in each CZ; the
top 1% income share is defined as the fraction of total parent family income in each CZ accruing to the richest 1% of parents in that CZ; the
Gini Bottom 99% is defined as the Gini coefficient minus the top 1% income share; and the fraction between p25 and p75 is the fraction of
parents in each CZ whose family income is between the 25th and 75th percentile of the national distribution of parent family income for
those in the core sample. In Columns 6-8, the dependent variable is the log-log IGE estimate by country from Corak (2013, Figure 1). The
Gini coefficients across countries are obtained from the OECD Income Distribution Database (series "Income Distribution and Poverty: by
country"). We interpret these coefficients as applying to the bottom 99% because the surveys on which they are based are typically topcoded. The top 1% income share across countries is from the World Top Income Database (series "Top 1% Income Share"). The
independent variables are measured in 1985 in Columns 6 and 7 and in 2005 in Column 8.

TABLE VI
Correlates of Intergenerational Mobility: Comparing Alternative Hypotheses
Dep. Var.:

Absolute Upward Mobility

(1)
(2)
(3)

Relative Mobility
(4)
(5)

Absolute Upward Mobility

(6)
(7)
(8)

Fraction Short Commute

0.302
(0.065)

0.227
(0.077)

0.314
(0.052)

-0.290
(0.061)

-0.325
(0.064)

0.331
(0.070)

0.319
(0.065)

Gini Bottom 99%

-0.009
(0.053)

-0.017
(0.043)

0.060
(0.097)

0.006
(0.071)

0.343
(0.095)

-0.287
(0.059)

-0.021
(0.054)

High School Dropout Rate

-0.147
(0.055)

-0.120
(0.038)

-0.109
(0.085)

0.010
(0.064)

0.181
(0.056)

-0.288
(0.059)

-0.140
(0.055)

Social Capital Index

0.169
(0.047)

0.065
(0.050)

0.173
(0.060)

0.154
(0.060)

0.154
(0.070)

0.168
(0.059)

0.168
(0.045)

Fraction Single Mothers

-0.487
(0.062)

-0.477
(0.071)

-0.555
(0.089)

0.591
(0.049)

Fraction Black
State Fixed Effects

Observations

-0.579
(0.061)

0.056
(0.073)

0.132
(0.051)

Urban Areas Only

R-Squared

-0.808
(0.085)

x
0.757

0.859

0.671

0.48

0.324

0.651

0.584

0.763

709

709

325

709

709

709

709

709

Notes: Each column reports coefficients from an OLS regression with standard errors clustered at the state level reported in
parentheses. The regressions are run using data for the 709 CZs with at least 250 children in the core sample. The dependent
variable in Columns 1-3 and 6-8 is our baseline measure of absolute upward mobility, the expected rank of children whose
parents are at the 25th national percentile. The dependent variable in columns 4 and 5 is relative mobility, the rank-rank slope
within each CZ. All independent and dependent variables are normalized (in the relevant estimation sample) to have mean 0 and
standard deviation 1. Column 1 reports unweighted estimates across all CZs. Column 2 includes state fixed effects. In Column 3,
we restrict to CZs that intersect MSAs. Columns 4-8 replicate the unweighted specification in Column 1 with different dependent
and independent variables. The fraction with short commutes is the share of workers that commute to work in less than 15
minutes calculated using data for the 2000 Census. Gini bottom 99% is the Gini coefficient minus the top 1% income share within
each CZ, computed using the distribution of parent family income within each CZ for parents in the core sample. Incomeresidualized high school dropout rate is the residual from a regression of the fraction of children who drop out of high school in
the CZ, estimated using data from the NCES Common Core of Data for the 2000-01 school year, on mean household income in
2000. Social capital index is the standardized index of social capital constructed by Rupasingha and Goetz (2008). Fraction
single mothers is the fraction of children being raised by single mothers in each CZ. Fraction black is the number of people in the
CZ who are black alone divided by the CZ population. We code the high school dropout rate as 0 for 116 CZs in which dropout
rate data are missing for more than 25% of the districts in the CZ, and include an indicator for having a missing high school
dropout rate. We do the same for 16 CZs with missing data on social capital. See Section VI, Online Data Table IX, and Online
Appendix G for additional details on the definitions of each of these variables.

ONLINE APPENDIX TABLE I

Sample Sizes vs. Vital Statistics Counts by Birth Cohort
Base national Base CZdataset
level dataset
Size of Birth
Cohort
(in '000s)

1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1980-1991

Percentage in
DM1 database,
US citizens,
and matched
alive
to a parent

with positive
parent income
in 1996-2000

and with valid

parental geo
information

(1)

(2)

(3)

(4)

(5)

3,327
3,333
3,494
3,612
3,629
3,681
3,639
3,669
3,761
3,757
3,809
3,910
4,041
4,158
4,111
45,776

95.9%
97.0%
97.6%
99.2%
104.6%
105.5%
105.4%
105.1%
104.8%
104.7%
104.7%
104.5%
105.0%
104.7%
104.5%
104.4%

55.0%
72.4%
80.9%
85.6%
91.6%
93.8%
95.4%
96.7%
97.5%
98.0%
98.4%
98.5%
98.5%
98.6%
98.5%
96.0%

85.2%
91.1%
93.2%
94.7%
95.8%
96.4%
96.6%
96.8%
96.8%
96.7%
96.7%
96.6%
94.8%

84.4%
90.3%
92.4%
93.8%
94.9%
95.4%
95.6%
95.8%
95.7%
95.6%
95.6%
95.5%
93.8%

Notes: Column 1 reports the size of each birth cohort from 1987-1991, based on data from vital
statistics obtained from the US Statistical Abstract 2012, Table 78. The remaining columns report
the number of individuals in the population tax data as a percentage of the total number in the
birth cohort, imposing the additional restrictions listed in the header of each column. Column 2
reports the number of individuals born in each cohort who are in the DM1 tax database, are
current US citizens, and are alive in 2013. This column can differ from the birth cohort due to
immigration and naturalization, emigration, and deaths before 2012. The percentage of citizens in
the DM1 data rises in 1981 because citizenship status is missing for some individuals born before
1981. Column 3 further requires the individuals to be matched to parents (i.e., claimed as children
dependents on individual income tax returns by a person aged 15-40 at the time of the birth of the
child) in 1996 or after. Column 4, which requires in addition that parents have positive mean
income between 1996-2000, is our key sample of interest for all national level statistics. Column 5
further requires valid geographical information (ZIP code) for parents. Column 5 is our key sample
of interest for all local area statistics. The core sample includes the 1980-2 cohorts. The extended
sample includes the 1980-91 cohorts.

ONLINE APPENDIX TABLE II

SOI Sample Counts by Birth Cohort
Number of Observations

Number of Unique Children

Cohort

(1)

(2)

1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
Total

4,383
7,787
10,831
14,330
17,736
17,938
18,459
17,756
18,375
19,545
19,916
22,331
24,599
28,221
31,711
33,221
35,382
38,139
42,450
47,768
52,821
523,699

4,383
5,569
6,154
7,065
8,207
8,246
8,156
7,958
7,614
7,732
8,155
9,929
10,927
12,390
13,476
13,540
14,234
15,362
18,162
19,805
21,231
228,295

Notes: This table reports the sample size for the Statistics of Income stratified
random sample by birth cohort. Column 1 reports the total number of observations
per cohort. Column 2 reports the number of unique children per cohort. See
Appendix A for details on the construction of the SOI sample.

ONLINE APPENDIX TABLE III

Summary Statistics for Core Sample: Children Born in 1980-82
Variable

Mean
(1)

Std. Dev.
(2)

Median
(3)

Parents:
Family Income (1996-2000 average)
Top Earner's Income (1999-2003 average)
Fraction Single Parents
Fraction Female among Single Parents
Father's Age at Child Birth
Mother's Age at Child Birth
Father's Age in 1996
Mother's Age in 1996

87,219
68,854
30.6%
72.0%
28.5
26.1
43.5
41.1

353,430
830,487
46.1%
44.9%
6.2
5.2
6.3
5.2

60,129
48,134

Children:
Family Income (2011-12 average)
Fraction with Zero Family Income
Individual Income
Individual Earnings
Fraction Female
Fraction Single
Attend College between 18-21
Fraction of Females with Teen Birth
Child's Age in 2011

48,050
6.1%
31,441
30,345
50.0%
44.3%
58.9%
15.8%
30.0

93,182
23.9%
112,394
98,692
50.0%
49.7%
49.2%
36.5%
0.8

34,975

Number of Children

28
26
43
41

24,931
23,811

30

9,867,736

Notes: The table presents summary statistics for the core sample (1980-82 birth cohorts); see notes to
Table I for further details on the definition of the core sample. Child income is mean income in 2011-12
(when the child is approximately 30 years old), while parent family income is mean income from 19962000. Family income is total pre-tax household income. Top earner's income is the income of the higherearning parent from 1999-2003 (when W-2's are available). Parents' marital status is measured in the
year the parent is matched to the child. Child's individual income is the sum of W-2 wage earnings, UI
benefits, and SSDI benefits, and half of any remaining income reported on the 1040 form. Individual
earnings includes W-2 wage earnings, UI benefits, SSDI income, and self-employment income. A child is
defined as single if he/she does not file with a spouse in 2011 and 2012. College attendance is defined as
ever attending college from age 18 to 21, where attending college is defined as presence of a 1098-T
form. Teenage birth is defined (for females only) as having a child while being aged 19 or less. See
Section III.B and Online Appendix A for additional details on sample and variable definitions. All dollar
values are reported in 2012 dollars, deflated using the CPI-U.

ONLINE APPENDIX TABLE IV

Comparison of Administrative Tax Data to CPS and ACS Survey Datasets
Tax Data
Tax Data
2011-2012
Full Sample Core Sample
CPS
(1)
(2)
(3)
Income Distribution:
% Zero
% Negative
Mean
Std. Deviation
P10
P25
P50
P75
P90

9.74%
0.00%
44,278
104,528
63
12,724
32,165
62,095
96,995

Demographics:
% Married
% Female
% Live in South
% College

42.43%
50.03%
36.83%
54.62%

44.31%
49.97%
37.94%
58.93%

11,262,459
11,262,459

9,867,736
9,867,736

Observations
Sum of Samp. Weights

Earned Family Income

7.32%
9.23%
0.00%
0.00%
46,805
54,313
109,667
58,556
1,624
1,307
14,984
18,843
34,737
40,829
65,148
75,000
99,911
115,000

49.32%
50.43%
38.33%
66.20%

2011-2012
ACS
(4)
12.64%
0.00%
42,382
47,879
0
12,000
31,642
57,000
91,865

Tax Data
Tax Data
2011-2012
Full Sample Core Sample
CPS
(5)
(6)
(7)
8.54%
0.33%
45,406
90,594
521
12,842
32,273
62,992
98,802

Total Family Income

6.11%
5.44%
0.34%
0.04%
48,050
56,438
93,182
59,145
2,810
6,431
14,919
20,414
34,975
42,768
66,169
76,554
101,770
118,050

2011-2012
ACS
(8)
8.00%
0.05%
44,845
50,072
1,500
14,000
33,000
60,000
96,243

46.17%
49.98%
37.56%
61.34%

14,246
190,561
10,845,147 11,043,039

11,262,459
11,262,459

9,867,736
9,867,736

14,246
194,501
10,845,147 11,043,039

Notes: Columns (1) and (5) include all individuals in the Data Master-1 file from the SSA who were born in 1980-1982, are current U.S. citizens, and
lived through 2012. In Columns (2) and (6), we impose the additional restriction that an individual was claimed as a dependent on a tax return in the
years 1996-2012 by parents with positive income as described in the text. CPS sample consists of civilian, non-institutionalized citizens age 29-31 in
the 2011 wave and 30-32 in 2012 waves of the Current Population Survey. ACS sample consists of civilian, non-institutionalized citizens born between
1980-1982 in the 2011 and 2012 American Community Surveys. Earned income refers to wages and salary plus social security and unemployment
insurance plus positive self-employment income, except for the ACS measure, which does not include unemployment insurance. IRS wages and
salary income is defined as the amount of all wages, tips, and other compensation before any payroll deductions (total of all amounts reported on all
Forms W-2, Box 1). IRS unemployment compensation is defined as the amount of Unemployment Compensation and Railroad Retirement Board
payments prior to tax withholding as reported on Form 1099-G, Box 1. IRS social security income is defined as total Social Security Administration
benefits, as reported on Form SSA-1099 (as well as any Railroad Retirement Board benefits paid, as reported on Form RRB-1099, Box 3). IRS selfemployment income is defined as the profit reported on Form 1040 Schedule C. In the CPS, self-employment income is business income; in the ACS,
it is both farm and non-farm business income. In the tax data, total income is the sum of Adjusted Gross Income, social security, and tax exempt
interest. Total income in CPS and ACS is all reported income including negative business and investment income. All dollar amounts are in 2012
dollars. Married refers to filing of joint return in 2011-2012 period for the tax data, and self-report of currently married in CPS/ACS samples. College
means attended a degree granting institution between the ages of 18 and 21 in the tax data and self-report of more than high school attainment in
CPS/ACS samples. South refers to filing a federal tax return in (for tax data) or being surveyed in (for ACS/CPS) one of the following states: DE, DC,
FL, GA, MD, NC, SC, VA, WV, AL, KY, MS, TN, AR, LA, OK, TX. ACS and CPS moments computed using sampling weights (inverse probability of
inclusion in sample). For the ACS and CPS, the sum of the sample weights is the average of the sum of the sample weights in 2011 and in 2012.

ONLINE APPENDIX TABLE V

Estimates of Intergenerational Mobility Using Surname Means vs. Individual Incomes
Name Freq.
Restriction

Number of
Children
(1)

Number
of Names
(2)

1. No restriction
2. < 25
3. < 50
4. < 100
5. > 100
6. > 1,000
7. > 10,000
8. > 20,000

4,843,629
1,135,624
1,437,280
1,784,635
3,053,494
1,650,583
390,187
202,734

395,439
375,753
384,576
389,611
5,773
546
22
7

Rank-Rank Slope
Surname
Individual
(3)
(4)
0.39
0.30
0.31
0.33
0.46
0.41
0.41
0.75

0.30
0.27
0.27
0.28
0.31
0.31
0.33
0.34

Log-Log IGE
Surname
Individual
(5)
(6)
0.42
0.33
0.34
0.36
0.50
0.43
0.45
0.81

0.33
0.30
0.30
0.31
0.33
0.34
0.35
0.36

Notes: This table compares estimates of rank-rank slopes and log-log IGEs based on individual-level data to estimates
based on surname means, as in Clark (2014). In this table, we restrict the core sample to children who have the same
surname (in 2012) as their parents. The first row uses all children who satisfy this restriction. Rows 2-4 limit the sample to
rare surnames: those that occur less than 25 times, 50 times, and 100 times in the sample. Conversely, rows 5-8 limit the
sample to common surnames: those that occur more than 100, 1000, 10,000, and 20,000 times. Column 1 shows the
number of children in each subsample (i.e., the number of observations used to estimate the rank-rank slope). Column 2
shows the number of distinct surnames in each sample. We estimate the individual-level rank-rank slopes and log-log
IGE's (Columns 4 and 6) using OLS regressions on the microdata as in Table I. In Columns 3 and 5, we estimate the rankrank slopes and log-log IGE's using OLS regressions on a dataset collapsed to surname-level means, weighting by the
number of observations for each name. See Appendix D for further details.

ONLINE APPENDIX TABLE VI

National Quintile Transition Matrix: 1980-85 Cohorts

Child
Quintile

1
2
3
4
5

1st

2nd

33.1%
27.7%
18.7%
12.7%
7.8%

24.1%
24.0%
21.6%
17.7%
12.6%

Parent Quintile
3rd
17.7%
19.6%
21.9%
21.8%
18.9%

4th

5th

13.5%
16.1%
20.7%
24.1%
25.6%

11.7%
12.6%
17.0%
23.7%
35.1%

Notes. Each cell reports the percentage of children with family income in the quintile given by the row
conditional on having parents with family income in the quintile given by the column for children in the
1980-85 birth cohorts. See notes to Table I for income and sample definitions. See Table II for an
analogous transition matrix constructed using the 1980-82 birth cohorts.

ONLINE APPENDIX TABLE VII

Robustness of Spatial Variation in Intergenerational Mobility to Alternative Specifications
Correlation with Baseline Mobility Estimates and Ratio of Std. Dev.
Upward mobility Relative mobility Upward mobility Relative mobility
Unweighted
Unweighted
Pop. Weighted
Pop. Weighted
(1)
(2)
(3)
(4)

Change from Baseline Specification

A. Alternative Samples
1. Male children
2. Female children
3. Children of married parents
4. Children of single parents
5. Birth cohorts 1983-85
6. Birth cohorts 1986-88
7. Parent age at child birth within 5 years of median
8. Children who stay within CZ
9. Children matched to unique parents

0.99,
0.98,
0.97,
0.97,
0.97,
0.94,
0.98,
0.94,
0.99,

1.07
0.96
0.96
0.97
1.00
0.95
1.06
1.02
0.93

0.94,
0.95,
0.89,
0.61,
0.84,
0.73,
0.90,
0.87,
0.98,

1.03
1.09
0.92
1.14
1.08
1.11
1.16
1.09
0.90

0.98,
0.97,
0.91,
0.97,
0.96,
0.82,
0.98,
0.93,
0.98,

1.07
0.98
1.02
0.96
0.93
0.91
1.05
1.12
0.93

0.98,
0.98,
0.93,
0.83,
0.96,
0.88,
0.96,
0.95,
0.99,

1.01
1.02
0.89
1.02
1.05
0.98
1.02
1.04
0.93

0.97,
0.89,
0.86,
0.90,
0.87,
0.98,

1.00
0.80
0.82
1.01
1.02
0.99

0.99,
0.83,
0.82,
0.96,
0.97,
1.00,

1.04
0.97
0.93
1.14
1.15
0.98

0.99,
0.95,
0.93,
0.95,
0.94,
1.00,

0.99
0.81
0.82
0.97
0.95
0.99

B. Alternative Income Definitions

10. Top parent income
11. Individual child income
12. Individual child earnings
13. Individual child income (males only)
14. Indiv child income and top parent income (males only)
15. Parent Income 1999-2003

1.00,
0.94,
0.93,
0.96,
0.97,
1.00,

1.05
0.74
0.72
1.03
1.07
0.99

C. Adjustments for Cost of Living and Growth Rates

16. Cost of living adjusted income
17. Parent income measured in 2011/12
18. Controlling for growth

0.98, 1.06
0.97, 0.90
0.83, 0.83

0.99, 0.99
0.92, 0.89
0.92, 0.92

0.86, 1.01
0.94, 0.95
0.81, 0.83

0.99, 0.97
0.98, 0.93
0.96, 0.97

D. Alternative Measures of Mobility

19. Within-CZ ranks
20. Prob. Child in Q5 | Parent in Q1
21. Child income > poverty line

0.95, 0.94
0.91
0.94

0.96, 0.98
0.92
0.89

E. Alternative Child Outcomes

22. College Attendance (age 18-21)
23. College Quality (age 20)
24. Teenage Birth, females only

0.71
0.71
-0.61

0.68
0.51
-0.58

0.53
0.55
-0.64

0.72
0.65
-0.68

Notes: The first number in each cell of this table reports the correlation across CZs of a baseline mobility measure (using child family income rank
and parent family income rank in the core sample) with an alternative mobility measure. The second number in each cell reports the ratio of the
standard deviation of the alternative measure to the baseline measure. We do not report the ratio of standard deviations for statistics that are
measured in different units relative to the corresponding baseline measure. The alternative mobility measures are defined either using a different
sample (Panel A), a different income measure for parents or children (Panel B), adjusting for cost of living or local growth (Panel C), using alternative
statistics for mobility (Panel D), or using earlier outcomes (Panel E). Column (1) reports the unweighted correlation (and SD ratio) between the
alternative and baseline measure of absolute upward mobility, the expected rank of children whose parents are at the 25th national percentile in the
core sample. Column (2) reports the unweighted correlation (and SD ratio) between the alternative and baseline measure of relative mobility, the
slope of the rank-rank relationship in the core sample. Columns (3) and (4) repeat Columns (1) and (2), weighting the correlations and standard
deviations by CZ population as recorded in the 2000 Census. With the exception of the transition probability in row 20, all absolute and relative
mobility measures are constructed using OLS regressions of child outcomes on parent ranks as described in the text. Ranks are always defined in
the full sample, prior to defining specific subsamples, except in row 19. See Appendix F for details on the definition of each measure.

ONLINE APPENDIX TABLE VIII

Correlates of Intergenerational Mobility Across Commuting Zones
Dep. Var.:

Race

State FEs
(2)

Pop. Weighted
(3)

Urban Areas Only

(4)

Controls
(5)

-0.580

(0.066)

-0.353

(0.048)

-0.616

(0.074)

-0.673

(0.063)

Racial Segregation Theil Index

Income Segregation Theil Index
Segregation Segregation of Poverty (<p25)
Segregation of Affluence (>p75)
Share with Commute < 15 Mins

-0.361
-0.393
-0.407
-0.369
0.605

(0.045)
(0.065)
(0.066)
(0.064)
(0.126)

-0.274
-0.260
-0.261
-0.250
0.342

(0.027)
(0.036)
(0.038)
(0.035)
(0.092)

-0.311
-0.169
-0.216
-0.142
0.335

(0.092)
(0.105)
(0.098)
(0.106)
(0.115)

-0.360
-0.184
-0.210
-0.155
0.548

(0.068)
(0.068)
(0.066)
(0.070)
(0.080)

-0.273
-0.267
-0.274
-0.250
0.415

Household Income per Capita for Working-Age Adults

Gini coefficient for Parent Income
Income
Top 1% Income Share for Parents
Distribution
Gini Bottom 99%
Fraction Middle Class (Between National p25 and p75)

0.050
-0.578
-0.190
-0.647
0.679

(0.071)
(0.093)
(0.072)
(0.092)
(0.111)

-0.013
-0.281
-0.065
-0.433
0.500

(0.075)
(0.050)
(0.031)
(0.063)
(0.102)

0.046
-0.236
0.059
-0.416
0.293

(0.092)
(0.162)
(0.094)
(0.123)
(0.129)

0.043
-0.537
-0.144
-0.616
0.551

(0.076)
(0.120)
(0.069)
(0.114)
(0.126)

School Expenditure per Student

Teacher-Student Ratio
Test Score Percentile (Controlling for Parent Income)
High School Dropout Rate (Controlling for Parent Income)

0.246
-0.328
0.588
-0.574

(0.095)
(0.100)
(0.087)
(0.089)

0.026
-0.213
0.466
-0.413

(0.099)
(0.128)
(0.074)
(0.060)

0.219
0.062
0.176
-0.433

(0.088)
(0.139)
(0.220)
(0.100)

0.236
0.024
0.413
-0.441

Social Capital Index (Rupasingha and Goetz 2008)

Fraction Religious
Violent Crime Rate

0.641
0.521
-0.380

(0.091)
(0.085)
(0.146)

0.349
0.357
-0.163

(0.092)
(0.061)
(0.058)

0.299
0.410
-0.149

(0.131)
(0.096)
(0.166)

Fraction of Children with Single Mothers

Fraction of Adults Divorced
Fraction of Adults Married

-0.764
-0.486
0.571

(0.074)
(0.100)
(0.062)

-0.571
-0.333
0.417

(0.085)
(0.085)
(0.063)

-0.613
-0.389
0.221

Local Tax Rate

Local Government Expenditures per Capita
State EITC Exposure
State Income Tax Progressivity

0.325
0.186
0.245
0.207

(0.070)
(0.083)
(0.064)
(0.146)

0.135
0.074

(0.073)
(0.028)

Number of Colleges per Capita

Mean College Tuition
College Graduation Rate (Controlling for Parent Income)

0.200
-0.018
0.155

(0.114)
(0.067)
(0.062)

-0.015
-0.044
0.141

0.212
-0.261
-0.175
0.631

(0.086)
(0.091)
(0.078)
(0.087)

-0.258
-0.163
-0.027

(0.074)
(0.070)
(0.064)

K-12
Education

Social
Capital
Family
Structure

Tax

College

Fraction Black Residents

Relative Mobility

Absolute Upward Mobility

Baseline
(1)

Labor Force Participation Rate

Local Labor Fraction Working in Manufacturing
Market
Growth in Chinese Imports 1990-2000 (Autor and Dorn 2013)
Teenage (14-16) Labor Force Participation Rate
Migration

Migration Inflow Rate

Migration Outflow Rate
Fraction of Foreign Born Residents

(6)
0.631

(0.048)

(0.046)
(0.054)
(0.054)
(0.052)
(0.131)

0.406
0.183
0.218
0.146
-0.447

(0.048)
(0.063)
(0.059)
(0.063)
(0.074)

0.064
-0.362
-0.072
-0.470
0.458

(0.080)
(0.086)
(0.065)
(0.104)
(0.145)

-0.145
0.346
0.019
0.473
-0.451

(0.081)
(0.089)
(0.063)
(0.090)
(0.109)

(0.092)
(0.104)
(0.147)
(0.108)

0.053
-0.249
0.393
-0.440

(0.082)
(0.088)
(0.093)
(0.086)

-0.279
0.009
-0.317
0.328

(0.092)
(0.108)
(0.122)
(0.099)

0.517
0.417
-0.367

(0.116)
(0.096)
(0.145)

0.478
0.484
-0.244

(0.097)
(0.065)
(0.062)

-0.327
-0.101
0.217

(0.085)
(0.090)
(0.140)

(0.129)
(0.074)
(0.127)

-0.719
-0.346
0.377

(0.063)
(0.103)
(0.069)

-0.611
-0.569
0.365

(0.066)
(0.086)
(0.089)

0.641
0.158
-0.370

(0.046)
(0.088)
(0.078)

0.155
0.192
0.279
0.265

(0.092)
(0.087)
(0.076)
(0.070)

0.182
0.085
0.355
0.198

(0.073)
(0.079)
(0.073)
(0.098)

0.207
0.107
0.163
0.155

(0.071)
(0.083)
(0.073)
(0.133)

-0.328
-0.301
-0.144
-0.150

(0.061)
(0.080)
(0.047)
(0.106)

(0.118)
(0.039)
(0.052)

0.108
0.058
0.107

(0.088)
(0.096)
(0.089)

-0.045
-0.015
0.120

(0.076)
(0.087)
(0.095)

0.060
-0.029
0.173

(0.142)
(0.066)
(0.073)

-0.125
0.109
-0.025

(0.052)
(0.064)
(0.057)

-0.045
0.007
0.006
0.358

(0.052)
(0.079)
(0.023)
(0.098)

0.022
-0.158
0.001
0.299

(0.090)
(0.090)
(0.070)
(0.153)

0.267
-0.128
0.008
0.540

(0.113)
(0.096)
(0.102)
(0.109)

0.146
0.002
-0.107
0.388

(0.073)
(0.085)
(0.048)
(0.090)

-0.237
0.393
0.171
-0.516

(0.082)
(0.070)
(0.083)
(0.084)

-0.186
-0.162
-0.014

(0.049)
(0.048)
(0.039)

-0.146
0.062
0.237

(0.076)
(0.094)
(0.083)

-0.040
0.013
0.092

(0.078)
(0.076)
(0.064)

-0.285
-0.145
-0.004

(0.069)
(0.071)
(0.051)

-0.084
-0.150
-0.247

(0.067)
(0.070)
(0.055)

Notes: Each cell reports estimates from OLS regressions of a measure of mobility on the variable listed in each row, normalizing both the dependent and independent variables to have mean 0 and standard deviation 1 in the estimation sample,
so that univariate regression coefficients equal correlation coefficients. Standard errors, reported in parentheses, are clustered at the state level. The dependent variable in Columns 1-5 is our baseline measure of absolute upward mobility, the
expected rank of children whose parents are at the 25th national percentile. The dependent variable in Column 6 is relative mobility, the rank-rank slope in each CZ. All mobility estimates are constructed using the core sample (1980-82
cohorts) and baseline family income measures. Column 1 reports estimates from univariate unweighted regressions (raw correlation coefficients). Column 2 adds state fixed effects. Column 3 weights by Census 2000 population (and
normalizes variables by weighted standard deviations). In Column 4, we restrict to CZs that intersect a Metropolitan Statistical Area. In Column 5 we control for the black share and income growth between 2000 and 2006-2010 as measured in
Census data. The typical sample in Column 4 consists of 325 CZs that intersect MSAs. In the other columns the typical sample consists of the 709 CZs with at least 250 children in the core sample; however, some rows have fewer observations
due to missing values for the independent variable. See Section VI, Online Data Table IX, and Appendix G for definitions of each of the correlates analyzed in this table. See Online Data Table VIII for the CZ-level data on each covariate.

FIGURE I: Association between Childrens and Parents Incomes

80
60
40
20

Slope [Par Inc < P90] = 0.335

(0.0007)
Slope [P90 < Par Inc < P99] = 0.076
(0.0019)

Mean Child Household Income ($1000s)

100

A. Level of Child Family Income vs. Parent Family Income

100

200

300

400

Parent Household Income ($1000s)

10

12

0%
5%
10%
15%
20%
Percentage of Children with Zero Income

10.5
10

IGE = 0.344
(0.0004)
IGE [Par Inc P10-P90] = 0.452
(0.0007)

9.5

Mean Log Child Income

11

B. Log Child Family Income vs. Log Parent Family Income

14

Log Parent Income

Mean Log Child Inc.
Frac. Children with Zero Inc.

Notes: These figures present non-parametric binned scatter plots of the relationship between child income and parent income.
Both figures are based on the core sample (1980-82 birth cohorts) and baseline family income definitions for parents and
children. Child income is the mean of 2011-2012 family income (when the child is approximately 30 years old), while parent
income is mean family income from 1996-2000. Incomes are in 2012 dollars. To construct Panel A, we bin parent family income
into 100 equal-sized (centile) bins and plot the mean level of child income vs. mean level of parent income within each bin. For
scaling purposes, we do not show the point for the top 1% in Panel A. In the top 1% bin, mean parent income is $1.4 million
and mean child income is $114,000. In Panel B, we again bin parent family income into 100 bins and plot mean log income for
children (left y-axis) and the fraction of children with zero family income (right y-axis) vs. mean parents log income. Children
with zero family income are excluded from the log income series. In both panels, the 10th and 90th percentile of parents
income are depicted in dashed vertical lines. The coefficient estimates and standard errors (in parentheses) reported on the
figures are obtained from OLS regressions on the microdata. In Panel A, we report separate slopes for parents below the 90th
percentile and parents between the 90th and 99th percentile. In panel B, we report slopes of the log-log regression (i.e., the
intergenerational elasticity of income or IGE) in the full sample and for parents between the 10th and 90th percentiles.

FIGURE II: Association between Childrens and Parents Percentile Ranks

50
40
30

Mean Child Income Rank

60

70

A. Mean Child Income Rank vs. Parent Income Rank in the U.S.

20

Rank-Rank Slope = 0.341

(0.0003)
0

10

20

30

40

50

60

70

80

90

100

Parent Income Rank

50
40
30

Mean Child Income Rank

60

70

B. Cross-Country Comparisons

20

Rank-Rank Slope (Denmark) = 0.180

(0.006)
Rank-Rank Slope (Canada) = 0.174
(0.005)
0

10

20

30

40

50

60

Parent Income Rank

United States
Denmark

70

80

90

100

Canada

Notes: These figures present non-parametric binned scatter plots of the relationship between childrens and parents percentile
income ranks. Both figures are based on the core sample (1980-82 birth cohorts) and baseline family income definitions for
parents and children. Child income is the mean of 2011-2012 family income (when the child is approximately 30 years old),
while parent income is mean family income from 1996-2000. Children are ranked relative to other children in their birth
cohort, while parents are ranked relative to all other parents in the core sample. Panel A plots the mean child percentile rank
within each parent percentile rank bin. The series in triangles in Panel B plots the analogous series for Denmark, computed
by Boserup, Kopczuk, and Kreiner (2013) using a similar sample and income definitions. The series in squares plots estimates
of the rank-rank series using the decile-decile transition matrix from Corak and Heisz (1999). The series in circles in Panel
B reproduces the rank-rank relationship in the U.S. from Panel A as a reference. The slopes and best-fit lines are estimated
using an OLS regression on the microdata for the U.S. and on the binned series (as we do not have access to the microdata)
for Denmark and Canada. Standard errors are reported in parentheses.

FIGURE III: Robustness of Intergenerational Mobility Estimates

0.2
0

0.1

Rank-Rank Slope

0.3

0.4

A. Lifecycle Bias: Rank-Rank Slopes by Age of Child

22

25

28
31
34
37
40
Age at which Childs Income is Measured
Population
SOI 0.1% Random Sample

0.2
0

0.1

Rank-Rank Slope

0.3

0.4

B. Attenuation Bias: Rank-Rank Slopes by Number of Years Used to Measure Parent Income

10

13

16

Years Used to Compute Mean Parent Income

Notes: This figure evaluates the robustness of the rank-rank slope estimated in Figure IIa to changes in the age at which
child income is measured (Panel A) and the number of years used to measure parents income (Panel B). In both panels, child
income is defined as mean family income in 2011-2012. In Panel A, parent income is defined as mean family income from
1996-2000. Each point in Panel A shows the slope coefficient from a separate OLS regression of child income rank on parent
income rank, varying the childs birth cohort and hence the childs age in 2011-12 when the childs income is measured. The
circles use the extended sample in the population data, while the triangles use the 0.1% Statistics of Income stratified random
sample. The first point in Panel A corresponds to the children in the 1990 birth cohort, who are 21-22 when their incomes
are measured in 2011-12 (denoted by age 22 on the figure). The last point for which we have population-wide estimates
corresponds to the 1980 cohort, who are 31-32 (denoted by 32) when their incomes are measured. The last point in the SOI
sample corresponds to the 1971 cohort, who are 40-41 (denoted by 41) when their incomes are measured. The dashed line
is a lowess curve fit through the SOI 0.1% sample rank-rank slope estimates. In Panel B, we focus on children in the core
sample (1980-82 birth cohorts) in the population data. Each point in this figure shows the coefficient from the same rank-rank
regression as in Figure IIa, varying the number of years used to compute mean parent income. The first point uses parent
income data for 1996 only to define parent ranks. The second point uses mean parent income from 1996-1997. The last point
uses mean parent income from 1996-2012, a 17 year average.

FIGURE IV: Gradients of College Attendance and Teenage Birth by Parent Rank

100

20

20

Coll. Attendance Slope = 0.675

(0.0005)
Coll. Quality Gradient (P75-P25) = 0.191
(0.0010)

40
60
80
College Quality Rank at Age 20

Percent Attending College at Ages 18-21

40
60
80
100

A. Childrens College Attendance Rate and Quality vs. Parent Income Rank

10

20

30

40
50
60
70
80
90
100
Parent Income Rank
College Attendance Rate
College Quality Rank

20
10

Slope = -0.298
(0.0006)

Teenage Birth Rate (%)

30

B. Female Childrens Teenage Birth Rate vs. Parent Income Rank

10

20

30

40

50

60

70

80

90

100

Parent Income Rank

Notes: These figures present non-parametric binned scatter plots of the relationship between childrens college attendance
rates (Panel A, circles), college quality rank (Panel A, triangles), and teenage birth rates (Panel B) vs. parents percentile
rank. Both figures are based on the core sample (1980-82 birth cohorts). Parent rank is defined based on mean family income
from 1996-2000. In Panel A, the circles plot the fraction of children ever attending college between age 18-21 within each
parent-income percentile bin; the triangles plot the average college quality rank at age 20 within each parent-income percentile
bin. College attendance is defined as the presence of a 1098-T form filed by a college on behalf of the student. College quality
rank is defined as the percentile rank of the college that the child attends at age 20 based on the mean earnings at age 31 of
children who attended the same college (children who do not attend college are included in a separate no college group);
see Section III.B for further details. Panel B plots the fraction of female children who give birth while teenagers within each
parental percentile bin. Having a teenage birth is defined as ever claiming a dependent child who was born while the mother
was aged 13-19. The slopes and best-fit lines for college attendance and teenage birth are estimated using linear regressions
of the outcome of interest on parent income rank in the microdata. We regress college quality rank on a quadratic in parent
rank to match the non-linearity of the relationship. The college quality gradient is defined as the difference between the fitted
values for children with parents at the 75th percentile and parents at the 25th percentile using this quadratic specification.

FIGURE V: Intergenerational Mobility in Selected Commuting Zones

70
60
50
40
30

Salt Lake City:

Charlotte:

!""

"

!""

"

= 0.264,
= 0.397,

!"
!"

= 46.2
= 35.8

20

Mean Child Rank in National Income Distribution

A. Salt Lake City vs. Charlotte

20

40

60

80

100

Parent Rank in National Income Distribution

Salt Lake City

Charlotte

70
60
50
40
30

San Francisco:
Chicago:

!""

"

!""

"

= 0.250,
= 0.393,

!"
!"

= 44.4
= 39.4

20

Mean Child Rank in National Income Distribution

B. San Francisco vs. Chicago

20

40

60

80

100

Parent Rank in National Income Distribution

San Francisco

Chicago

Notes: These figures present non-parametric binned scatter plots of the relationship between child and parent income ranks
in selected CZs. Both figures are based on the core sample (1980-82 birth cohorts) and baseline family income definitions for
parents and children. Children are assigned to commuting zones based on the location of their parents (when the child was
claimed as a dependent), irrespective of where they live as adults. Parent and child percentile ranks are always defined at
the national level, not the CZ level. To construct each series, we group parents into 50 equally sized (two percentile point)
bins and plot the mean child percentile rank vs. the mean parent percentile rank within each bin. We report two measures
of mobility based on the rank-rank relationships in each CZ. The first is relative mobility (
r100 r0 ), which is 100 times the
rank-rank slope estimate. The second is absolute upward mobility (
r25 ), the predicted child income rank at the 25th percentile
of parent income distribution, depicted by the dashed vertical line in the figures. All mobility statistics and best-fit lines are
estimated on the underlying microdata (not the binned means).

FIGURE VI: The Geography of Intergenerational Mobility

A. Absolute Upward Mobility: Mean Child Rank for Parents at 25th Percentile (
r25 ) by CZ

B. Relative Mobility: Rank-Rank Slopes (

r100

r0 )/100 by CZ

Notes: These figures present heat maps of our two baseline measures of intergenerational mobility by commuting zone (CZ).
Both figures are based on the core sample (1980-82 birth cohorts) and baseline family income definitions for parents and
children. Children are assigned to commuting zones based on the location of their parents (when the child was claimed as
a dependent), irrespective of where they live as adults. In each CZ, we regress child income rank on a constant and parent
income rank. Using the regression estimates, we define absolute upward mobility (
r25 ) as the intercept + 25(rank-rank
slope), which corresponds to the predicted child rank given parent income at the 25th percentile (see Figure V). We define
relative mobility as the rank-rank slope; the difference between the outcomes of the child from the richest and poorest family
is 100 times this coefficient (
r100 r0 ). The maps are constructed by grouping CZs into ten deciles and shading the areas so
that lighter colors correspond to higher absolute mobility (Panel A) and lower rank-rank slopes (Panel B). Areas with fewer
than 250 children in the core sample, for which we have inadequate data to estimate mobility, are shaded with the cross-hatch
pattern. In Panel B, we report the unweighted and population-weighted correlation coefficients between relative mobility and
absolute mobility across CZs. The CZ-level statistics underlying these figures are reported in Online Data Table V.

FIGURE VII: Relationship Between Absolute and Relative Mobility

0.5
0
-0.5

Mean Pivot Point = 85.1th Percentile

-1.0

Coef. from Regression of Child Rank on Relative Mobility

A. Association Between Absolute and Relative Mobility by Parent Income Rank

20

40

60

80

100

Parent Rank in National Income Distribution

= 85.1

60

Average Pivot Point:

50

Low Rank-Rank Slope

30

40

High Rank-Rank Slope

20

Child Rank in National Income Distribution

70

B. Illustrative Schematic of Pivot in Rank-Rank Relationship

20

40

60

80

100

Parent Rank in National Income Distribution

Notes: These figures illustrate the correlation between relative mobility and absolute mobility at various percentiles of the
income distribution. To construct Panel A, we first calculate the mean income rank of children in CZ c with parents in
(national) percentile p, denoted by
pc . We then run a CZ-level regression of
pc on relative mobility (
r100c r0c ) at each
percentile p separately. Panel A plots the resulting regression coefficients p vs. the percentile p. The coefficient p can be
interpreted as the mean impact of a 1 unit increase in relative mobility on the absolute outcomes of children whose parents are
at percentile p. We also plot the best linear fit across the 100 coefficients. This line, estimated using an OLS regression, crosses
zero at percentile p = 85.1. This implies that increases in relative mobility are associated with higher expected rank outcomes
for children with parents below percentile 85.1 and lower expected rank outcomes for children with parents above percentile
85.1. To illustrate the intuition for this result, Panel B plots hypothetical rank-rank relationships in two representative CZs,
one of which has more relative mobility than the other. Panel A implies that in such a pairwise comparison, the two rank-rank
relationships cross at the 85th percentile on average, as illustrated in Panel B.

FIGURE VIII: Correlates of Spatial Variation in Upward Mobility

G SEG
MIG LAB COLL TAX FAM SOC K-12 INC

Frac. Black Residents (-)

Racial Segregation (-)
Segregation of Poverty (-)
Frac. < 15 Mins to Work (+)
Mean Household Income (+)
Gini Coef. (-)
Top 1% Inc. Share (-)
Student-Teacher Ratio (-)
Test Scores (Inc Adjusted) (+)
High School Dropout (-)
Social Capital Index (+)
Frac. Religious (+)
Violent Crime Rate (-)
Frac. Single Moms (-)
Divorce Rate (-)
Frac. Married (+)
Local Tax Rate (+)
State EITC Exposure (+)
Tax Progressivity (+)
Colleges per Capita (+)
College Tuition (-)
Coll Grad Rate (Inc Adjusted) (+)
Manufacturing Share (-)
Chinese Import Growth (-)
Teenage LFP Rate (+)
Migration Inflow (-)
Migration Outflow (-)
Frac. Foreign Born (-)

0.2

0.4

0.6

0.8

1.0

Correlation
Notes: This figure shows the correlation of various CZ-level characteristics with absolute upward mobility (
r25 ) across CZs.
For each characteristic listed on the y axis, the dot represents the absolute value of the unweighted correlation of the variable
with r25 across CZs. The horizontal bars show the 95% confidence interval based on standard errors clustered at state level.
Positive correlations are shown by (+) on the y axis; negative correlations are shown by (-). We consider covariates in ten
broad categories: racial demographics, segregation, properties of the income distribution, K-12 education, social capital, family
structure, local tax policies, college education, labor market conditions, and migration rates. The categories with the highest
correlations are highlighted. See Column 1 of Appendix Table VII for the point estimates corresponding to the correlations
plotted here. See Section VI, Online Data Table IX, and Online Appendix G for definitions of each of the correlates. CZ-level
data on the covariates used in this figure are reported in Online Data Table VIII.

FIGURE IX: Race and Upward Mobility

A. Upward Mobility for Individuals in 80%+ White ZIP Codes

.6
.4
.2

on

Coef. from Regression of

.8

B. Impact of Changing Racial Composition of Sample on CZ-Level Estimates of Upward Mobility

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Fraction of White Individuals in Restricted Sample

Empirical Estimates

Prediction with No Spatial

Heterogeneity Cond. on Race

Notes: Panel A presents a heat map of absolute upward mobility for individuals living in ZIP codes with 80% or more white
residents. This figure replicates Figure VIa, restricting the sample used to estimate the rank-rank regression in each CZ to
parents living in ZIP codes with 80% or more white residents. Note that we color the entire CZ based on the resulting estimate
of upward mobility (not just the ZIP codes used in the estimation) for comparability to other figures. CZs with fewer than
250 children living in ZIP codes with >80% white share are omitted and shaded with the cross-hatch pattern. We report the
unweighted and population-weighted correlation coefficients between this measure and absolute upward mobility presented
in Figure VIa across CZs. To construct Panel B, we first compute upward mobility in each CZ, restricting the sample to
w
w
individuals living in ZIP codes that are more than w% white, which we denote by r25,c
. We then regress r25,c
on r25,c , our
baseline estimates of upward mobility based on the full sample, using an unweighted OLS regression with one observation
per CZ with available data. We vary w from 0% to 95% in increments of 5% and plot the resulting regression coefficients
against the fraction of white individuals in each of the subsamples. The confidence interval, shown by the dotted lines around
the point estimates, is based on standard errors clustered at the state level. The dashed diagonal line shows the predicted
relationship if there were no spatial heterogeneity in upward mobility conditional on race.

ONLINE APPENDIX FIGURE I

Dollar-Weighted vs. Traditional IGE Estimates

11.5
11
10.5
10

Mean of Log Child Income (triangles)

Dollar-Weighted IGE= 0.335

(0.008)
Dollar-Weighted IGE P10-P90 = 0.414
(0.004)

9.5

10.5

11

11.5

Baseline IGE = 0.344

(0.0004)
Baseline IGE P10-P90 = 0.452
(0.0007)

10

Log of Mean Child Income (circles)

12

A. Log of Mean Child Income vs. Mean of Log Child Income

10
12
14
Log Mean Parent Income
Log of Mean Child Income
Mean of Log Child Income

0.2
0.1
0

Dollar-Weighted IGE

0.3

0.4

B. Dollar-Weighted IGE by Age of Child Income Measurement

22

24

26

28

30

32

Age at which Child's Income is Measured

Notes: This figure compares dollar-weighted (Mitnik et al. 2014) and traditional IGE estimates. Panel A is based on the core
sample (1980-82 birth cohorts) and baseline family income definitions for parents and children. The series in circles (left axis)
plots log of mean child income against log of mean parent income. The series is constructed by taking the logs of the points in
Figure Ia; however, here we do not omit the top income bin. The slope coefficients, which correspond to the dollar-weighted
IGE defined in Appendix C, and standard errors are estimated by OLS on the binned data. The series in triangles (right
axis) reports the mean of log child income vs. the mean of log parent income (reproducing the series in Figure Ib). The slope
coefficients and standard errors for the traditional IGE are estimated on the microdata. The dashed lines in Panel A show
the 10th and 90th percentiles of the parent income distribution. Panel B shows how the dollar-weighted IGE varies with the
age at which child income is measured. We estimate the dollar-weighted IGE by grouping parents into 100 bins based on their
income rank and regressing the log of mean child income on the log of mean parent income across the 100 bins. The figure
plots the slope from this regression vs. the age at which child income is measured. We measure child income in 2011-12 and
analyze how the IGE varies across birth cohorts, as in Figure IIIa; see notes to that figure for further details. The first point
corresponds to the children in the 1990 birth cohort, who are 21-22 when their incomes are measured in 2011-12 (denoted by
age 22 on the figure). The last point corresponds to the 1980 cohort, who are 31-32 (denoted by 32) when their incomes are
measured.

ONLINE APPENDIX FIGURE II

Additional Evidence on Robustness of Intergenerational Mobility Estimates
B. Rank-Rank Slope by Age of Parent Income Measurement

0.3

22

25

0.1

0.2

Rank-Rank Slope

0.4
0.2

Rank-Rank Slope

0.6

0.4

A. IGE Estimates by Age of Child Income Measurement

28
31
34
37
40
Age at which Childs Income is Measured
Population
SOI 0.1% Random Sample

41

45

47

49

51

53

55

Mothers Age when Parent Income Measured

C. College Attendance Gradient by Age of Child

D. Rank-Rank Slope by Number of Years

Used to Measure Child Income

0.2
0

0.2

0.1

0.4

Rank-Rank Slope

0.6

0.3

0.8

0.4

When Parent Income is Measured

College Attendance Gradient

43

12

15

Age of Child when Parent Income is Measured

18

Years used to Compute Mean Child Income

Notes: This figure evaluates the robustness of intergenerational mobility measures to lifecycle and attenuation bias. Panel A
evaluates the robustness of the IGE to changes in the age at which child income is measured. Panel B evaluates the robustness
of the rank-rank slope to changes in the age at which parent income is measured. Panel C evaluates the robustness of the
college attendance gradient to the age of the child when parent income is measured. Panel D evaluates the robustness of
the rank-rank slope to the number of years used to measure the childs income. In Panel A, we estimate the log-log IGE
(excluding children with zero income), varying the age at which child income is measured. We restrict the sample to parents
with income between the 10th and 90th percentile when estimating the IGE, as shown in Figure Ib. We measure child income
in 2011-12 and analyze how the IGE varies across birth cohorts, as in Figure IIIa; see notes to that figure for further details.
In Panel B, each point shows the slope coefficient from an OLS regression of child income rank on parent income rank (as in
Figure IIa), using the core sample and varying the age at which parent income rank is measured. The first point measures
parent income in 1996, when the mean age of mothers is 41. The last point measures income in 2010, when parents are 55.
Panel C reproduces Appendix Figure 2b from Chetty et al. (2014). In this figure, each point shows the slope coefficient from
an OLS regression of an indicator for the child attending college at age 19 on parent income rank (similar to Figure IVa),
varying the year in which parent income rank is measured from 1996 to 2011. In this series, we use data from the 1993 birth
cohort, which allows us to analyze parent income starting when children are 3 years old in 1996. We list the age of the child
on the x axis to evaluate whether the gradient differs when children are young (although parent age is of course also rising in
lockstep). In Panel D, each point shows the slope coefficient from the same rank-rank regression as in Panel B using the core
sample, but here we always use a five-year (1996-2000) mean to measure parent income and vary the number of years used to
compute mean child income. The point for one year measures child income in 2012 only. The point for two years uses mean
child income in 2011-12. We continue adding data for prior years; the 6th point uses mean income in years 2007-2012.

ONLINE APPENDIX FIGURE III

Boston Commuting Zone

Essex

Middlesex
Worcester

Suffolk

Boston

Norfolk

Plymouth

Barnstable

Notes: This figure shows a map of the counties that comprise the Boston Commuting Zone. The city of Boston is shown by
the arrow.

Boston, MA

Bridgeport, CT

Chicago, IL

Cleveland, OH

Dallas, TX

Detroit, MI

Houston, TX

Los Angeles, CA

Miami, FL

Minneapolis, IN

New York, NY

Newark, NJ

Philadelphia, PA

Phoenix, AZ

Sacramento, CA

San Diego, CA

San Francisco, CA

Seattle, WA

Washington DC

.5

.4
.2

1 1.5 2 2.5

.8
.6

.5

.4
.2

1 1.5 2 2.5

.8
.6

.5

.4
.2

1 1.5 2 2.5

.8
.6
.2

.5

.4

Mean Child Rank in National Distribution

.6

1 1.5 2 2.5

.8

Atlanta, GA

Relative Density of Parent Income Distribution

ONLINE APPENDIX FIGURE IV

Rank-Rank Relationships and Income Distributions in the 20 Largest CZs

50

100

50

100

50

100

50

100

50

100

Parents' Percentile Rank in National Income Distribution

Notes: These figures present non-parametric binned scatter plots (shown by the points and solid line, left y-axis) of the
relationship between child and parent income ranks in the twenty largest CZs based on population in the 2000 Census. All
figures are based on the core sample (1980-82 birth cohorts) and baseline family income definitions for parents and children.
Children are assigned to commuting zones based on the location of their parents. Parent and child percentile ranks are always
defined at the national level, not the CZ level. To construct each rank-rank series, we group parents into 50 equally sized
(two percentile point) bins and plot the mean child percentile rank vs. the mean parent percentile rank within each bin. The
dashed curve (right y-axis) in each panel depicts the income distribution in the CZ relative to the national distribution. This
curve plots the share of parents with income in each bin in the CZ divided by the share in the same bin in the national income
distribution. By construction, this curve averages to one in each CZ, shown by the horizontal dashed line in each panel.

ONLINE APPENDIX FIGURE V

Estimates of Absolute Upward Mobility Pooling 1980-82 and 1980-85 Cohorts

Notes: The figure presents the map of absolute upward mobility by CZ shown on the project homepage (www.equality-ofopportunity.org). For the 709 CZs that have at least 250 children in the 1980-82 cohorts, we compute absolute upward mobility
exactly as in Figure VIa. For an additional 22 CZs that have fewer than 250 children in the 1980-82 cohorts but at least
250 children in the 1980-85 cohorts, we report estimates of absolute upward mobility using the 1980-85 birth cohorts. We
estimate absolute upward mobility using exactly the same procedure as described in the notes to Figure VIa. The map is
constructed by grouping CZs into ten deciles based on the hybrid absolute mobility measure and shading the areas so that
lighter colors correspond to higher absolute mobility. Areas with fewer that 250 children in the 1980-85 cohorts are shaded
with the cross-hatch pattern.The CZ-level statistics underlying this map are reported in Online Data Table V.

ONLINE APPENDIX FIGURE VI

Alternative Measures of Upward Mobility
A. Absolute Upward Mobility Adjusted for Local Cost-of-Living

B. Probability of Reaching Top Quintile from Bottom Quintile

C. Fraction of Children Above Poverty Line Given Parents at 25th Percentile

Notes: These figures present heat maps for alternative measures of upward income mobility. Children are assigned to commuting zones based on the location of their parents (when the child was claimed as a dependent), irrespective of where they live
as adults. All panels use baseline family income definitions for parents. Panels A and C use the core sample (1980-82 birth
cohorts) and panel B uses the 1980-85 birth cohorts. Panel A replicates Figure VIa, adjusting for differences in cost-of-living
across areas. To construct this figure, we first deflate parent income by a cost-of-living index (COLI) for the parents CZ when
he/she claims the child as a dependent and child income by a COLI for the childs CZ in 2012. We then compute parent
and child ranks using the resulting real income measures and replicate the procedure in Figure VIa exactly. The COLI is
constructed using data from the ACCRA price index combined with information on housing values and other variables as
described in Appendix A. Panel B presents a heat map of the probability that a child reaches the top quintile of the national
family income distribution for children conditional on having parents in the bottom quintile of the family income distribution
for parents. These probabilities are taken directly from Online Data Table VI. Panel C shows the fitted values at parent
rank 25 from a regression of an indicator for child family income being above the poverty line on parent income rank (see
Appendix F for details). The maps are constructed by grouping CZs into ten deciles and shading the areas so that lighter colors
correspond to higher mobility. Areas with fewer that 250 children in the core sample (or the 1980-85 cohorts for Panel B), for
which we have inadequate data to estimate mobility, are shaded with the cross-hatch pattern. We report the unweighted and
population-weighted correlation coefficient across CZs between these mobility measures and the baseline measure in Figure
VIa. The CZ-level statistics underlying Panels A and C are reported in Online Data Table V.

ONLINE APPENDIX FIGURE VII

The Geography of College Attendance by Parent Income Gradients
A. Slope of College Attendance-Parent Rank Gradients by CZ

B. College Attendance Rates for Children with Parents at the 25th Percentile by CZ

Notes: To construct these figures, we regress an indicator for college attendance on parent income rank (in the national
distribution) for each CZ separately. College attendance is defined by the presence of a 1098-T form filed by a college on
behalf of the student. We use the core sample (1980-82 birth cohorts) and baseline family income definitions for parents.
Children are assigned to commuting zones based on the location of their parents (when the child was claimed as a dependent),
irrespective of where they live as adults. In Panel A, we map the slope coefficients on the college attendance indicator from
the CZ-level regressions. Panel B maps the fitted values from the regressions at parent rank 25. The maps are constructed
by grouping CZs into ten deciles and shading the areas so that lighter colors correspond to higher mobility (smaller slopes
in Panel A and higher fitted values in Panel B). Areas with fewer that 250 children in the core sample, for which we have
inadequate data to estimate mobility, are shaded with the cross-hatch pattern. We report the unweighted and populationweighted correlation coefficients across CZs between these mobility measures and the baseline measures in Figure VI. The
CZ-level statistics underlying these figures are reported in Online Data Table V.

ONLINE APPENDIX FIGURE VIII

The Geography of College Quality by Parent Income Gradients
A. College Quality Gradient (P75-P25) by CZ

B. Mean College Quality Rank for Children with Parents at the 25th Percentile by CZ

Notes: To construct these figures, we regress college quality rank on a quadratic in parent income rank (in the national
distribution) for each CZ separately. College quality rank is defined as the percentile rank of the college that the child attends
at age 20 based on the mean earnings at age 31 of children who attended the same college (children who do not attend college
are included in a separate no college group); see Section III.B for further details. We use the core sample (1980-82 birth
cohorts) and baseline family income definitions for parents. Children are assigned to commuting zones based on the location
of their parents (when the child was claimed as a dependent), irrespective of where they live as adults. In Panel A, we map
the college quality income gradient, defined as the difference between the fitted values at parent rank 75 and parent rank 25
from the CZ-level regressions. Panel B maps the fitted values of college quality rank at parent rank 25 from these regressions.
The maps are constructed by grouping CZs into ten deciles and shading the areas so that lighter colors correspond to higher
mobility (smaller gradients in Panel A and higher fitted values in Panel B). Areas with fewer that 250 children in the core
sample, for which we have inadequate data to estimate mobility, are shaded with the cross-hatch pattern. We report the
unweighted and population-weighted correlation coefficients across CZs between these mobility measures and the baseline
measures in Figure VI. The CZ-level statistics underlying these figures are reported in Online Data Table V.

ONLINE APPENDIX FIGURE IX

The Geography of Teenage Birth by Parent Income Gradients
A. Slope of Teenage Birth-Parent Rank Gradients by CZ

B. Teenage Birth Rates for Children with Parents at the 25th Percentile by CZ

Notes: To construct these figures, we regress an indicator for teenage birth on parent income rank (in the national distribution)
for each CZ separately. Teenage birth is defined as ever claiming a dependent child who was born while the mother was aged
13-19. We use female children in the core sample (1980-82 birth cohorts) and baseline family income definitions for parents.
Children are assigned to commuting zones based on the location of their parents (when the child was claimed as a dependent),
irrespective of where they live as adults. In Panel A, we map the slope coefficient on the teenage birth indicator from the CZlevel regressions. Panel B maps the fitted values from these regressions at parent income rank 25. The maps are constructed
by grouping CZs into ten deciles and shading the areas so that lighter colors correspond to smaller slopes (in magnitudes)
in Panel A and smaller fitted values in Panel B. Areas with fewer that 250 female children in the core sample, for which we
have inadequate data to estimate mobility measures, are shaded with the cross-hatch pattern. We report the unweighted and
population-weighted correlation coefficients across CZs between these mobility measures and the baseline measures in Figure
VI. The CZ-level statistics underlying these figures are reported in Online Data Table V.

ONLINE APPENDIX FIGURE X

Segregation and Upward Mobility

40

45

Correlation = -0.361
(0.045)

35

Upward Mobility

50

55

A. Upward Mobility vs. Theil Index of Racial Segregation in CZ

0.01

0.02

0.05

0.14

0.37

Theil Index of Racial Segregation in 2000 (log scale)

40

45

Correlation = -0.393
(0.065)

35

Upward Mobility

!"

50

55

B. Upward Mobility vs. Rank-Order Index of Income Segregation in CZ

0.002

0.007

0.018

0.050

0.135

Rank-Order Index of Income Segregation (log scale)

Notes: Panel A presents a binned scatter plot of absolute upward mobility (

r25 ) vs. a multi-group Theil index of racial
segregation (based on census tract level data from the 2000 Census). To construct this figure, we group CZs into twenty
equally sized bins (vingtiles) based on their segregation index. We then plot the mean level of absolute upward mobility vs.
the mean segregation index within each of the twenty bins (using a log scale on the x axis). Panel B presents an analogous
binned scatter plot of absolute upward mobility vs. the rank-order index of income segregation from Reardon (2011). See
text for details on the construction of these segregation indices. Note that these binned scatter plots provide a non-parametric
representation of the conditional expectation function, but they do not show the variance in the underlying data across CZs.
The correlations between the variables are estimated using the underlying CZ-level data, with standard errors (reported in
parentheses) clustered by state. The correlations are estimated in levels (not logs) for consistency with Appendix Table VII.

ONLINE APPENDIX FIGURE XI

Local Income Distributions and Upward Mobility
B. Upward Mobility vs. Gini Coefficient in CZ
The Great Gatsby Curve Within the U.S.

55
)

50
45

Correlation = -0.578
(0.093)

40

Upward Mobility

55
45
40

Upward Mobility

50

A. Upward Mobility vs. Mean Income in CZ

35

35

Correlation = 0.050
(0.071)

22.0

26.9

32.9

40.1

49.0

0.3

Mean Income per Working Age Adult ($1000s, log scale)

0.4

0.5

0.6

Gini Coef. for Parent Family Income (1996-2000)

40

45

Correlation = -0.190
(0.072)

35

Upward Mobility

50

55

C. Upward Mobility vs. Top 1% Income Share in CZ

0.05

0.08

0.14

0.22

Top 1% Income Share Based on Parent Family Income (1996-2000, log scale)

Notes: Panel A presents a binned scatter plot of absolute upward mobility (

r25 ) vs. mean income per working age adult
in the CZ (based on data from the 2000 Census). To construct this figure, we group CZs into twenty equally sized bins
(vingtiles) based on mean income levels. We then plot the mean level of absolute upward mobility vs. the mean income
level within each of the twenty bins (using a log scale on the x axis). Panel B presents an analogous binned scatter plot of
absolute upward mobility vs. the Gini coefficient in the CZ, computed based on the core sample and mean parent income for
1996-2000. Panel C presents a binned scatter plot of absolute upward mobility vs. the fraction of income in the CZ accruing
to parents in the top 1% of the local distribution (using a log scale on the x axis), again using the core sample and parents
average income for 1996-2000. Note that these binned scatter plots provide a non-parametric representation of the conditional
expectation function, but they do not show the variance in the underlying data across CZs. The correlations between the
variables are estimated using the underlying CZ-level data, with standard errors (reported in parentheses) clustered by state.
The correlations are estimated in levels (not logs) for consistency with Appendix Table VII.

ONLINE APPENDIX FIGURE XII

Single-Parent Families and Upward Mobility

50
40

45

Correlation = -0.764
(0.074)

35

Upward Mobility

!"

55

A. Upward Mobility vs. Fraction Single Mothers in CZ

10

15

20

25

30

35

% Single Mothers

50
40

45

Correlation = -0.662
(0.087)

35

Upward Mobility

!"

55

B. Upward Mobility for Children with Married Parents vs. Fraction Single Mothers in CZ

10

15

20

25

30

35

% Single Mothers

Notes: Panel A presents a binned scatter plot of absolute upward mobility (

r25 ) vs. the fraction of children being raised by
single mothers in the CZ (based on data from the 2000 Census). To construct this figure, we group CZs into twenty equally
sized bins (vingtiles) based on the fraction of single parents. We then plot the mean level of absolute upward mobility vs.
the mean fraction of single parents within each of the twenty bins. Panel B replicates Panel A, restricting the sample used
to estimate upward mobility in each CZ to children whose own parents are married in the year they first claim the child as
a dependent. Note that these binned scatter plots provide a non-parametric representation of the conditional expectation
function, but they do not show the variance in the underlying data across CZs. The correlations between the variables are
estimated using the underlying CZ-level data, with standard errors (reported in parentheses) clustered by state.

.2

.25

Rank-Rank Slope
.3
.35

.4

ONLINE APPENDIX FIGURE XIII

Predicted vs. Actual Time Trends in Relative Mobility

1970

1980
Birth Cohort
Rank-Rank Slope
Gini Bottom 99%

1990

Coll. Forecast of R-R Slope

Frac. Religious

HS Dropout

Racial Seg.
Frac. Single Mothers

Notes: This figure compares actual trends in rank-rank slopes at the national level, estimated in Chetty et al. (2014), with
projected changes based on trends in the five factors most strongly correlated with differences in mobility across CZs in the
cross-section. The series in circles is from Chetty et al. (2014, Figure 2). The solid circles show estimates of rank-rank
slopes by birth cohort using the SOI 0.1% sample. The open circles show forecasts of the rank-rank slope based on income
measured at age 26 and the college attendance rates using the population data. The other series show projections of trends,
each based on a different factor: (1) Theil index of racial segregation, (2) high school dropout rate, (3) Gini coefficient, (4)
violent crime arrest rate, and (5) fraction of single parents. We construct these projections based on unweighted univariate
CZ-level regressions of relative mobility on each factor separately. We normalize the projections (by adding a constant) so
that their values match the mean observed rank-rank slope (i.e., the mean value of the series in circles) from 1971-1990. See
Appendix I for further details.