The Fading American Dream:
Trends in Absolute Income Mobility Since 1940

Raj Chetty,1 David Grusky,2 Maximilian Hell,2Nathaniel Hendren,3 Robert Manduca,4 and Jimmy Narang5

December 2016
Abstract
We estimate rates of “absolute income mobility” – the fraction of children who earn more than theirparents – by combining historical data from Census and CPS cross-sections with panel data for recent
birth cohorts from de-identified tax records. Our approach overcomes the key data limitation that has
hampered research on trends in intergenerational mobility: the lack of large panel datasets linking parents
and children. We find that rates of absolute mobility have fallen from approximately 90% for children
born in 1940 to 50% for children born in the 1980s. The result that absolute mobility has fallen sharply
over the past half century is robust to the choice of price deflator, the definition of income, andaccounting for taxes and transfers. In counterfactual simulations, we find that increasing GDP growth
rates alone cannot restore absolute mobility to the rates experienced by children born in the 1940s. In
contrast, changing the distribution of growth across income groups to the more equal distribution
experienced by the 1940 birth cohort would reverse more than 70% of the decline in mobility. These
results imply that reviving the “American Dream” of high rates of absolute mobility would require
economic growth that is spread more broadly across the income distribution.

Affiliations
1

Stanford University, Dept. of Economics

2

Stanford University, Dept. of Sociology

3

Harvard University, Dept. of Economics

4

Harvard University, Dept. of Sociology

5

University of California-Berkeley, Dept. of Economics



We thank Rebecca Diamond, Guido Imbens, Xavier Jaravel, Sean Reardon, and numerous seminar participants forhelpful comments, Robert Fluegge and our other pre-doctoral fellows for outstanding research assistance, and David
Leonhardt for posing the question that led to this research. This paper incorporates results from an independentworking paper by Robert Manduca entitled “Opportunity No More: Declining Absolute Mobility in the UnitedStates, 1940-2010.” This research was funded by Stanford University, Harvard University, the Bill and Melinda
Gates Foundation, and the Robert Wood Johnson Foundation.

One of the defining features of the “American Dream” is the ideal that children have a higher
standard of living than their parents (Samuel 2012). When children are asked to assess theireconomic progress, they frequently compare their own standard of living to that of their parents(Goldthorpe 1987, Hoschschild 2016). Such measures of absolute income mobility – the fraction ofchildren earning or consuming more than their parents – are also often the focus of policy makers
when judging the degree of economic opportunity in the U.S. (e.g., Obama 2013).1
In this paper, we assess whether the U.S. is living up to this ideal by studying two questions.
First, what fraction of children earn more than their parents today? Second, how have rates ofabsolute mobility changed over time? Despite longstanding interest in these questions, evidence on
absolute income mobility remains scarce (Halikias and Reeves 2016), largely because of the lack oflarge, high-quality panel datasets linking children to their parents in the U.S.2
We overcome this data problem by developing a new method of estimating rates of absolutemobility that can be implemented using existing datasets covering the 1940-84 birth cohorts. Our
approach combines two inputs: marginal income distributions for parents and children and the
copula of the parent and child income distribution, defined as the joint distribution of parent andchild income ranks.
We estimate marginal income distributions for parents and children of the 1940-1984 birthcohorts using cross-sectional data from the decennial Census and Current Population Surveys (CPS).
In our baseline analysis, we measure income in pre-tax dollars at the household level when parents
and children are approximately thirty years old, adjusting for inflation using the CPI-U-RS. We thenshow the robustness of our results to a variety of specification choices, such as using alternative
inflation adjustments, adjusting for taxes and transfers, and measuring income at later ages.
We estimate the fraction of children who earn more than their parents in each birth cohort by
combining the marginal income distributions with the copula in each cohort. For recent birth cohorts,
we follow Chetty et al. (2014a) and directly estimate the joint distribution of parent and child ranks
using information from de-identified federal income tax returns covering the U.S. population. For
earlier birth cohorts, such population-level panel data are not available. We instead proceed in two
1

In a 2013 speech on economic mobility, President Obama noted that “people’s frustrations” are partly rooted “inthe fear that their kids won’t be better off than they were.”2
Prior research has studied the level of absolute income mobility for recent cohorts in the U.S. using panel surveys
such as the Panel Study of Income Dynamics (e.g., Isaacs, Sawhill, and Haskins 2008, Lopoo and DeLeire 2012;
Bengali and Daly 2013; Acs, Elliott, and Kalish 2016). These studies yield conflicting results because estimates ofabsolute mobility using available panel income datasets are sensitive to econometric assumptions and sample
specification (Halikias and Reeves 2016). To the best of our knowledge, there is no evidence on trends in absoluteincome mobility, although prior studies have documented declining absolute mobility in terms of occupational status(Hauser et al. 2000) and educational attainment (Hout and Janus 2011).

1

steps. First, we report estimates of absolute mobility under the assumption that the copula remained
stable across all birth cohorts, a benchmark motivated by evidence of copula stability since the 1970s(Chetty et al. 2014b).3 Because we have no evidence that the copula was in fact stable prior to 1970,
we then construct upper and lower bounds on absolute mobility for each birth cohort by searchingover all plausible copulas using linear programming methods.4 The key technical result of the paper
is that these bounds are very tight for the 1940-1950 birth cohorts, allowing us to obtain a reliable
time series on rates of absolute mobility despite the lack of historical panel data.
Using this methodology, we find that rates of absolute upward income mobility in the UnitedStates have fallen sharply since 1940. Under the benchmark of copula stability, the fraction ofchildren earning more than their parents fell from 92% in the 1940 birth cohort to 50% in the 1984birth cohort. Rates of absolute mobility fell the most for children with parents in the middle class.
Relaxing the copula stability assumption for earlier cohorts, we find that the rate of absolutemobility for the 1940 birth cohort is bounded between 84% and 98% across all plausible copulas,well above the rates observed for recent cohorts. Absolute mobility is not very sensitive to the copula
for the 1940 birth cohort because income grew very rapidly at all quantiles of the distribution
between 1940 and 1970. As a result, nearly all children earned more than the highest-income earners
in their parents’ generation, implying rates of absolute mobility near 100% regardless of whichchildren were linked to which parents.
In more recent cohorts, the copula – i.e., which parents are linked to which children – mattersmuch more because there has been little income growth across most of the distribution since 1980.
For the 1984 cohort, the bounds on absolute mobility under alternative copulas span 14% to 88%.
Fortunately, the copula is directly observed for these cohorts in tax records. In short, the key piece of
missing data that has hampered direct measurement of absolute mobility – the lack of historical panel
data linking parents and children – turns out to be inessential for characterizing trends in mobility.
The marked decline in absolute mobility since 1940 is robust to a range of alternative
specifications. Most importantly, the qualitative results do not change when we account for potentialchanges in the quality of goods and new product innovation, which could have important effects onreal income. Prior work on bias due to new products in inflation indices suggests that the annual
3

Copula stability implies that relative mobility – the correlation between children’s earnings and their parents’earnings – has not changed over time. Several studies have documented that relative mobility has not changed
significantly in recent decades using both transition matrices (copulas) and other statistics such as intergenerationalelasticities of income and rank-rank correlations (e.g., Lee and Solon 2009, Hauser 2010, Chetty et al. 2014b).
4
We define the set of “plausible” copulas as copulas under which the distribution of children’s incomes is weakly
increasing with their parents’ incomes (in the sense of first-order stochastic dominance). This restriction rules out
perverse copulas that generate negative intergenerational income persistence.

2

inflation rate measured by the CPI-U-RS may be biased upward by 0.8% (Meyer and Sullivan 2009,
Broda and Weinstein 2010). Subtracting 0.8% from the inflation rate each year, we find that absolutemobility declined from 93% to 59% between the 1940 and 1984 cohorts. We also obtain similar
results when we (a) use post-tax and post-transfer measures of income instead of pre-tax measures,(b) calculate children’s incomes at age 40 (for the 1940-74 birth cohorts) instead of age 30, and (c)adjust for changes in family size over time. Other metrics for upward mobility, such as the ratio ofchildren’s income to their parents’ incomes, also exhibit similar declines.
We find robust evidence of declines in absolute mobility across subgroups. Absolute mobility
fell in all 50 states between the 1940 and 1980 cohorts, although the rate of decline varied, with thelargest declines concentrated in states in the industrial Midwest states such as Michigan and Illinois.
We also find substantial declines in absolute mobility for both sons and daughters when income ismeasured at the household level. The decline in absolute mobility is especially steep – from 95% in
the 1940 cohort to 41% in the 1984 cohort – when we compare the individual earnings of sons totheir fathers.
Why have rates of upward income mobility fallen so sharply over the past half century?
There have been two important macroeconomic trends that have affected the incomes of children
born in the 1980s relative to those born in the 1940s: lower Gross Domestic Product (GDP) growth
rates and greater inequality in the distribution of growth (Goldin and Katz 2008). We consider two
counterfactual scenarios to assess the relative contribution of these two factors.
First, we consider a “higher GDP growth” scenario, in which children in the 1980 cohort
experience GDP growth from birth to age 30 that is comparable to what was experienced by the 1940
cohort, but GDP is distributed in proportion to GDP shares by income percentile in 2010. Thiscounterfactual expands the size of the economic pie, dividing it in the proportions by which it isdivided today. In this scenario, absolute mobility rises to 62%, closing 29% of the gap in absolutemobility between the 1940 and 1980 birth cohorts. Thus, the slowdown in aggregate economic
growth in recent decades, although important, does not explain most of the observed decline inabsolute mobility.
Second, we consider a “more broadly shared growth” scenario, in which the actual GDP in2010 is allocated across income percentiles as it was in the 1940 cohort. This counterfactual keeps
the size of the economic pie fixed at its observed level, but divides it more evenly, as in the past. In
this scenario, the rate of absolute mobility rises to 80%, closing 71% of the gap in absolute mobility
between the 1940 and 1980 cohorts.

3

Together, these counterfactual simulations show that increasing GDP growth withoutchanging the current distribution of growth would have modest effects on rates of absolute mobility.
Under the current distribution of GDP, we would need real GDP growth rates above 6% per year toreturn to the rates of absolute mobility seen in the 1940s. Intuitively, because a large fraction of
GDP goes to a small number of high income earners today, higher GDP growth does notsubstantially increase the number of children who earn more than their parents. Of course, this does
not mean that GDP growth does not matter: changing the distribution of growth naturally has smaller
effects on absolute mobility when there is very little growth to be distributed.5 The key point is that
reviving the “American Dream” of high rates of absolute mobility would require more broadly
shared economic growth rather than just higher GDP growth rates.
The remainder of the paper is organized as follows. Section I summarizes our methodology
and data sources. Section II provides baseline estimates under the benchmark assumption of a stable
copula. Section III establishes the key result that estimates of absolute mobility for early cohorts areinsensitive to the copula. Section IV assesses the sensitivity of the results to alternative pricedeflators and other specification choices, and presents results on heterogeneity by gender and state.
Section V presents the counterfactuals, and Section VI concludes. Details on the methods andsupplementary results are presented in the Supplementary Appendix. Code to replicate the results andstatistics on absolute mobility by birth cohort, parent percentile, state, and gender can be downloaded
from www.equality-of-opportunity.org.

I. Methods and Data𝑝𝑘
Let 𝑦𝑖𝑐
denote the income of child i in birth cohort c and let 𝑦𝑖𝑐 denote the income of his/herparents. In our baseline analysis, we measure income as pre-tax family income (summing income
across spouses) at age 30. We measure incomes in 2014 dollars, adjusting for inflation using the CPIU-RS (research series).6 In sensitivity analyses, discussed in Section IV, we consider several variantsof this income concept: using alternative price deflators, measuring income at age 40, measuringincome after taxes and transfers, and adjusting for family size.
We define the rate of absolute mobility in cohort c, 𝐴𝑐 , as the fraction of children in cohort cthat earn more than their parents:
5

Moreover, policies that promote higher GDP growth could also lead to more broadly distributed growth.
The CPI-U-RS is available from 1977 onward. Prior to 1977, we use the CPI-U multiplied by the ratio of the CPIU-RS to the CPI-U in 1977 to rescale the CPI-U in previous years.
6

4

1

𝑝

𝑘
𝐴𝑐 = 𝑁 ∑𝑖 1{𝑦𝑖𝑐≥ 𝑦𝑖𝑐 },𝑐(1)

where 𝑁𝑐 is the number of children in the cohort.
We estimate 𝐴𝑐 by decomposing the joint distribution of parent and child income into themarginal distributions of parent and child income and the joint distribution of the ranks (the copula).
Let 𝑟𝑖𝑐𝑘 denote the percentile rank of child i in the income distribution for children in birth cohort c.
𝑝

Similarly, let 𝑟𝑖𝑐 denote the percentile rank of child i’s parent in the income distribution of parents
who have children in cohort c. The joint distribution of parent and child ranks for cohort c is given by
𝐶𝑐 (𝑟 𝑘 , 𝑟 𝑝 ), the probability density function (pdf) of observing a child with income rank 𝑟 𝑘 and𝑝parental income rank 𝑟 𝑝 . Let 𝑄𝑐𝑘 (𝑟) and 𝑄𝑐 (𝑟) denote the rth quantile of the child and parent income𝑝distributions (measured in dollars), respectively. 𝑄𝑐𝑘 (𝑟) and 𝑄𝑐 (𝑟) summarize the marginal
distributions of parent and child incomes. With this notation, we can write absolute mobility as:𝑝

𝐴𝑐 = ∫ 1{𝑄𝑐𝑘 (𝑟 𝑘 ) ≥ 𝑄𝑐 (𝑟 𝑝 )} 𝐶𝑐 (𝑟 𝑘 , 𝑟 𝑝 )𝑑𝑟 𝑘 𝑑𝑟 𝑝

(2)

Intuitively, a child with rank 𝑟 𝑘 earns more than her parent with rank 𝑟 𝑝 if the 𝑟 𝑘 -th quantile of thechild’s income distribution is higher than the 𝑟 𝑝 -th quantile of the parent’s income distribution, i.e.
𝑝

𝑄𝑐𝑘 (𝑟 𝑘 ) ≥ 𝑄𝑐 (𝑟 𝑝 ). The copula, 𝐶𝑐 (𝑟 𝑘 , 𝑟 𝑝 ), measures the probability that each pair of ranks (𝑟 𝑘 , 𝑟 𝑝 )𝑝occurs. Absolute mobility is the fraction of cases where 𝑄𝑐𝑘 (𝑟 𝑘 ) ≥ 𝑄𝑐 (𝑟 𝑝 ), integrating over the
copula.
Equation (2) shows that absolute mobility can be calculated by estimating (a) the marginalincome distribution for children (which yields 𝑄𝑐𝑘 ), (b) the marginal income distributions for parents𝑝(which yields 𝑄𝑐 ), and (c) the copula, 𝐶𝑐 (𝑟 𝑘 , 𝑟 𝑝 ). The rest of this section summarizes how weestimate these three distributions; a detailed description is provided in the Supplementary Appendix.
Children’s Marginal Income Distributions. We obtain marginal income distributions at age 30 for
children in the 1940-1984 birth cohorts directly from the 1970-2014 March Current Population
Surveys (CPS). The sample of children includes U.S.-born members of the 1940-84 birth cohorts
who, at age 30, were present in the U.S. and not institutionalized. We exclude immigrants in order tohave a consistent sample in which we observe both parents’ and children’s incomes.7 We computefamily income as the sum of spouses’ personal pre-tax income.

7

The CPS does not ask for respondents’ birthplace prior to 1994; hence, for children born before 1964, we cannot
exclude immigrants from the sample. Most of the growth in the foreign-born share of the population occurred inrecent decades, limiting the bias created by the inclusion of immigrants in early cohorts (National Academy of5

Parents’ Marginal Income Distributions. Estimating the income distributions of parents at age 30
who have children in a given birth cohort is more complicated because of the lack of historical panel
data. We construct parents’ income distributions for children in each of the 1940-84 birth cohorts bypooling data from Census cross-sections between 1940 and 2000 (using the 1 percent IPUMS
samples). In order to cover all parents using decennial Censuses, we estimate parents’ incomes when
the highest earner is between the ages of 25 and 35, a symmetric window around age 30.8
For example, we estimate the income distribution of parents of children in the 1970 birthcohort as follows. First, we use the 1970 Census and select parents between the ages of 25 and 35
who have a child less than one year old in 1970. Next, we turn to the 1980 Census and select parents
between the ages of 26 and 35 who have ten year old children (i.e., individuals who had a child in1970 when they were between the ages of 16 and 25).9 Third, to identify parents between ages 35 and45 who had children less than one year old in 1970, we turn to the 1960 Census and select allindividuals aged 25-35. We give this group a weight equal to the fraction of individuals in the 1970
Census between the ages of 35 and 45 who have a child less than one year old in 1970. Thisapproach assumes that the income distribution of those who have children after age 35 isrepresentative of the income distribution of the general population. Such an assumption is
unavoidable as one cannot identify parents who will have children in the future in cross-sectional
data. Fortunately, this assumption turns out to be inconsequential in practice because most children
are born before their parents are 35.10
We estimate income distributions for parents with children in each of the other birth cohorts
from 1940-1984 using an analogous approach. Summary statistics on parents’ and children’s incomesby birth cohort are reported in Table S1.

Sciences, Engineering, and Medicine 2015). Moreover, because immigrants’ earnings are lower than natives’
earnings on average, this bias likely reduces our estimates of absolute mobility in the early cohorts, rendering ourestimate of the amount of decline more conservative than the true decline for natives.
8
The measures of total pre-tax income available in the Census change over time. From 1970 onward, we use thesum of spouses’ personal pre-tax income minus income from public assistance. In 1960, we use the sum of spouses’
personal pre-tax income. In 1950, we use total family income. In 1940, only income from wages and salaries isavailable, along with an indicator for non-wage, non-salary income, which we use to impute non-wage income. See
the Supplementary Appendix for further details.
9
For simplicity, we restrict attention to individuals who have children between the ages of 16 and 45 throughout ouranalysis.
10
In the Supplementary Appendix, we show that restricting attention to parents who have children between the agesof 25 and 35 – thereby avoiding this assumption entirely – yields very similar results.

6

Copula. For children born in the 1980s, we estimate a non-parametric copula – a 100 x 100 matrix
giving the probability of each child and parent rank pair (𝑟 𝑘 , 𝑟 𝑝 ) – exactly as in Chetty et al. (2014a,
Online Data Table 1). The sample includes all children born between 1980 and 1982 who are linked
to parents based on dependent claiming on tax forms.11
For both parents and children, we define family income in the tax records in a manner that is
as similar to the measures in the CPS and Census as possible. For those who file tax returns, wedefine income as aggregate gross income (AGI) plus the non-taxable portion of Social Security andDisability Income. For non-filers, we measure income using third-party information returns, defining
income as the sum of the W-2 wage earnings, Social Security and Disability Income, andUnemployment Insurance income.12 If individuals do not file a tax return and have no information
returns filed on their behalf, taxable income is coded as 0.13
Following Chetty et al. (2014a), we measure children’s incomes as mean income in 2011 and2012, when children in the 1980-82 birth cohorts are between the ages of 30 and 32. We measureparents’ incomes as mean taxable income between 1996 and 2000, the first five years in which
population tax records are available.14 Parents are between the ages of 30 and 60 when we measure
their incomes because we limit the sample to parents who have children between the ages of 15 and
40 in 1980-82. Chetty et al. (2014a) show that the distribution of income ranks is stable between theages of 30 and 60. Because of this rank stability, this approach provides an accurate estimate of the
copula that one would obtain if one could observe income ranks at age 30 for all parents.
We exclude parents with zero or negative income when constructing the copula because
parents with no earnings typically do not file a tax return and hence cannot be linked to their children
based on dependent claiming. This does not pose a problem for measuring absolute mobility because
children whose parents have zero income always earn at least as much as their parents. We calculate
the fraction of parents with zero income in each cohort based on Census data and include these11This definition of “parents” – based on who claims a child as a dependent – differs from the biological definitionof parents used in the CPS and Census. Using birth certificate data to link parents to children yields very similar
estimates of the copula (not reported). The population in the tax data also differs slightly from that in the CPS andCensus because it includes institutionalized individuals.
12
For non-filers, we cannot include the spouse’s income. However, the vast majority of non-filers of working age
are single (Cilke 1998).
13
Importantly, these observations are true zeros rather than missing data. Because the dataset includes all tax
records, we know that these individuals have 0 taxable income.
14
Chetty et al. (2014a) use multi-year averages of income to mitigate the influence of transitory income fluctuations;however, they show (Chetty et al., Appendix Figure IID) that using annual income measures yields very similar
estimates of rank distributions because the degree of transitory variance in income ranks is small in tax records.

7

individuals when computing average rates of absolute mobility, assigning the group of children
whose parents have zero income an absolute mobility rate of 100%.
We define children’s percentile ranks 𝑟𝑖𝑐𝑘 based on their incomes relative to other children in
their birth cohort. We include children with 0 income when constructing these ranks, breaking ties at
the mean.15 Likewise, parents are assigned percentile ranks based on their incomes relative to otherparents (among those with positive income). The copula is then estimated as a 100×100 matrix thatgives the joint probability of each child and parent rank pair (𝑟 𝑘 , 𝑟 𝑝 ).
For children born before 1980, we lack the panel data necessary to estimate the copula.
Chetty et al. (2014b) use a 0.1% IRS Statistics of Income panel to show that the copula (relative
mobility, measured by percentile ranks) is approximately stable from the 1971 birth cohort to the1984 birth cohort.16 Motivated by this result, we begin by assuming copula stability across all cohorts
since 1940, applying the copula estimated for the 1980-82 cohorts to all cohorts. We then computebounds on absolute mobility searching over alternative copulas, as there is no empirical evidence that
copula stability holds going back to 1940.

II. Baseline Estimates

This section presents our baseline estimates of absolute mobility, which assume copula
stability from 1940-84 and measure family income in real pre-tax dollars at age 30. Figure 1A plots
rates of absolute mobility by parental income percentile for the decadal birth cohorts, 1940-1980.
Each series shows the percentage of children earning more than their parents vs. their parents’income percentile, limiting the sample to parents with positive income.
In the 1940 birth cohort, nearly all children grew up to earn more than their parents
regardless of their parental income. Naturally, rates of absolute mobility were lower at the highest
parental income levels, as children have less scope to do better than their parents if their parents hadvery high incomes.
Rates of absolute mobility have fallen substantially since 1940, especially for families in the
middle and upper class. At the 10th percentile of the parental income distribution, children born in1940 had a 94% chance of earning more than their parents, compared with 70% for children born in
15

For example, if 10% of a birth cohort has 0 income, all children with 0 income receive a percentile rank of 5.
The 0.1% sample used by Chetty et al. (2014b) is adequate to assess the stability of the copula using statistics suchas rank-rank correlations and quintile probabilities, but it is not sufficiently large to directly estimate the 100 x 100
percentile copula for each birth cohort from 1971-84. This is why we use the 1980 copula estimated from the
population tax data for all cohorts.
16

8

1980. At the 50th percentile, rates of absolute mobility fell from 93% for children born in 1940 to
45% for those born in 1980. And at the 90th percentile, rates of absolute mobility fell from 88% to
33% over the same period.
Figure 1B aggregates the rates of absolute mobility across parental incomes (including thosewith zero income) and plots average absolute mobility (𝐴𝑐 ) for each birth cohort from 1940-1984.
Absolute mobility declined starkly across birth cohorts: on average, 92% of children born in 1940
grew up to earn more than their parents. In contrast, only 50% of children born in 1984 grew up toearn more than their parents. The downward trend in absolute mobility was especially sharp between
the 1940 and 1964 cohorts. The decline paused for children born in the late 1960s and early 1970s,
whose incomes at age 30 are measured in the midst of the economic boom of the late 1990s.
Absolute mobility then continued to fall steadily in the remaining birth cohorts.

III. Bounds Under Alternative Copulas

We now assess the sensitivity of the estimates reported in Figure 1 to the assumption that the
copula remained stable at the values observed for the 1980 birth cohort going back to 1940. We do soby deriving bounds on the rate of absolute mobility in each birth cohort, searching over all copulas
𝐶𝑐 (𝑟 𝑘 , 𝑟 𝑝 ), defined non-parametrically by a 100 x 100 percentile-level matrix.
We restrict attention to copulas satisfying the intuitive requirement that children from higher
income families are less likely to have lower incomes. Formally, we assume that the income
distribution of children with higher-income parents first-order stochastically dominates (FOSD) the
income distribution of children from lower income families:𝑟𝑘∫0 𝐶𝑐 (𝑟, 𝑟 𝑝 )𝑑𝑟 is weakly decreasing in 𝑟 𝑝 for all 𝑟 𝑘 (3)For each birth cohort, we calculate bounds on absolute mobility by solving for the copulas
𝐶𝑐 (𝑟 𝑘 , 𝑟 𝑝 ) that minimize and maximize 𝐴𝑐 , as defined in equation (2), given the empirically𝑝observed marginal distributions, 𝑄𝑐𝑘 (𝑟 𝑘 ) and 𝑄𝑐 (𝑟 𝑝 ). We impose two sets of constraints on thisproblem: the FOSD requirements for each (𝑟 𝑘 , 𝑟 𝑝 ) pair in (3) and integration constraints requiringthat the columns and rows of 𝐶𝑐 (𝑟 𝑘 , 𝑟 𝑝 ) sum to 1. This optimization problem has 100 x 100 = 10,000
arguments, which might appear to be computationally intractable. Fortunately, since the objectivefunction in (2) and all the constraints are linear, this problem can be solved rapidly using a standard
linear programming algorithm.

9

The results of this bounding exercise are presented in Figure 2A. The series in circles
reproduces the baseline estimates under the assumption of copula stability shown in Figure 1B. The
dashed lines show the upper and lower bounds on absolute mobility. The bounds are very tight inearly cohorts but grow much wider for more recent cohorts. For example, for the 1940 birth cohort,the bounds on absolute mobility span only 84% to 98%. In contrast, for the 1984 birth cohort, thebounds span 14% to 88%.
The dashed vertical line in Figure 2A demarcates the point after which the copula is known to
be stable based on the analysis of tax records in Chetty et al. (2014b). Quite conveniently, the panel
data necessary to estimate the copula happen to be available for precisely the cohorts where thebounds are least informative. For earlier cohorts, where the data needed to estimate the copula are
missing, the bounds are quite narrow and the copula therefore proves to be unimportant. The upshotof Figure 2A is that even though we cannot identify the copula in early cohorts, we can be certainthat absolute mobility has declined sharply since the 1940s.
The rest of this section explains why the bounds are tight in the 1940-50 cohorts but growwider in more recent cohorts. To begin, Figure 2B plots the marginal distribution of income forchildren in the 1940 birth cohort and their parents. Income grew very rapidly across all quantiles of
the income distribution between 1940 and 1970. As a result, there is very little overlap between theincome distributions of children born in 1940 and their parents. For example, a child born to parents
at the 80th percentile of the parent income distribution needed to reach just the 14th percentile of thechildren’s income distribution to exceed her parent’s income. In the extreme case in which the
distribution of child income lies everywhere above the distribution of parental income – i.e., thepoorest child earns more than the richest parent – absolute mobility would be 100% irrespective of
which children are linked to which parents. Although the 1940 parent and child income distributions
are not fully separated, we show below that they are sufficiently close to this scenario to render the
copula unimportant for calculating absolute mobility.
In contrast, recent cohorts experienced much less growth across most quantiles of the income
distribution (e.g., Goldin and Katz 2008, Autor 2014). Figure 2C illustrates this point by replicating
Figure 2B for the 1980 birth cohort. Because growth rates were much lower between 1980 and 2010,
there is substantial overlap between parents’ and children’s income distributions (at age 30) for
children born in 1980. Children with parents at the 80th percentile of the income distribution now
need to reach the 74th percentile of their cohort’s income distribution to earn more than their parents.
Figure 2D shows why the greater degree of overlap between children’s and parents’ income
distributions in recent cohorts leads to wider bounds on absolute mobility. The curves in this figure
10plot the income rank a child must reach to earn more than her parents as a function of her parents’income percentile, separately for the 1940 and 1980 birth cohorts. For example, in order to earn morethan parents at the 80th percentile, children need to reach the 14th percentile in the 1940 cohort andthe 74th percentile in the 1980 cohort, as shown in Figures 2B and 2C.
The copula can be visualized in Figure 2D as the distribution of mass within the (𝑟 𝑘 , 𝑟 𝑝 )square. Absolute mobility 𝐴𝑐 can be calculated by summing the mass in the copula that lies above therelevant curve. The empirically observed copula for the 1980-82 cohorts used in our baseline analysis
is shown by the shading in the figure, with darker colors representing areas with higher density. The
mass is clustered around the diagonal, reflecting positive intergenerational persistence of income.
Absolute mobility is 50% for the 1980 cohort because half of the mass of this copula lies above thecurve plotted for the 1980 cohort.
Our bounding procedure minimizes and maximizes the amount of mass in the copula that
falls above the curves in Figure 2D, subject to the FOSD and integration constraints specified above.
Since the child rank required to beat parents is very close to the 45-degree line for the 1980 cohort,
rates of absolute mobility are very sensitive to whether the mass in the copula lies just above or
below the diagonal. This shows why we obtain wide bounds when searching over all copulas for the1980 cohort.17 In contrast, because the child rank required to earn more than parents is very low atnearly all percentiles of the parent income distribution for the 1940 cohort, all feasible copulas
generate high levels of absolute mobility for that cohort.

IV. Sensitivity and Heterogeneity Analysis

In this section, we first assess the sensitivity of our baseline estimates to key specification
choices, such as the price deflator and definition of income. We then examine heterogeneity in trends
in absolute mobility across subgroups.

Sensitivity Analysis. We begin by considering alternative price deflators. Prior work has argued that
the CPI-U-RS may overstate inflation by failing to account adequately for improvements in productquality and for the introduction of new goods (Boskin et al. 1996, Broda et al. 2009). Prior work on
the measurement of trends in poverty recommends subtracting 0.8 percentage points from the annual
17

The copulas for the 1980 cohort used to produce the upper and lower bounds in Figure 2A are displayed in Figure
S1. The copula that generates the upper bound concentrates mass just below the 1980 curve shown in Figure 2D,
while the copula that generates the lower bound concentrates mass just above that curve.

11

inflation rate implied by the CPI-U-RS to account for such biases (Meyer and Sullivan 2009, Broda
and Weinstein 2010). The series in squares in Figure 3A replicates the baseline series on absolutemobility by cohort in Figure 1B using this adjusted price index. As expected, this adjustment
increases absolute mobility in recent cohorts, as it increases real income growth rates across the
distribution. However, the magnitude of the change is small: with the adjusted series, absolutemobility falls from 93% in 1940 to 59% in the 1984 cohort. Even subtracting 2 percentage points
from the inflation rate implied by the CPI-U-RS – a conservative adjustment larger than virtually all
existing estimates of the bias due to new goods – still results in a 26 percentage point decline inabsolute mobility from 1940-1984 (Figure S2).
We also consider a variety of other commonly used price indices: (a) the Personal
Consumption Expenditure Price Index (PCEPI), an index that includes a broader bundle of goods
than the CPI; (b) the Producer Price Index (PPI), an index constructed based on prices at the producer
level; (c) the GDP deflator, an index that covers all goods used domestically; and (d) the CPI-U
series that is most commonly used to measure inflation.18 All of these alternative indices produce
time series of absolute mobility very similar to our baseline estimates (Figure 3A, Figure S2).
Our baseline analysis uses pre-tax measures of earnings rather than net income after taxes
and transfers. Conceptually, it is not clear which of these income definitions provides a bettermeasure of absolute mobility, as individuals’ sense of progress might differ if they achieve upward
mobility through government transfers rather than their own earnings. We assess whether the
distinction matters empirically in Figure 3B by replicating our baseline analysis using post-tax andtransfer incomes. We estimate tax liabilities for parents and children using the National Bureau of
Economic Research TAXSIM model, which is available since 1960. Before 1960, we use data on
federal marginal tax rates, adjusted for personal exemptions by marital status and number of children,
applying the data in Wilson (2002). We estimate the value of transfers as the sum of Aid to Families
with Dependent Children, General Assistance, Supplemental Security Income, and the cash value of
in-kind transfers.19 Accounting for taxes and transfers increases the level of absolute mobility byaround 3 percentage points in all cohorts, but does not affect the trend in absolute mobility
appreciably. This is because taxes and transfers affect the incomes of both parents and their children,
18

The CPI-U-RS (research series) adjusts the CPI-U by correcting for substitution between existing products
following Boskin et al. (1996), and generates inflation rates about 0.5% lower than the CPI-U.
19
We obtain estimates of in-kind transfers from Fox et al. (2015), who estimate total benefits from SNAP, WIC,
housing assistance, the School Lunch Program, and LIHEAP by combining CPS and administrative data. These data
are available starting in 1967; we do not account for in-kind transfers before 1967. Meyer, Mok, and Sullivan (2015)
show that transfers are under-reported by approximately 50% in survey data; we find that doubling the amount oftransfers reported does not affect our estimates significantly.

12and because the expansion of transfer programs in recent years has targeted the bottom of the income
distribution, where rates of absolute mobility are already high even in pre-tax terms (Figure 1A).
In our baseline analysis, we measure children’s incomes at age 30. One may be concernedthat children take a longer time to reach peak lifecycle earnings in more recent cohorts, which could
lead to a spurious downward trend in rates of absolute mobility. Figure 3C addresses this concern by
replicating our baseline analysis measuring income at age 40 for children (for the 1940-74 cohorts)
and at ages 35-45 for parents. This series continues to exhibit a sharp decline in absolute mobility
across birth cohorts. The time pattern of the decline is shifted backward by approximately 10 years,
consistent with measuring incomes 10 years later.
The fraction of individuals who are married at age 30 and the size of families have bothfallen steadily in recent decades (Parker 2015). One widely used approach to adjusting for changes inhousehold size is to divide family income by the square root of the number of family members in thehousehold (e.g., Johnson et al. 2005). Figure 3D shows that when we divide our baseline income
measures by the square root of family size, rates of absolute mobility fall from 93% in 1940 to 60%
in 1984.20 As an alternative approach, one can measure income at the individual rather thanhousehold level. The series in triangles in Figure 3D compares the individual earnings of sons to theirfathers, as in prior studies of intergenerational mobility (e.g., Lee and Solon 2009). Here, we find asteeper decline in absolute mobility than in our baseline specification: the fraction of sons earning
more than their fathers fell from 95% in 1940 to 41% in 1984. Together, these results show that
accounting for trends in family size and the number of earners does not affect the qualitative
conclusion that absolute mobility has fallen substantially.
Beyond the specific factors considered above, one may be concerned that levels of absolutemobility for recent cohorts may still be understated because of increases in fringe benefits, nonmarket goods, or under-reporting of income in the CPS (Bollinger et al. 2015, Piketty, Saez, andZucman 2016). As an omnibus approach to assessing the potential bias from such factors, werecalculate absolute mobility for the 1984 birth after increasing each child’s income by various fixed
dollar amounts. Adding $1,000 to every child’s income in 2014 would increase absolute mobility forthe 1984 cohort to 51% from the baseline estimate of 50%; adding $10,000 would increase absolutemobility to only 61% (Figure S4). These calculations show that plausible adjustments to children’s
incomes are unlikely to change the conclusion that absolute mobility has fallen sharply from the ratesof 80-90% experienced by children born in the 1940s and 1950s.
20

Even the most conservative adjustment of dividing by the total number of people in the family continues to show
a 26 percentage point decline in absolute mobility (Figure S3).

13

In our baseline analysis, we define absolute mobility using a discrete measure of whether
children earn more than their parents. Figure S5 shows that using other thresholds or a more
continuous definition of absolute mobility yields similar results. Panel A shows the fraction ofchildren earning 20% more than their parents or 20% less than their parents. Both of these thresholds
generate very similar declines in absolute mobility. In Panel B, we plot the median ratio of child toparent income, a statistic that accounts for the magnitude of the difference between parents’ andchildren’s incomes. This statistic declines from approximately 3 in the 1940 cohort to slightly lessthan 1 in the 1984 cohort. These results show that our findings are not sensitive to the exact metricused to compare children’s earnings to their parents.
Finally, in the Supplementary Appendix (Figures S6-S9), we show that the results are also
robust to a set of other technical issues that arise from data limitations: (a) adjusting for changes inthe definition of family income across Censuses; (b) including immigrants in all years to account for
missing data on immigrant status in early cohorts; (c) using a single Census to measure parents’income instead of pooling data across multiple Censuses; and (d) using data from either the Census
or CPS to measure the incomes of both parents and children from a single dataset.

Heterogeneity. Next, we examine how trends in absolute mobility vary across subgroups. We begin
by examining heterogeneity across states. We define parents’ states as based on where they live when
we measure their incomes (between ages 25-35). We define children’s state as their state of birth toaccount for the possibility that children who grow up in a given state may move elsewhere as adults.
Since children’s state of birth is not observed in the CPS, we use the Census for both parents andchildren.21
Figure 4 presents the results by state. Panel A shows absolute mobility by cohort for selectedstates (see Table S2 for estimates for all states). Panel B presents a heat map of the change inabsolute mobility from 1940 to 1980 by state, with darker colors representing areas with larger
declines. Absolute mobility fell substantially in all 50 states between the 1940 and 1980 birthcohorts. Absolute mobility fell particularly sharply in the industrial Midwest, where rates of absolutemobility fell by 48 percentage points in Michigan and approximately 45 percentage points in Indiana,

21

To increase precision, our state-level analysis includes all children aged 25-35 and uses the 100% Census in 1940
and 5% IPUMS sample in 1980. Measuring children’s incomes from ages 25-35 rather than just at age 30 createssmall differences in levels of absolute mobility. To adjust for these differences, we calculate the difference between
the baseline national estimates and population-weighted national means of our state-level estimates for each cohort,and add these differences to the state-level estimates.

14

Illinois, and Ohio. The smallest declines occurred in states such as Massachusetts, New York, andMontana, where absolute mobility fell by approximately 35 percentage points.
Next, we examine heterogeneity by gender. When comparing children’s family incomes totheir parents’ family incomes as in our baseline analysis, we find similar declines in absolutemobility for sons and daughters (Figure S10). However, the patterns differ by gender when we focus
on individual earnings. As noted above, sons’ chances of earning more than their fathers fell steeply,
from 95% in 1940 to 41% in 1984, underscoring the sharp decline in the economic prospects ofAmerican men. In contrast, the fraction of daughters earning more than their fathers fell from 43%
for the 1940 birth cohort to 22% in 1960, and then rose slightly to 26% in 1984. The pattern for
women’s individual earnings differs because of the rise in female labor force participation rates andearnings over the period we study (Figure S11).
In sum, the subgroup analysis shows that declines in absolute mobility have been asystematic, widespread phenomenon throughout the United States since 1940.

V. Counterfactual Scenarios

Why have rates of absolute income mobility fallen so sharply over the last half century, andwhat policies can restore absolute mobility to earlier levels? We use counterfactual simulations toevaluate the effects of two key trends over the past half century: declining rates of GDP growth andgreater inequality in the distribution of GDP (Piketty and Saez 2003, Goldin and Katz 2008).
We consider two counterfactual scenarios. The first, a “higher GDP growth” scenario, asks
what would have happened to absolute mobility for the 1980 cohort if the economy had grown as
quickly during their lifetimes as it did in the mid-twentieth century, but with GDP distributed acrosshouseholds as it is today. The second “more broadly shared growth” scenario asks the converse: what
if total GDP grew at the rate observed in recent decades, but GDP was allocated across households as
it was for the 1940 birth cohort? The first scenario expands the size of the economic pie, dividing itin the proportions by which it is divided today. The second keeps the size of the pie fixed, but divides
it more evenly as in the past.
We calculate children’s counterfactual incomes under the “higher GDP growth” scenario as
follows. Let 𝐺𝑡𝑂 denote the observed GDP per working-age family in year t.22 We first define the22

We define “working-age families” as families with at least one member between the ages of 18 and 64. We
normalize GDP by the number of working-age families to control for changes in GDP due to changes in the numberof working-age adults.

15

𝑘share of GDP that goes to children at percentile q of the 1980 cohort in 2010 as 𝜋𝑞,1980=𝑘𝑂𝑘𝑦𝑞,1980/𝐺2010, where 𝑦𝑞,1980
is the qth percentile of the income distribution in 2010 for children in the1980 cohort. We then construct a counterfactual level of GDP per working-age family in 2010,
𝐶
𝑂
𝐺2010
= 𝐺1980
× 1.02530 , under the assumption that real GDP per family grew at a rate of 2.5% peryear from 1980 to 2010. This 2.5% growth rate is comparable to the real growth rate per working-age
family from 1940-1970, and is one percentage point per year higher than the actual annualized
growth rate from 1980-2010 of 1.5%.23 Finally, we define a counterfactual marginal income
distribution for children in the 1980 cohort as𝑘,𝐶1𝑘
𝐶𝑦𝑞,1980= 𝜋𝑞,1980
× 𝐺2010(4)The counterfactual income for children at percentile q is given by the share of GDP going to 30 year
olds at percentile q in 2010 multiplied by the level of GDP that would have prevailed in 2010 had
children in the 1980 cohort experienced GDP growth from birth to age 30 comparable to thatexperienced by children born in the 1940s.
For the “more broadly shared growth” scenario, we follow the same approach as above to𝑘calculate the share of GDP that goes to children at percentile q of the 1940 cohort in 1970, 𝜋𝑞,1940=𝑘𝑂𝑦𝑞,1940/𝐺1970. We then apply these shares to the observed level of 2010 GDP to construct a

counterfactual income distribution for the 1980 birth cohort:𝑘,𝐶2𝑘𝑂𝑦𝑞,1980= 𝜋𝑞,1940
× 𝐺2010(5)This counterfactual represents the incomes 30 year olds would have had in 2010 if GDP in 2010 wereallocated across households in the same proportions as in 1970.
After calculating the counterfactual income distributions for children in the 1980 cohort,𝑘,𝐶1 100𝑘,𝐶2 100{𝑦𝑞,1980}𝑞=1 and {𝑦𝑞,1980}𝑞=1 , we use the same copula and parent marginal income distributions asabove to compute counterfactual rates of absolute mobility by parent income percentile. Figure 5A
presents the results. The top and bottom curves in the figure reproduce the empirical series for the1940 and 1980 cohorts from Figure 1A. The dotted and dashed series show absolute mobility rates
that would have been observed for the 1980 cohort under the counterfactuals in (4) and (5).
Under the higher growth counterfactual, the mean rate of absolute mobility is 62%. This rate
is 12 percentage points higher than the empirically observed value of 50% in 1980, but closes only
29% of the decline relative to the 92% rate of absolute mobility in the 1940 cohort. The increase inabsolute mobility is especially modest given the magnitude of the change in the aggregate economy:
23

The 1.5% growth rate of GDP per working-age family corresponds to total real GDP growth of 2.8% per year,
while the 2.5% growth rate of GDP per working-age family corresponds to total real GDP growth of 3.8% per year.

16

a growth rate of 2.5% per working-age family from 1980 to 2010 would have led to GDP of $20
trillion in 2010, $5 trillion (35%) higher than the actual level.
The more broadly shared growth scenario increases the average rate of absolute mobility to80%, closing 71% of the gap in absolute mobility between the 1940 and 1980 cohorts. The broadly
shared growth counterfactual has larger effects on absolute mobility at the bottom of the income
distribution, whereas the higher growth counterfactual has larger effects at higher income levels.
Since income shares of GDP are larger for high-income individuals, higher growth rates benefit thosewith higher incomes the most, while a more equal distribution benefits those at the bottom the most.
The results in Figure 5A imply that much of the decline in absolute mobility is due tochanges in the distribution of growth rather than reductions in aggregate growth rates. In Figure 5B,
we ask what rates of GDP growth would be necessary to return to mid-century rates of absolutemobility under today’s income distribution. We plot mean rates of upward mobility under real GDP𝐶
per family growth rates from 1% to 10%, recalculating 𝐺2010
and applying (4) to generate

counterfactual income distributions. Achieving rates of absolute mobility above 80% under today’s
income distribution would require sustained real per-family growth greater than 5% per year (or total
real GDP growth above 6.4%), well above the historical experience of the United States since WorldWar II.
To see why absolute mobility is not very responsive to the growth rate when growth isdistributed unequally, consider the extreme case in which one child obtains all of the increase in
GDP. In this case, higher GDP growth rates would have no effect on absolute mobility. Moregenerally, GDP growth has larger effects on absolute mobility when growth is spread more broadly,
allowing more children to achieve higher living standards than their parents. Higher GDP growth anda broader distribution of growth have a multiplicative effect on absolute mobility: absolute mobility
is highest when GDP growth rates are high and growth is spread broadly across the distribution.
In the Supplementary Appendix, we show that similar results are obtained when using
counterfactuals for the change in incomes from 1980 to 2010 based on shares of GDP growth overthat period rather than counterfactuals for the level of incomes in 2010. Measuring incomes at age 40
instead of 30 also yields similar results (Figure S12).
In sum, the counterfactuals show that higher growth rates alone are insufficient to restore
absolute mobility to the levels observed in mid-century America. A broader distribution of income

17

growth is necessary to revive absolute mobility, and can itself be sufficient to reverse much of thedecline since 1940 even if growth were to remain at current levels.24

VI. Conclusion
The analysis in this paper yields two main results. First, children’s prospects of earning morethan their parents have faded over the past half century in the U.S. The fraction of children earning
more than their parents fell from approximately 90% for children born in 1940 to around 50% forchildren entering the labor market today. Absolute income mobility has fallen across the entire
income distribution, with the largest declines for families in the middle class. These findings contrast
with prior research showing that relative mobility – measured, for instance, by the correlation
between parents’ and children’s incomes – remained stable in recent decades (e.g., Lee and Solon
2009, Chetty et al. 2014b). The measures of absolute mobility we focus on in this study differ from
relative mobility because they compare levels of earnings across generations by bringing in data on
the marginal income distributions of parents and children. Absolute mobility has fallen over time
while relative mobility has remained stable because income growth has stagnated across much of theincome distribution in recent decades.
Second, most of the decline in absolute mobility is driven by the more unequal distribution of
economic growth in recent decades rather than the slowdown in GDP growth rates. In this sense, therise in inequality and the decline in absolute mobility are closely linked. Growth is an importantdriver of absolute mobility, but high levels of absolute mobility require broad-based growth acrossthe income distribution. With the current distribution of income, higher GDP growth rates alone areinsufficient to restore absolute mobility to the levels experienced by children in the 1940s and 1950s.
If one wants to revive the “American Dream” of high rates of absolute mobility, then one must havean interest in growth that is spread more broadly across the income distribution.

24

Plausible changes in relative mobility (the copula) also have modest effects on average rates of absolute mobility.
For example, a uniform copula – where children’s ranks are independent of their parents’ ranks – would still
produce absolute upward mobility for the 1980 cohort of 50%. Greater relative mobility produces higher rates ofabsolute mobility for children with low-income parents while reducing rates of absolute mobility for children withhigh-income parents, leaving average absolute mobility essentially unchanged.

18

ReferencesAcs, Gregory, Diana Elliott, and Emma Kalish. 2016. “What Would Substantially Increased Mobility
From Poverty Look Like?” Working Paper, The Urban Institute.
Autor, David H. 2014. “Skills, Education, and the Rise of Earnings Inequality Among the ‘Other 99
Percent.’” Science, 344(6186), 843–851.
Bengali, Leila, and Mary Daly. 2013. “U.S. Economic Mobility: The Dream and the Data.” Federal
Reserve Bank of San Francisco Economic Letter 2013:06.
Bollinger, Christopher R., Barry T. Hirsch, Charles M. Hokayem, and James P. Ziliak. 2015.
“Trouble in the Tails? Earnings Nonresponse and Response Bias across the Distribution.” Working
Paper.
Boskin, Michael J., Ellen R. Dulberger, Robert J. Gordon, Zvi Griliches, and Dale W. Jorgenson.
1998. “Consumer Prices, the Consumer Price Index, and the Cost of Living.” Journal of Economic
Perspectives 12(1): 3-26.
Broda, Christian, Ephraim Leibtag, and David E. Weinstein. 2009. “The Role of Prices in Measuring
the Poor’s Living Standards.” Journal of Economic Perspectives 23(2): 77-97.
Broda, Christian and David E. Weinstein. 2010. “Product Creation and Destruction: Evidence andPrice Implications.” American Economic Review 100(3): 691-723.
Chetty, Raj, Nathaniel Hendren, Patrick Kline, and Emmanuel Saez. 2014a. “Where is the Land of
Opportunity? The Geography of Intergenerational Mobility in the United States.” Quarterly Journalof Economics 129 (4): 1553-1623.
Chetty, Raj, Nathaniel Hendren, Patrick Kline, Emmanuel Saez, Nicholas Turner. 2014b. “Is theUnited States Still a Land of Opportunity? Recent Trends in Intergenerational Mobility.” American
Economic Review 104(5): 141-47.
Cilke, James. 1998. “A Profile of Non-Filers.” U.S. Department of the Treasury, Office of Tax
Analysis Working Paper No. 78.
Feenberg, Daniel and Elizabeth Coutts. 1993. “An Introduction to the TAXSIM Model.” Journal of
Policy Analysis and Management 12: 189-194. http://www.nber.org/taxsim
Fox, L., Wimer, C., Garfinkel, I., Kaushal, N., & Waldfogel, J. 2015. “Waging war on poverty:
Poverty trends using a historical supplemental poverty measure.” Journal of Policy Analysis andManagement 34: 567–592.
Goldin, Claudia and Lawrence F. Katz. 2008. The Race Between Education and Technology.
Cambridge, MA: Belknap Press of Harvard University Press, 2008.
Goldthorpe, John H. 1987. Social Mobility and Class Structure in Modern Britain. Oxford: Oxford
University Press.
Halikias, Bimitrios and Richard V. Reeves. 2016. “How Many People Are Better Off than Their
Parents? Depends on How You Cut the Data.” Brookings Institution.
19https://www.brookings.edu/blog/social-mobility-memos/2016/08/10/how-many-people-are-betteroff-than-their-parents-depends-on-how-you-cut-the-data/
Hauser, Robert M. 2010. “Intergenerational Economic Mobility in the United States: Measures,
Differentials, and Trends.” UW-Madison Center for Demography and Ecology Working Paper.
Hauser, Robert M., John Robert Warren, Min-Hsiung Huang, and Wendy Y. Carter. 2000.
“Occupational Status, Education, and Social Mobility in the Meritocracy.” In Meritocracy andEconomic Inequality, edited by Kenneth J Arrow, Samuel Bowles, and Steven Durlauf, 179–229.
Princeton, N.J.: Princeton University Press
Hochschild, Arlie. 2016. Strangers in their Own Land: Anger and Mourning on the American Right.
New York, NY: The New Press.
Hout, Michael and Richard Janus. 2011. “Educational mobility in the United States since the 1930s.”
In Whither Opportunity: Rising Inequality, Schools, and Children's Life Chances, edited by Greg J.
Duncan and Richard J. Murnane, 165--186. New York: Russell Sage Foundation.
Isaacs, Julia B., Isabel Sawhill, and Ron Haskins. 2008. “Getting Ahead or Losing Ground:
Economic Mobility in America.” The Brookings Institution.
Johnson, David S., Timothy M. Smeeding, and Barbara Boyle Torrey. 2005. “Economic Inequality
Through the Prisms of Income and Consumption,” Monthly Labor Review 128 (4): 11-24.
Lee, Chul-In and Solon, Gary. 2009. “Trends in Intergenerational Income Mobility.” Review of
Economics and Statistics 91(4): 766-772.
Lopoo, Leonard, and Thomas DeLeire. 2012. “Pursuing the American Dream: Economic Mobility
Across Generations.” The Pew Charitable Trusts.
Meyer, Bruce, Wallace Mok, and James Sullivan. 2015. “The Under-Reporting of Transfers inHousehold Surveys: Its Nature and Consequences.” Working Paper, previously circulated as NBER
Working Paper No. 15181, National Bureau of Economic Research.
Meyer, Bruce and James Sullivan. 2009. “Five Decades of Consumption and Income Poverty.”
NBER Working Paper No. 14827, National Bureau of Economic Research.
National Academies of Sciences, Engineering, and Medicine. 2015. The Integration of Immigrants
into American Society. Washington, DC: The National Academies Press.
Obama, Barack. 2013. Remarks by the President on Economic Mobility. December 4, 2013.
https://www.whitehouse.gov/the-press-office/2013/12/04/remarks-president-economic-mobility
Parker, Kim. 2015. “Parenting in America.” Pew Research Center.
http://www.pewsocialtrends.org/2015/12/17/1-the-american-family-today/
Piketty, Thomas and Emmanuel Saez. 2003. “Income Inequality in the United States, 1913-1998.”
Quarterly Journal of Economics 118(1): 1-41.
Piketty, Thomas, Emmanuel Saez, and Gabriel Zucman. 2016. “Distributional National Accounts:
Methods and Estimates for the United States.” Working Paper.
20

Ruggles, Steven, Katie Genadek, Ronald Goeken, Josiah Grover, and Matthew Sobek.
2015. Integrated Public Use Microdata Series: Version 6.0. Minneapolis: University of Minnesota.
Samuel, Lawrence R. 2012. The American Dream: A Cultural History. Syracuse Univ. Press
Wilson, Robert. 2002. “Personal Exemptions and Individual Income Tax Rates.” SOI Bulletin Data
Release with Historical Data, Internal Revenue Service.

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Supplementary Appendix
This appendix contains three sections. Section I describes how we construct our samples and define
the key variables used in the baseline specifications and sensitivity analyses. Section II presents a setof supplementary robustness checks that address various limitations of our data. Section III presents
further detail on the methods underlying the counterfactual simulations and supplementary
counterfactual results. Stata and Matlab code to reproduce all of the results in the paper from publicly
available data can be downloaded from www.equality-of-opportunity.org.

Section I: Sample Construction and Variable Definitions
We construct estimates of absolute mobility by combining three sets of data. First, we construct a
series of marginal income distributions for parents using the decadal Census data. Second, weconstruct a series of marginal income distributions for children using CPS data. Third, we construct
the joint distribution of parent and child rank (the copula) using de-identified data from federal
income tax returns.
In this section, we describe how we construct each of these three elements. We then discuss how we
combine them to estimate absolute mobility in our baseline specification. Finally, we summarize
supplementary data used for sensitivity analyses, such as alternative price deflators and data on taxes
and transfers.
A. Parents’ Income Distributions
Sample Construction
We obtain data on parents’ incomes from the 1940 to 2000 U.S. Censuses, retrieved via the
University of Minnesota’s Integrated Public Use Microdata Series (IPUMS). We use the 1% nationalrandom samples provided by IPUMS (except for the state-level analysis in Figure 4, where we use
the 100% sample for 1940 and the 5% sample for 1980). We use the Form 1 Metro sample in 1970
and the Metro sample in 1980 (which are, contrary to their labels, full population samples) and theunweighted samples in 1990 and 2000.
To construct a sample that can be used without weights, we restrict the 1940 and 1950 Censuses toself-weighting sample-line persons and their families. Since the CPS data that we use to estimate
children’s incomes does not sample institutional group quarters, we render the Census and CPS
samples comparable by excluding from the Census individuals residing in institutional group quarters(i.e., correctional and mental institutions, as well as institutions for the elderly and the handicapped)
and residents of the military non-institutional group quarters. For every birth cohort from 1940 to
1984, we restrict our sample to parents who had children between the ages of 16 and 45 (inclusive).
In two-parent households, we define the “representative parent” as the spouse with the higher total
personal income, and use this parent’s age when restricting the sample.
We follow the rules established by IPUMS to determine parent-child relationships, as well as
whether and to whom a respondent is married.25 Children for whom no parent-child link can be made25

We determine marital status and partner using both the SPLOC and MARST variables. For more detail, see
https://usa.ipums.org/usa/chapter5/chapter5.shtml.

22

– that is, for whom both mother’s and father’s location in the household are not recorded – aredropped from the sample.
Baseline Income Definitions
Our baseline definition of family income varies across Census years because the income variables
change across the Censuses. A complete list of the underlying IPUMS-USA variables used toconstruct our measures of parental income in each Census year is given in Table S3.
In the 1970 to 2000 Census years, we define parents’ family income as the sum of spouses’ pre-tax
total personal income, minus income derived from Aid to Families with Dependent Children, General
Assistance, and Supplemental Security Income.
Prior to 1970, data on income from public assistance programs is unavailable in the Census.
Therefore, in the 1960 Census, parental income is defined simply as the sum of spouses’ total
personal income. In 1950, where personal income is only available for sample-line household heads,
the sum of spouses’ income cannot be computed. Here, we define parents’ family income as the sumof the sample-line household head’s total income, plus any income from other members of the
primary family (including business, farm, and wage income, as well as from other, unspecified
sources).
In the 1940 Census, only data on wages and salaries is available, as well as an indicator of whether
respondents had more than $50 in non-wage, non-salary income. For 1940, we therefore imputeaverage non-wage, non-salary income from the 1950 Census (adjusted for inflation) for eachcombination of occupation (using the detailed 1950 Census Bureau occupational classification), selfemployed status, race (black, white, other), and the indicator for non-wage income above $50.
Parents’ family income in 1940 thus comprises the sum of spouses’ wages, as well as their imputed
non-wage income.
Inflation Adjustment
In our baseline specifications, we adjust for inflation using the Consumer Price Index Research
Series (CPI-U-RS), available from the Bureau of Labor Statistics from 1977 onward. For all prioryears, we follow the Census Bureau in applying the 1977 CPI-U-RS-to-CPI-U ratio to the CPI-U ofprevious years. Since income in Census and CPS refers to income earned in the previous calendar
year, inflation adjustments are also applied to that calendar year. For instance, in the 1960 Census,
income refers to income earned in 1959; our inflation adjustment thus pertains to 1959 U.S. dollars.
Construction of Marginal Distributions
As described in Section I of the text, we combine several Censuses to measure income between ages
25-35 (inclusive) for parents who had children in a given birth cohort c. In particular, we pool all
individuals between the ages of 25 and 35 (at the time of the survey) in the available Census samples
who had a child in cohort c. However, when drawing records from Censuses before year c (i.e., forparents who had children after age 35), we measure the incomes of all adults between ages 25-35 and23

assign them weight equivalent to the fraction of adults who have children in cohort c after age 35.
This is because we naturally cannot observe who will have children in the future.26
For children born in 1940, we cannot secure income measurements from prior Censuses because
income data were not collected prior to the 1940 Census. We therefore use income measurementsfrom the 1940 Census itself for these older parents, pooling parents up to age 45.27 Likewise, because
we can only reach back to the 1940 Census for the 1941-1949 birth cohorts, the income
measurements for parents who had children in these earlier birth cohorts are also taken at slightly
older ages on average relative to the measurements for parents who had children more recently.
These age differences make it slightly more difficult for children of these early cohorts to exceed theincome of their parents, reducing our estimate of the decline in absolute mobility.
We compute marginal income distributions for parents of children in each birth cohort by firstestimating the cutoff values for the 100 percentile ranks and then calculating mean incomes withineach percentile. We exclude parents with zero income when estimating the parental marginal income
distribution. Parents with zero income are reintroduced in the final step of our absolute mobility
calculations, described in Subsection D below.
B. Children’s Income Distributions
Sample Construction
We obtain data on children’s incomes from the 1970-2014 Annual Social and Economic
Supplements of the Current Population Surveys (CPS-ASEC). We include only respondents who are
30 years old. We exclude all respondents who reported a birthplace outside of the United States
starting in 1994 (information on birthplace is unavailable prior to 1994).
Baseline Income Definitions
Children’s income is defined analogously to parents’ family income, namely as the sum of spouses’
total personal income minus income from welfare and Supplemental Security Income. Table S4 lists
the variables in the IPUMS-CPS that we use to construct our measures of children’s income.
To account for the different thresholds used to top code income across different years of the CPSASEC, we use the Census Bureau’s income component rank proximity swap values for 1976-2010(which are constructed using restricted CPS data that are not top-coded).28 We apply this procedure
to all income components separately (such as wages and business income), and then sum them toobtain total personal income.
Construction of Marginal Distributions

26

Our approach double counts the incomes of individuals who have children at exactly age 25 or 35. We adopt thisapproach to obtain a symmetric window around age 30. Measuring incomes when parents are between ages 25 and34 or 26 and 35 to avoid double counting yields estimates of absolute mobility that bracket the estimates we report.
27
Because we do not use data on parents’ incomes from earlier Censuses, the number of observations used toconstruct parents’ income distributions for the 1940 birth cohort is lower than for subsequent cohorts (Table S1).
28
For further detail on this procedure, see https://cps.ipums.org/cps/income_cell_means.shtml

24

To construct marginal income distributions for each birth cohort, we again estimate the cutoff values
for every percentile and then calculate mean incomes within each percentile. We account for the
CPS’s stratified sampling scheme by using person-level sampling weights provided for use withASEC when estimating the percentile cutoff values.
Our income estimates from our CPS-ASEC samples closely match the trends in median individual
income by gender published in Table P-8 of the Census Bureau’s Historical Income Tables based on
CPS data (see Figure S11). For purposes of this comparison, we extend our sample to include allindividuals aged 25-34 and exclude individuals with no reported individual income.
C. Copula
The copula we use is the 100 x 100 percentile transition matrix constructed by Chetty et al. (2014a,
Online Data Table 1).29 We briefly summarize the methodology used to construct this copula below;
see Chetty et al. (2014a, Appendix A) for further information.
Sample Construction
The sample consists of the set of children in Social Security Administration population records whoare born between 1980-1982 and are U.S. citizens as of 2013. For each child, we then define theparent(s) as the first person(s) who claim the child as a dependent on a 1040 tax form. Ninety percent
of children born between 1980 and 1982 can be linked to parents based on dependent claiming. We
limit the sample to children who can be linked to parents.
Income Definitions
We define both parents’ and children’s family income in the tax data as follows. In years where theindividual files a tax return, we define family income as Adjusted Gross Income (as reported on the1040 tax return) plus tax-exempt interest income and the non-taxable portion of Social Security andDisability benefits. In years where the individual 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). In years
where the individual has no tax return and no information returns, family income is coded as zero.
We average parents’ family income over the five years from 1996 to 2000 (the earliest years
available in the sample) to obtain a proxy for parent lifetime income that is less affected by transitory
fluctuations. We define child family income as mean income over the last two years in the data (2011and 2012), when children in the 1980-82 cohorts are in their early thirties.
Construction of Copula
We exclude parents with zero or negative income when constructing the copula because parents withno earnings typically do not file a tax return and hence cannot be linked to their children based on
dependent claiming. After excluding parents with zero income, we assign parents percentile ranks
based on their incomes relative to other parents in the sample. Children are assigned percentile ranks
based on their incomes relative to other children in the same birth cohort. We estimate the copula
29

This table can be downloaded from http://www.equality-of-opportunity.org/index.php/data.

25

non-parametrically as a 100×100 matrix that gives the joint probability of each child and parent
percentile rank pair.
For simplicity, we use the same copula when analyzing subgroups (by gender and state). Using
gender-specific or state-specific copulas yields very similar estimates of mean absolute mobility bycohort (not reported). We also use the same copula when measuring income at age 40, motivated byevidence that distribution of income ranks is stable between the ages of 30 and 60 (Chetty et al.
2014a).
D. Constructing Absolute Mobility
We combine the copula and the marginal income distributions for each birth cohort to calculate thefraction of children who earn as much or more than their parents at each parental income percentile.
The mean absolute mobility for a given cohort is simply the average of the rates of absolute mobility
across all parental income levels. We include parents with zero income when computing thesecohort-level averages, noting that children whose parents have zero income always earn at least as
much as their parents. Formally, we calculate mean absolute mobility in cohort c as
Ac = zc + (1 – zc)Ac | Par_Inc >0 ,(1)where zc is the fraction of parents with zero income in cohort c and Ac | Par_Inc >0 is mean absolutemobility for positive parental income (computed as an unweighted mean of absolute mobility acrosspercentiles).
E. Variable Definitions for Sensitivity and Heterogeneity Analysis
This subsection defines the variables used for the sensitivity and heterogeneity analysis in Section IVof the paper.
Alternative Price Deflators
We obtain additional deflators (PCEPI, PPI, GDP Deflator, CPI-U) from the Federal Reserve
Economic Data (FRED) database from the Federal Reserve Bank of St. Louis.
Taxes and Transfers
We estimate taxes using the NBER TAXSIM model (Feenberg et al. 1993). TAXSIM provides
federal tax estimates starting in 1960. We use it to estimate federal tax liability after credits forchildren in all cohorts and for parents in 1960 and thereafter. To estimate taxes for parents prior to1960, we use data on federal marginal tax rates and exemptions from Wilson (2002).
We compute taxes in TAXSIM using the following variables: year, marital status, age of the primaryand secondary taxpayers, wages and salary income (replicating the definitions in our baseline income
specification), and number of dependents. We use the output variable FIITAX, the federal income tax
liability after credits. When using marginal tax rates (prior to 1960), we determine exemptions basedon marital status and the number of dependents.
We use two sources of data to measure transfers. First, we use the CPS and Census to measure thevalue of cash transfers from welfare programs and Supplemental Security Income. In particular, we26

add in the variables incwelfr and incssi in IPUMS-CPS, and incwelfr and incsupp in IPUMS-USA.
We are able to measure these transfers for children in all years and for parents from 1970 onward.
Second, we include estimates of in-kind transfers from Fox et al. (2015), which cover SNAP, WIC,
housing assistance, the School Lunch Program, and LIHEAP. Data on in-kind transfers are only
available from 1967 onward. Prior to 1967, these transfers are set to zero. Fox et al. (2015) use CPS
and administrative data to estimate mean transfers (with and without tax credits) by marital status,
number of children, age categories, and family income decile for each year. We use these four
criteria to bin our observations and then assign everyone in each bin the corresponding averagetransfer amount. Families with positive income are assigned the mean transfer excluding tax credits,and families with incomes of zero or less are assigned mean transfer including tax credits. This isbecause families with positive incomes have already had their tax-credits accounted for by
TAXSIM.30
Alternative Income Measures
We use the following alternative income definitions for sensitivity analyses (Figure S6):
Total family income is defined as the sum of personal incomes of all co-residing members of thesame primary family (e.g., siblings, parents, or any other relatives). In our baseline analysis, we use
the sum of spouses’ total personal income minus income from welfare after 1950; however, we rely
on total family income to measure parents’ income in the 1950 Census as spouses’ total personal
income is not reported. The total family income definition is consistent across all years starting withthe 1950 Census.
Wage and salary income is defined as the sum of spouses’ income from wages and salaries. In ourbaseline analysis, we use wage and salary income to measure incomes in the 1940 Census(supplemented by imputed non-wage, non-salary income) because measures of total family income
and spousal income are not available. The wage and salary income measure is consistent across all
years starting with the 1940 Census.
Section II: Additional Robustness Checks
In this section, we present a set of supplementary robustness checks that address various limitationsof the data we use.
First, our baseline analysis measures parents’ family income as the sum of spouses’ total personal
income in the 1960-1980 Censuses. However, the 1950 Census only reports total family income,while the 1940 Census includes only wages and salaries, forcing us to use different income
definitions in these earlier years as discussed above. Figure S6 shows that the trend in absolutemobility is very similar if we use alternative income definitions that do not change across Censuses:
the sum of the spouses’ wage and salary income only or total family income, defined as the sum of
income earned by all co-residing members of the primary family.

30

The estimates on credits provided by TAXSIM are frequently higher than Fox et al. (2015), consistent with underreporting of credits in the survey data (Meyer, Mok, and Sullivan 2015). To check whether such under-reporting
affects our results, we implement specifications doubling the transfers reported by Fox et al. (2015). Our baseline
estimates of absolute mobility are not affected appreciably by such a correction.

27

Second, the CPS data does not record individuals’ birthplace before 1994. As a result, our baseline
series excludes immigrants starting with the 1964 cohort. To verify that this change in the treatmentof immigrants does not affect our results, Figure S7 includes immigrants in the calculation ofchildren’s marginal income distributions for all cohorts. Absolute mobility is slightly lower when
immigrants are included because immigrants tend to have lower earnings than natives on average, but
the trends are similar to our baseline results.
Third, in our baseline analysis, we pool data across multiple Censuses to measure the incomes of allparents between the ages of 25 and 35. This procedure provides an imperfect measure of parents’incomes because it relies on the assumption that the income distribution of those who have children
after age 35 is representative of the income distribution of the general population and because it does
not account for mortality or changes in parents’ marital status across Censuses. To assess therobustness of our findings to these concerns, we replicate our analysis using only a single Census tomeasure parents’ incomes, restricting parents’ age at childbirth to be between 25 and 35. Figure S8shows that we obtain very similar results when we focus on this subsample of parents.
Finally, the baseline results combine data for parents from the Census with data from the CPS forchildren. The use of the CPS for children permits measurement of children’s income in each birthcohort at exactly age 30, while the use of the Census for parents allows us to obtain data on parents’incomes back to 1940 (as the CPS began collecting comprehensive income data only in 1967). To
ensure that mixing income information from two different datasets does not produce bias, weestimate marginal income distributions using either the Census or the CPS for both parents andchildren. Figure S9 shows that we obtain very similar estimates of absolute mobility when we use
data from only the Census or only the CPS for both parents and children for the cohorts where data
are available.31

Section III: Counterfactuals
This section provides further detail on the methodology used to construct the counterfactuals
discussed in Section V of the text and presents an additional set of counterfactuals to assess therobustness of our conclusions.
A. Methods for Baseline Counterfactuals
Higher GDP Growth Scenario
To construct the higher growth counterfactual, we first calculate the ratio of income at each𝑘percentile q of the income distribution at age 30 for children in the 1980 birth cohort (𝑦𝑞,1980) to𝑂
𝑂
GDP per working-age family in 2010 (𝐺2010 ). We measure 𝐺2010 using annualized real GDP datafrom FRED (https://fred.stlouisfed.org/series/GDPCA). The number of working-age families is
31

For simplicity, when we measure parents’ incomes in the CPS, we only include parents between the ages of 25
and 35 who have a child less than one year old at the time of the survey. Unlike in our baseline analysis, we do notpool earlier or later surveys to include parents who have children before age 25 or after age 35 when estimating
parents’ incomes using the CPS. This is why the levels of absolute mobility in this series are closer to those in
Figure S8, which shows comparable estimates from our baseline Census-CPS specification. When we estimate
children’s incomes using the Census, we include individuals born in the U.S. who are 30 years old.

28

calculated by summing the household weights of all “famunits” that contain at least one person aged
18-64 in the Census, excluding those living in group quarters (GQ = 3 or 4).
𝐶
We then compute counterfactual GDP per working-age family in 2010 (𝐺2010) by applying 30 yearsof a 2.5% annual growth to the 1980 GDP per working-age family of $87,908. This gives a𝐶counterfactual GDP per family of 𝐺2010=$184,393= $87,908×1.02530 in 2010, compared to the𝑂observed value of 𝐺2010 = $136,198. Finally we create the counterfactual incomes by multiplying the𝑘𝑘𝑂𝐶observed income-to-GDP ratios (𝜋𝑞,1980= 𝑦𝑞,1980/𝐺2010) by the counterfactual GDP 𝐺2010.

We use analogous methods to calculate absolute mobility under the alternative annual growth rates of
1-10% presented in Figure 5B.
More Broadly Shared Growth Scenario

To construct the more broadly shared growth counterfactual, we first calculate the ratio of income𝑘at each percentile of the income distribution at age 30 for children in the 1940 birth cohort (𝑦𝑞,1940)
𝑂
to GDP per working-age family in 1970 (𝐺1970 ). We then multiply this ratio by the observed 2010𝑂
GDP per working-age family of 𝐺2010= $136,198 to obtain a counterfactual income distribution forchildren in the 1980 birth cohort.
B. Robustness to Alternative Counterfactuals
Measuring Income at Older Ages
Our more broadly shared growth counterfactual reallocates income not just across different income
groups but also across individuals of different ages. In this subsection, we assess whether thisreallocation across ages affects our conclusion that a broader distribution of growth across income
groups would substantially increase absolute mobility.
To motivate the issue, note that by using the ratio of child incomes at age 30 to GDP per working-age
family to characterize the income distribution, our counterfactuals combine three channels throughwhich the allocation of GDP affects children’s marginal income distributions. First, within the set of
30 year olds in our sample, the allocation of income has become more unequal over time. In 1970,
the difference between the 90th and 10th percentile of the income distribution of 30 year olds was$70,011; this difference grew to $118,347 in 2010. Second, the total amount of GDP per working-age
family that accrues to 30 year olds has declined. The average income of 30 year olds in our sample
fell from 69% of GDP per working-age family in 1970 to 44% in 2010. Finally, the total amount of
national income captured in the CPS and Census has declined with the rise of profits and the increase
in top income shares, which are not fully recorded in surveys (Bollinger et al. 2015, Piketty, Saez,
Zucman 2016). The ratio of total income in the CPS to total GDP declined from 73% in 1970 to 60%
in 2010.
To understand the contributions of these three components to our counterfactuals under the broadly
shared growth scenario, we first consider a counterfactual that uses the total income in the CPS (per𝑂
working-age family) instead of GDP to measure 𝐺2010. This lowers the estimated rate of absolutemobility from the baseline value of 80% to 72%. As expected, a broadly shared growth scenario that
does not fully account for the rise of incomes not captured in the CPS generates a lower rate ofabsolute upward mobility.
29

𝑂
Second, we consider a counterfactual that replaces GDP (𝐺2010) with the total amount of income that
accrues to 30 year olds in the CPS. In this scenario, absolute mobility would be 57%. This resultshows that a significant portion of the increase in absolute mobility in our baseline more broadly
shared growth counterfactual is driven by the fact that 30 year olds today earn a smaller fraction of
GDP than in the past. This finding raises the potential concern that the effects of distributing income
more equally on absolute mobility might differ if we measure incomes at older ages.

We evaluate this concern by repeating our counterfactuals, measuring incomes at age 40 instead ofage 30. We construct counterfactuals for the 1970 cohort, the most recent decadal birth cohort forwhom we can measure income at age 40. For the higher growth scenario, we use the same
counterfactual level of GDP per working-age family in 2010 used for the age 30 counterfactuals,
𝐶
𝐺2010=$184,393.32 However, we multiply the observed income-to-GDP ratios for 40 year olds in𝑘𝑘𝑂𝐶2010 (𝜋𝑞,1970= 𝑦𝑞,1970/𝐺2010) by 𝐺2010
to create the counterfactual income distribution at age 40
for the 1970 cohort under higher GDP growth. For the more broadly shared growth scenario, we
calculate income-to-GDP ratios using incomes and GDP in 1980, when the 1940 cohort was 40 years
𝑂old. We then multiply these ratios by observed GDP per working-age family in 2010 (𝐺2010) toconstruct estimates of what the 1970 cohort would have earned at age 40 if GDP in 2010 wereallocated more evenly.
Panel A of Figure S12 presents the results of these counterfactuals, along with the actual levels of
absolute mobility observed at age 40 for the 1940 and 1970 birth cohorts. In the data, mean absolutemobility at age 40 fell from 86% for the 1940 cohort to 56% for the 1970 cohort. Our counterfactual
analysis shows that mean absolute mobility for the 1970 cohort would be 68% under the higher
growth counterfactual, closing 39% of the gap between the two cohorts. Mean absolute mobility
would rise to 74% for the 1970 cohort under the more broadly shared growth counterfactual, closing
59% of the observed gap between the two cohorts. Hence, the qualitative conclusion that more
broadly shared growth would have a substantial effect on absolute mobility is unaffected bymeasuring income at later ages. Intuitively, the effect of the changing age distribution of growth
noted above is partly offset by the greater degree of inequality in incomes at older ages, which
increases the impact of changing the income distribution.
Using Shares of GDP Growth Instead of Levels
In our baseline analysis, we construct counterfactual incomes by allocating GDP based on
individuals’ observed shares of the level of GDP at age 30. An equally reasonable alternative is toconstruct counterfactuals based on individuals’ observed shares of GDP growth from birth to age 30.
In this subsection, we assess whether using growth shares would affect our conclusions.
To construct counterfactual incomes under the higher growth scenario using growth shares, we first
calculate the difference in income between children and parents at each percentile q for the 1980𝑘𝑃
cohort (𝑦𝑞,1980− 𝑦𝑞,1980). We then calculate the change in GDP per working-age family from 1980
𝑂𝑂
to 2010 (𝐺2010− 𝐺1980). Dividing the difference in income at a given percentile by the change in
GDP gives us the ratio of income to GDP growth at each percentile for the 1980 cohort. We then32

We use the same counterfactual GDP – applying 30 years of a 2.5% annual growth rate to GDP in 1980 – eventhough children are 40 years old when we measure their incomes because children’s incomes are still measured
approximately 30 years after their parents’ incomes.

30multiply these ratios by the counterfactual GDP per family growth of $96,485 – the counterfactual𝐶
GDP per working-age family of 𝐺2010=$184,393 minus observed 1980 GDP of $87,908 – and addthem to the 1980 parent incomes at each percentile to obtain counterfactual incomes for children.
To construct counterfactual incomes under the more broadly shared growth scenario using growthshares, we first calculate the difference in parent versus child incomes at each percentile of the𝑘𝑃
income distribution for the 1940 cohort (𝑦𝑞,1940− 𝑦𝑞,1940). We then divide these differences by the𝑂𝑂
increase in GDP per working-age family from 1940 to 1970 (𝐺1970− 𝐺1940) to obtain the ratio ofincome to GDP growth at each percentile for the 1940 cohort. We then multiply these ratios by theobserved change in GDP per working-age family from 1980-2010 of $48,291 ($136,198 in 2010
minus $87,908 in 1980) and add them to the 1980 parent incomes at each percentile to obtaincounterfactual incomes for children.
The results of this alternative approach are presented in Panel B of Figure S12. We find an evenlarger impact of the broadly shared growth counterfactual relative to the high growth counterfactual
than in our baseline counterfactuals. Under the broadly shared growth counterfactual, mean absolutemobility rises to 80%; under the higher growth counterfactual, mean absolute mobility falls to 47%.
This is because many percentiles of the children’s income distribution have fallen relative to theirparents for the 1980 birth cohort. For these groups, allocating growth in accord with how it has
been allocated between 1980-2010 (i.e., using negative growth shares) decreases their incomes
further. Conversely, changing the distribution to the more equal shares of growth experienced by the1940 cohort has very large effects.
In Panel C of Figure S12, we replicate the growth shares counterfactuals in Panel B, measuringincomes at age 40 for the 1970 cohort. These counterfactuals are constructed in the same way as
above, except that they use income growth to GDP growth ratios for the years 1950-1980 rather than
1940-1970 in the more broadly shared growth counterfactual. The results at age 40 are very similar
to those at age 30.
In sum, these alternative counterfactuals reinforce the conclusion that higher GDP growth itself
cannot increase absolute mobility unless it is more broadly distributed.

31

Figure 1. Baseline Estimates of Absolute Mobility by Birth Cohort

Pct. of Children Earning more than their Parents

A. Selected Cohorts by Parent Income Percentile
100
1940
80

1950

60

1960
1970

40

1980
20

0
0

20
40
60
80
Parent Income Percentile (conditional on positive income)100

Pct. of Children Earning more than their Parents

B. Mean Rate of Absolute Mobility by Cohort
100

90

80

70

60

50
1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure plots the fraction of children earning more than their parents (“absolutemobility”) by parental income percentile for selected child birth cohorts (Panel A) and on
average by child birth cohort (Panel B). Panel A includes only parents with positive income;within this group, parents’ income percentiles are constructed based on their ranks in the
distribution of parents’ incomes within each child cohort. Panel B includes parents with 0
income, defining absolute mobility as 100% for that subgroup when computing the mean rate ofabsolute mobility by cohort. Children’s income is measured at age 30 in the CPS-ASEC as thesum of individual and spousal income, excluding immigrants after 1994. Parental income ismeasured in the Census as the sum of the spouses’ incomes for families in which the highest
earner is between age 25-35. Children’s and parents’ incomes are measured in real 2014 dollars
using the CPI-U-RS. Absolute mobility is calculated by combining these income distributions
with the copula estimated for the 1980-82 cohorts in tax data by Chetty et al. (2014a)

Figure 2. Effects of Copula on Absolute Mobility by Cohort
A. Bounds on Absolute Mobility Across All Copulas
Pct. of Children Earning more than their Parents

100

B. Family Income Distributions: 1940 Birth Cohort

Upper Bound

80

CopulaObserved

80th percentile of parents distribution

Density60

Baseline Estimates

40

14th percentileof children's
distribution

Lower Bound
20

Parents

1940

1950

1960
1970
Child's Birth Cohort

1980

0

C. Family Income Distributions: 1980 Birth Cohort

27kChildren

50k
100k
Income (Measured in Real 2014$)

150k

D. Child Rank Needed to Beat Parents and 1980-82 Copula
100

Density

80th percentile of parents distribution

74th percentile ofchildren's distribution

Child Income Percentile

80(80,74)

60

1980
40

20
Parents(80,14)
1940

Children

0
0

50k

80k
100k
Income (Measured in Real 2014$)

150k

0

20

40
60
Parent Income Percentile

80

100

Notes: These figures show how the copula affects estimates of absolute mobility by birth cohort. Panel A plots bounds on absolute mobility for eachcohort over all copulas satisfying first-order stochastic dominance of children’s income distributions as parent income rises. The bounds are estimatedseparately by cohort. The solid circles in Panel A replicate the baseline estimates shown in Figure 1B, with the section to the right of the dashed verticalline corresponding to the cohorts (1971-1984) for which Chetty et al. (2014b) document copula stability. Panel B plots the marginal family income
distributions of children in the 1940 birth cohort and their parents, measured at approximately age 30. Corresponding to the analysis in Figure 1A, parents
with zero income are excluded, but children with zero income are included when estimating these kernel densities. For scaling purposes, incomes above$200,000 are excluded. Panel C plots analogous income distributions for children in the 1980 birth cohort and their parents. Panel D plots the income
percentile that a child must reach in order to earn more than his or her parents for the 1940 and 1980 cohorts, with labels corresponding to the examples
shown by the dashed vertical lines in Panels B and C. Panel D also shows a heat map of the baseline copula for the 1980-82 birth cohorts. The copula is a
100x100 matrix where each cell (x,y) gives the probability of a child being in income percentile y and having parents in income percentile x (conditional
on parents having positive income). Darker colors represent areas with higher density in the copula.

Figure 3. Trends in Absolute Mobility: Sensitivity Analysis
A. Alternative Price Deflators
Baseline: CPI-U-RS
CPI-U-RS minus 0.8%
PCEPI
PPI

90

80

70

60

100

Pct. of Children Earning more than their Parents

Pct. of Children Earning more than their Parents

100

B. Taxes and Transfers

50

Baseline: Pre-Tax Income
Including Taxes
Including Taxes and Transfers

90

80

70

60

50
1940

1950

1960
1970
Child's Birth Cohort

1980

1940

C. Income Measured at Age 40

1960
1970
Child's Birth Cohort

1980

D. Adjusting for Family Size

Baseline: Children Age 30, Parents 25-35
Children Age 40, Parents 35-45

90

80

70

60

100

Pct. of Children Earning more than their Parents

Pct. of Children Earning more than their Parents

100

1950

Baseline - Family Income, All Children
Divide by Sqrt(Family Size)
Individual Income, Fathers-Sons

90

80

70

60

50

40

50
1940

1950

1960
1970
Child's Birth Cohort

1980

1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure plots absolute mobility by child birth cohort using a set of alternative income definitions. Panel A presents estimates that use
alternative price deflators to adjust for inflation, including the producer price index (PPI) and the personal consumption expenditure price index (PCEPI).
We also consider a price index that adjusts for bias in the CPI-U-RS due to new and higher quality products by subtracting 0.8% from the annual
inflation rate implied by the CPI-U-RS (Meyer & Sullivan 2009, Broda and Weinstein 2010). Panel B presents estimates using income after including
federal taxes and transfers. Taxes are estimated using the NBER TAXSIM model (Feenberg 1993) for years after 1960, and historical marginal tax rates
before 1960. Transfers include cash and in-kind transfers. Cash transfers are obtained from Census and CPS data. In-kind transfers are obtained from
calculations by Fox et al. (2015) using CPS data from calendar year 1967 onward; prior to 1967, in-kind transfers are set to zero. Panel C plots absolutemobility when children’s income is measured at age 40 and parental income is measured between ages 35-45. Note that the last year of income data in
our sample is 2014, so absolute mobility can only be measured at age 40 until the 1974 birth cohort. Panel D presents estimates that adjust income forfamily size and number of earners. In the series in open circles, we divide the baseline measures of family income by the square root of family size
(defined as the number of dependent children plus the number of adults) for both parents and children. In the series in triangles, we estimate the fractionof sons whose individual incomes are greater than or equal to their fathers’ individual incomes. Individual income is defined in the same way as thebaseline family income measure, but does not include spousal income.

Figure 4. Trends in Absolute Mobility by State
A. Absolute Mobility by Birth Cohort for Selected States
Pct. of Children Earning more than their Parents

100

Massachusetts
New York
Ohio
Michigan

90

80

70

60

50

40
1940

1950

1960
Child's Birth Cohort

1970

1980

B. Decline in Absolute Mobility from 1940 to 1980 Cohort by State

Notes: This figure shows trends in absolute mobility by state. Panel A shows estimates for decadalbirth cohorts for selected states; data by cohort for all other states is reported in Table S2. Panel B
shows a heat map of the magnitude of the decline in absolute mobility from the 1940 to 1980
cohorts, with darker colors representing states with larger declines. For parents, state refers tolocation at the time incomes are measured (between ages 25-35); for children, state refers tolocation at birth. Since children’s state of birth is not observed in the CPS, we use the Census forboth parents and children. To increase precision, we include all children aged 25-35 and use the
100% Census in 1940 and 5% IPUMS sample in 1980. Measuring children’s incomes from ages
25-35 rather than just at age 30 creates small differences in levels of absolute mobility. To adjust
for these differences, we calculate the difference between the baseline national estimates andpopulation-weighted national means of our state-level estimates for each cohort, and add thesedifferences to the state-level estimates.

Figure 5. Absolute Mobility for 1980 Birth Cohort: Counterfactual Scenarios
A. Counterfactual Rates of Absolute Mobility by Parent Income Percentile
Pct. of Children Earning more than their Parents

100

Mean AM:91.5%

80

1940 Empirical

Mean AM:79.6%

60
Mean AM:61.9%

40

Mean AM:50.0%
1980 Empirical

20
1980 GDP/family growth rate (1.5%), 1940 income shares
1940 GDP/family growth rate (2.5%), 1980 income shares

0
0

20
40
60
80
Parent Income Percentile (conditional on positive income)100

B. Counterfactual Absolute Mobility for 1980 Cohort vs. GDP Growth Rate
Pct. of Children Earning more than their Parents

100
1940 Empirical
90

80

70

60
1980 Empirical

50

40
0

2

4
6
Real GDP/Family Growth Rate (%)

810Notes: This figure shows how absolute mobility for the 1980 cohort would change under counterfactual
scenarios varying GDP growth rates or the distribution of income. Panel A plots absolute mobility by parent
income percentile. The solid curves replicate the baseline estimates of observed absolute mobility by parent
income percentile from Figure 1A for the 1940 and 1980 birth cohorts. The dashed series, “1940 GDP/family
growth rate (2.5%), 1980 income shares,” plots the rates of absolute mobility that the 1980 cohort would haveexperienced had GDP per working-age family grown at 2.5% annually from 1980-2010 instead of the actual
rate of 1.5%. The resulting higher level of GDP in 2010 is allocated to households based on the ratio ofincome to GDP per working family at each percentile of the family income distribution for 30 year olds in2010. The dotted series, “1980 GDP/family growth rate (1.5%), 1940 income shares” plots the rates ofabsolute mobility that the 1980 cohort would have experienced had GDP in 2010 been allocated in the samemanner across households as it was for the 1940 cohort. In this counterfactual, GDP remains at the observed
level in 2010, but income is allocated to households based on the ratio of income to GDP per working family
at each percentile in the 1940 cohort. For each series, we also report the mean level of absolute mobility(AM), averaging across all income percentiles (including parents with zero incomes, whose children
mechanically have absolute mobility of 100% and are not shown in the figure). In Panel B, the solid line plots
mean absolute mobility for the 1980 cohort had they experienced alternative GDP growth rates. Theseestimates are constructed in the same way as the estimate of AM for the “1940 GDP/family growth rate
(2.5%), 1980 income shares” series in Panel A, using growth rates ranging from 1% to 10%. The dashedhorizontal lines show the actual levels of AM for the 1940 and 1980 birth cohorts. See Section III of the
Supplementary Appendix for further details on these counterfactuals.

Figure S1. Copulas that Maximize and Minimize Absolute Mobility for 1980 Cohort

A. Copula that Generates Upper Bound for Absolute Mobility
100Child Income Percentile

80

60

40

20

0
0

20
40
60
80
Parent Income Percentile (conditional on positive income)100

B. Copula that Generates Lower Bound for Absolute Mobility
100Child Income Percentile

80

60

40

20

0
0

20
40
60
80
Parent Income Percentile (conditional on positive income)100

Notes: This figure depicts the copulas that generate the bounds on absolute mobility for the 1980 cohort in Figure 2A. Panel A
presents the copula that generates the upper bound on absolute mobility, while Panel B presents the copula that generates thelower bound on absolute mobility. Darker shades represent cells with greater mass in the copula. The solid curve in both panels
shows the rank that a child must reach in order to surpass the income of their parents by parental income percentile in the 1980birth cohort, as in Figure 2D.

Pct. of Children Earning more than their Parents

Figure S2. Alternative Price Deflators

100

Baseline: CPI-U-RS
CPI-U-RS Minus 2%
GDP Deflator
CPI-U

90

80

70

60

50
1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure plots absolute mobility by birth cohort, replicating Figure 3A with alternatives to our baseline price deflator(the CPI-U-RS): the GDP deflator, the CPI-U, and a price index that subtracts 2% from the annual inflation rate implied by the
CPI-U-RS.

Figure S3. Alternative Adjustments for Family Size

Pct. of Children Earning more than their Parents

100

90

80

70

60
Baseline
Divide by Nr of Adults
Divide by Family Size

50
1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure plots absolute mobility by cohort, replicating Figure 3D using alternative adjustments for family size. We
divide the baseline family income measures for both parents and children by either the total number of adults in the household(triangles) or by family size (open circles). The number of adults is defined as one plus an indicator for being married. In the
CPS, family size is defined as the number of own children plus the number of spouses. In the Census, family size is defined as
the number of own family members residing with each individual.

Pct. of Children Earning more than their Parents

Figure S4. Effects of Increasing Child Income on Absolute Mobility for 1984 Cohort

100

90

80

70

60

50
0

10,00020,00030,00040,000Magnitude of Income Increase for Children in 2010

50,000Notes: This figure recalculates absolute mobility for the 1984 birth after increasing each child’s income in 2010 by fixed dollar
amounts ranging from 0 to $50,000 (measured in real 2014 dollars). Aside from these increments to children’s incomes, all otheraspects of the specification are identical to the baseline.

Figure S5. Alternative Measures of Absolute Mobility

Pct. of Children Earning 20% More/Less than Parents

A. Alternative Income Thresholds
100

Baseline
20% Less
20% More

90

80

70

60

50

40
1940

1950

1960
1970
Child's Birth Cohort

1980

Median Child Income / Parent Income

B. Median Ratio of Children’s Income to Parents’ Income

3

2.5

2

1.5

1
1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure shows estimates of absolute mobility by birth cohort using alternative measures of mobility. Panel A shows thefraction of children earning 20% more than their parents or 20% less than their parents. Panel B plots the median ratio of child toparent income. All other aspects of the absolute mobility calculations are identical to those used in the baseline specification.

Pct. of Children Earning more than their Parents

Figure S6. Alternative Income Definitions

100

Baseline
Wage Income Only
Family Income

90

80

70

60

50

1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure plots absolute mobility by cohort, replicating Figure 1B using alternative income definitions for parents andchildren. Wage Income is computed as the sum of wage and salary income of the individual and spouse (if applicable). Family
income is total income from all co-residing members of the primary family. The Supplemental Appendix provides further details
on how these measures are defined. Aside from these changes to the income definition, all other aspects of the specification are
identical to the baseline.

Pct. of Children Earning more than their Parents

Figure S7. Effect of Including Immigrants

100

Baseline
Including Immigrants

90

80

70

60

50
1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure plots absolute mobility by cohort, replicating Figure 1B including immigrants in the sample of children. The
CPS-ASEC did not collect data on birthplace prior to 1994, so the 1964 cohort is the first cohort for which immigrants are
excluded from our baseline sample.

Pct. of Children Earning more than their Parents

Figure S8. Sensitivity to Parent Age at Child Birth100

Baseline
Parents Who Have Children
Between Ages 25-35 Only

90

80

70

60

50
1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure replicates Figure 1B after restricting the sample to parents who have a child between ages 25-35, the ages atwhich we measure parents’ incomes. All other aspects of the specification are identical to the baseline. The baseline estimates
include all parents who have a child between ages 16-45 by pooling data across multiple Censuses.

Pct. of Children Earning more than their Parents

Figure S9. Alternative Data Sources for Marginal Income Distributions

100

Baseline
CPS Only
Census Only

90
80
70
60
50
40
1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure plots absolute mobility by cohort, measuring both parents’ and children’s incomes using the same dataset
rather than using annual CPS data for children and decadal Census data for parents as in our baseline specification. In the Census
only series, parents’ incomes are identical to the baseline, while children’s income distributions are defined using total family
income among all 30-year olds. In the CPS only series, children’s incomes are identical to the baseline, while parents’ income
distributions are calculated using total family income for parents of newborns in families where the higher-earning parent is aged
25-35. The CPS only series therefore excludes parents who have children after age 35 or before age 25, as in Figure S8. The CPS
only series begins in 1968 because consistent income definitions for parents are not readily available in prior years. All otheraspects of the specifications in both series are identical to the baseline.

Figure S10. Heterogeneity by GenderPct. of Children Earning more than their Parents

100

Baseline
Son vs. Parents' Family Income
Daughter vs. Parents' Family Income
Son vs. Father Individual Income
Daughter vs. Father Individual Income

90
80

70
60
50

40
30
20
1940

1950

1960
1970
Child's Birth Cohort

1980

Notes: This figure plots absolute mobility by cohort for sons and daughters using individual income and family income(including spousal income). The series in solid triangles plots the fraction of sons whose family income exceeds their parents’family income, replicating Figure 1B for sons. Similarly, the series in hollow triangles plots the fraction of daughters whosefamily income exceeds their parents’ family income. The series in circles plots the fraction of sons whose individual income
exceeds their fathers’ individual income, replicating the series in Figure 3D. The series in squares plots the fraction of daughters
whose individual income exceeds their fathers’ individual income.

Figure S11. Median Incomes by Year, Individuals Aged 25-34

50000

Income (Real 2014$)

40000

30000

20000

Our Sample - MalesCPS Historical Income Tables - Males
Our Sample - Females
CPS Historical Income Tables - Females

10000
1970

1980

1990
Year

2000

2010

Notes: This figure plots the median income of individuals aged 25-34 in the CPS as published by the Census Bureau (Historical
Income Tables: People P-8) alongside our own estimates, constructed from the CPS-ASEC. Both series use total personal(individual) income, adjusting for inflation using CPI-U-RS. In contrast to our baseline marginal income distributions, we poolindividuals from ages 25-34 and drop individuals with zero income for comparability with the published Census tables.

Figure S12. Alternative Counterfactuals
B. Shares of GDP Growth, Age 30
Pct. of Children Earning more than their Parents

Pct. of Children Earning more than their Parents

A. Baseline Specification, Age 40
100
Mean AM:85.8%
1940 Empirical

80

Mean AM:73.6%

Mean AM:67.5%

60
Mean AM:55.8%

40
1970 Empirical
1970 GDP/family growth rate (1.5%), 1940 income shares

20

1940 GDP/family growth rate (2.5%), 1970 income shares

0

20
40
60
80
Parent Income Percentile (conditional on positive income)

100

100

Mean AM:91.5%

80

1940 Empirical

Mean AM:79.7%

60
Mean AM:50.0%

40Mean AM:46.5%
1980 Empirical

20
1980 GDP/family growth rate (1.5%), 1940 income growth shares
1940 GDP/family growth rate (2.5%), 1980 income growth shares

0
0

20
40
60
80
Parent Income Percentile (conditional on positive income)100

Pct. of Children Earning more than their Parents

C. Shares of GDP Growth, Age 40
100
Mean AM:85.8%
1940 Empirical

80

Mean AM:74.4%
Mean AM:57.1%

60
Mean AM:55.8%

40
1970 Empirical

20
1970 GDP/family growth rate (1.5%), 1940 income growth shares
1940 GDP/family growth rate (2.5%), 1970 income growth shares

0
0

20
40
60
80
Parent Income Percentile (conditional on positive income)100

Notes: This figure presents the alternative counterfactual scenarios described in Section III of the Supplemental Appendix. Panel A replicates thecounterfactuals in Figure 5A, measuring incomes at age 40 instead of age 30. We use the 1970 cohort instead of the 1980 cohort for the age 40 analyses
as it is the most recent decadal cohort for which income at age 40 can be observed. Panel B reports results from GDP growth shares counterfactuals, inwhich counterfactual incomes for children in the 1980 cohort are constructed based on observed shares of GDP growth from birth to age 30 (19802010) rather than shares of GDP levels in 2010. Panel C replicates Panel B, measuring incomes at age 40 instead of age 30. In all panels, the dottedlines present the higher GDP growth counterfactuals, while the dashed lines present the more equal growth counterfactuals.

Table S1. Summary Statistics for Child and Parent Samples
Children (CPS)Child's
Birth
Cohort
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984

Parents (Census)

No. of Weighted Income at Age 30 ($)
ChildrenCount
MeanMedian
(1)
(2)
(3)
(4)

No. ofFamilies
(5)

Mean
(6)

Median
(7)

1,614
1,680
1,745
1,899
1,843
1,718
1,706
2,687
2,560
2,500
2,990
2,953
2,703
2,730
2,650
2,817
2,827
2,805
2,825
2,528
2,680
2,726
2,757
2,713
2,025
1,953
1,561
1,580
1,552
1,577
1,447
2,599
2,393
2,140
2,179
2,040
2,009
2,085
2,041
2,132
2,153
2,242
2,086
2,156
2,005

9,990
20,186
21,106
22,847
23,252
23,20323,56230,276
31,256
29,69928,767
20,952
22,88824,561
26,42328,57429,86831,813
33,631
34,69135,56436,52436,86636,86837,76536,47034,24333,12632,30133,312
33,91736,92133,45932,35930,71831,351
31,286
31,42632,222
32,48834,92835,81934,32635,91635,375

18,835
20,642
21,28022,29522,651
23,723
24,614
27,83629,44831,12432,96832,051
34,24435,36336,536
37,61039,06539,776
41,30442,17743,92044,595
46,17546,90447,54548,32049,11650,35851,12951,67553,43752,50452,71452,92853,86454,18554,77055,23855,95655,33357,02852,54853,20253,54254,586

17,836
18,694
19,322
19,857
19,857
19,857
20,06523,781
25,961
27,38329,51728,25930,86732,60634,34535,56235,91836,62938,05238,40740,18540,26342,31943,03043,56644,80945,52046,25946,94247,97249,282
48,25848,65948,82949,78750,25751,06051,69951,69951,68552,93046,204
46,84147,062
47,9472,256,476
2,371,403
2,652,364
2,903,434
2,901,957
2,809,649
2,718,989
3,606,320
3,583,373
3,566,347
3,590,742
3,674,309
3,860,927
3,970,066
3,901,364
4,153,580
4,373,260
4,432,183
4,517,124
4,412,732
4,481,928
4,510,418
4,602,943
4,610,697
3,730,913
3,644,244
3,357,382
3,396,908
3,292,186
3,281,357
3,089,620
3,422,277
3,191,262
2,910,392
3,031,181
2,825,818
3,017,329
3,062,028
3,092,305
3,175,792
3,153,461
3,328,443
3,225,419
3,381,167
3,212,377

57,15955,47356,58759,35262,06956,83956,44858,85358,90958,64259,85757,16354,89153,76552,73955,11856,33359,03358,26658,80956,69455,70054,83655,49657,17558,79359,39458,872
65,26363,261
69,381
71,011
68,17567,44868,171
65,86262,741
69,692
66,81564,67960,65058,08860,18957,64453,43553,51253,25953,70855,68957,79255,44052,43055,31154,88655,64555,60554,72951,84549,012
48,13650,75949,882
51,64452,226
51,17049,97647,63846,97247,53845,67450,61449,37749,60053,75952,431
56,85355,03753,934
54,10552,15552,65949,02952,85751,51349,814
46,37343,44847,38443,35042,687

Income Ages 25-35 ($)

Notes: The table presents summary statistics for the samples used to estimate parents' and children's
marginal income distributions in our baseline analysis. Columns 1-4 report statistics for children from the
CPS, while columns 5-7 report statistics for parents from the Census. Column 1 reports the total number ofchildren observed at age 30 in each birth cohort in the CPS; for example, the 1940 cohort is observed atage 30 in the 1970 CPS. Column 2 reports the sum of the sampling weights for each birth cohort in the
CPS, i.e. the weighted cohort size. Columns 3 and 4 report the mean and median incomes of thesechildren at age 30 using our baseline family income measure, which sums income across spouses.
Column 5 presents the number of families who have children in each birth cohort, drawing on data frommultiple Census years as described in the text. Columns 6 and 7 present the mean and median family
incomes of these parents. Incomes are expressed in 2014 dollars, adjusting for inflation using the CPI-URS.

Table S2. Absolute Mobility by State and Birth Cohort
Absolute Mobility Rate by Birth Cohort (%)

Change from

State

1940

1950

1960

1970

1980

1940-80

Alabama
AlaskaArizona
Arkansas
California
Colorado
Connecticut
DelawareDistrict of Columbia
FloridaGeorgia
Hawaii
Idaho
Illinois
Indiana
Iowa
KansasKentuckyLouisiana
Maine
Maryland
Massachusetts
MichiganMinnesota
Mississippi
MissouriMontana
Nebraska
NevadaNew Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
OregonPennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming

92.0
87.3
88.5
92.1
89.1
92.0
92.3
91.6
86.3
90.5
92.1
94.4
94.6
92.4
94.3
94.8
93.6
91.9
88.7
93.2
90.8
91.4
93.3
94.3
90.7
93.8
91.5
94.5
89.1
93.0
89.9
89.5
90.0
92.8
93.7
93.0
93.8
92.0
92.6
90.8
91.1
92.9
92.3
91.3
93.7
91.8
90.6
91.9
93.0
94.4
91.4

81.8

64.5
57.2
57.7
70.7
58.0
54.9
66.8
70.8
71.7
62.3
63.0
59.7
68.4
59.5
59.7
65.7
66.4
64.5
58.6
74.3
59.8
67.9
57.1
64.4
66.0
63.0
64.9
65.4
51.9
62.8
66.7
57.3
65.8
69.0
73.6
58.1
64.9
55.4
65.9
70.5
67.4
76.0
62.2
61.3
64.3
73.8
65.3
59.4
66.2
62.9
62.8

63.9
45.0
57.5
66.0
57.2
62.8
64.1

51.9
37.9
46.2
56.0
48.8
49.9
51.8
51.4
66.2
45.8
48.2
50.0
49.2
47.0
48.4
54.0
49.7
53.4
53.2
50.1
51.2
55.4
45.7
52.9
53.1
52.4
58.6
54.9
39.5
51.0
52.5
50.9
54.7
49.8
59.4
47.9
51.2
47.7
53.9
54.4
49.4
62.3
49.6
50.5
53.1
47.4
47.9
45.8
49.9
50.6
49.0

40.1
49.4
42.3
36.1
40.3
42.1
40.5
40.2
20.1
44.7
43.9
44.4
45.3
45.5
45.9
40.8
43.9
38.5
35.5
43.1
39.5
36.0
47.6
41.4
37.6
41.4
33.0
39.6
49.7
42.1
37.4
38.7
35.3
43.0
34.3
45.2
42.5
44.3
38.7
36.4
41.7
30.6
42.7
40.7
40.6
44.4
42.7
46.1
43.1
43.8
42.4

73.9
83.3
71.2
77.5
79.0
81.9
77.4
77.2
82.6
81.2
78.2
79.0
82.9
82.1
83.3
80.1
77.5
75.3
77.9
76.8
84.1
82.8
80.8
80.1
83.3
69.5
78.5
77.3
80.1
77.6
83.5
84.2
78.0
81.7
76.5
81.5
80.1
82.8
81.3
81.5
80.5
78.3
81.5
82.1
76.7
82.4
81.0
75.1

68.9
61.4
59.5
54.6
58.3
58.6
65.7
63.1
70.1
59.5
66.8
59.6
67.5
58.5
63.2
66.4
61.8
66.9
49.2
61.5
64.4
60.6
64.2
65.0
58.0
57.1
60.2
65.0
66.8
63.3
64.6
58.8
61.1
59.9
57.5
58.3
63.7

Notes: This table presents rates of absolute mobility by state for decadal cohorts from 1940-80; the final column shows themagnitude of the change from 1940 to 1980. Since children’s state of birth is not observed in the CPS, we use the Census forboth parents and children. To increase precision, we include all children aged 25-35 and use the 100% Census in 1940 and 5%
IPUMS sample in 1980. Measuring children’s incomes from ages 25-35 rather than just at age 30 creates small differences inlevels of absolute mobility. To adjust for these differences, we calculate the difference between the baseline national estimatesand population-weighted national means of our state-level estimates for each cohort, and add these differences to the statelevel estimates. State-cohort cells with insufficient data are blank.

Table S3. Income Variables Used to Measure Parents' Incomes, by Census Year
1940
1950
1960
1970
1980
1990
2000
INCWAGEFTOTINC
INCNONWG

INCWAGEINCBUSFM
INCOTHERINCWAGE INCWAGE INCWAGE INCWAGEINCBUSINCBUSINCBUSINCBUSINCFARM INCFARM INCFARM INCSS
INCSS
INCSS
INCSS
INCINVSTINCOTHER INCINVST INCINVST INCRETIRINCOTHER INCRETIR INCOTHERINCOTHER

Notes: This table lists the income variables in the IPUMS-USA that are used to construct the baseline
measures of parental family income by Census year.

Table S4. Income Variables Used to Measure Children's Incomes, by CPS Year
1970-1975
1976-1987
1988-2014
INCWAGEINCWAGEINCWAGEINCBUSINCBUSINCBUSINCFARM
INCFARM
INCFARM
INCSS
INCSS
INCSS
INCGOVINCGOVINCRETIR
INCIDR
INCRETIR
INCINTINCALOTHINCDRTINCUNEMP
INCINTINCWKCOMINCALOTHINCVETINCSURVINCDISABINCDIVID
INCRENTINCEDUC
INCCHILDINCALIMINCASISTINCOTHER
Notes: This table lists the income variables in the IPUMS-CPS that are used to construct the baseline
measures of children's family income by CPS year.