Bhash Mazumder

English

Research Papers in Economics

Chicago Fed Letter
Analyzing income mobility over generations
by Bhash Mazumder, economist
Recent research on the transmission of economic status from one generation to the
next suggests that the persistence in inequality is about 50% higher than previously
thought. While the underlying factors that cause substantial immobility in the U.S.
remain poorly understood, borrowing constraints among families with low net worth
may play a role in perpetuating inequality.
ESSAYS ON ISSUES THE FEDERAL RESERVE BANK SEPTEMBER 2002
OF CHICAGO NUMBER 181
1. Implied bias in intergenerational elasticity
percent bias
Number of years averaged
How economically mobile is the United
States? Do all children have the opportu-
nity to achieve economic success irrespec-
tive of their economic circumstances at
birth? Is there an economic underclass
that is essentially trapped in poverty
for generations? The answers to these
questions undoubtedly have a bearing
on whether America should
be viewed as an equal oppor-
tunity society and whether
additional policies are need-
ed to address long-term in-
equities. Despite the obvious
importance of economic
mobility in determining
public policies, economists
have only recently begun to
carefully study the dynam-
ics of inequality among
families over generations.
Several studies undertaken
in the 1990s found a rela-
tively high degree of trans-
mission of economic status
from fathers to sons, sug-
gesting that the U.S. is not nearly as
mobile a society as many had previously
thought. For example, the results im-
plied that about 40% of the gap in
earnings between black and white
men would persist from one genera-
tion to the next—roughly twice the
rate of persistence that previous re-
search had found.
Although these studies used substan-
tially better data than previous work,
they still suffer from a number of limita-
tions that have the effect of underesti-
mating the degree of intergenerational
persistence in inequality. In this Chicago
Fed Letter, I describe the results of recent
research that suggests that the persis-
tence in inequality is about 50% higher
than the consensus view among econo-
mists. Although the underlying factors
that cause substantial immobility in the
U.S. remain poorly understood, some
preliminary work suggests that borrow-
ing constraints among families with low
net worth may play a role in perpetuat-
ing inequality.
The Galton model
Beginning with Sir Francis Galton in
the nineteenth century, researchers have
tried to measure the rate of regression
to the mean of particular characteristics
across generations. In a famous exam-
ple, Galton (1889) plotted the height
of adults against their parents’ height
and calculated the slope of the line that
best fit the data.1 Galton found that, on
average, the height of children was about
two-thirds closer to the mean than the
height of their parents. Sociologists
were the first to apply this type of sta-
tistical model to characterize intergen-
erational inequality by calculating the
correlation of various measures of so-
cioeconomic status across generations.
0
10
20
30
40
50
1 5 10 15 20 25 30
NOTE: Number of years averaged is the number of years used to average
the father’s earnings.2. Estimated intergenerational elasticity
elasticity
Number of years averaged
In recent decades, economists have be-
gun to use the Galton model on more
traditional economic measures such as
wages and annual earnings. Essentially,
this involves using ordinary least squares
(OLS) to regress the log of the child’s
adult earnings on the log of the parent’s
earnings. Typically, studies have focused
on fathers and sons. The estimated co-
efficient, ρ, is referred to as the inter-
generational elasticity and almost always
takes on a value between 0 and 1.
An intergenerational elasticity of exact-
ly 1 would imply an extremely rigid so-
ciety, where the son’s position in the
earnings distribution would simply
replicate his father’s position in the pre-
vious generation. In contrast, an inter-
generational elasticity of 0 suggests an
extremely mobile society in which the
son’s earnings are essentially unrelated
to his father’s earnings. Values between
0 and 1 provide a useful gauge of the
degree of economic rigidity in society.
One minus ρ, on the other hand, pro-
vides a measure of the degree to which
earnings “regress” toward the mean and
can be viewed as a measure of mobility.
Therefore, a society with a high ρ may
be seen as a less mobile society than one
with a low ρ.
One useful way to illustrate the quanti-
tative significance of this measure is to
imagine what it implies about the evo-
lution of the black–white wage gap in
the United States. An intergeneration-
al elasticity of 0.2, for instance, implies
that only 20% of any earnings gap be-
tween groups would remain after a
generation (say 25 years).2 Using this
logic, the black–white wage differential
for young men that stood at about 25%
in 1980 would be reduced to just 5% by
2005. If instead, the intergenerational
coefficient were 0.6, then the black–
white wage gap would still be a sizable
15% in 2005. This measure is also use-
ful in thinking about other important
issues such as the persistence of poverty,
the rate of assimilation of immigrants,
and the second-generation effects of
income policies.
It’s all in the measurement
To successfully estimate the Galton mod-
el, we need good measures of economic
status for two generations of individuals
from the same family for a large, na-
tionally representative sample. What is
especially important is the number of
years used to measure economic status.
For a variety of reasons, such as layoffs,
promotions, and job switching, individ-
ual earnings in any particular year con-
tain a sizable “transitory” component
that makes this a rather noisy measure
of an individual’s lifetime economic
status. This is especially true for people
who are very young or very old. There-
fore, it is crucial to measure “perma-
nent” economic status by averaging
information over long periods. In the
context of a regression model, it is par-
ticularly important to accurately mea-
sure the lifetime economic status of the
fathers. Since this is a right-hand-side vari-
able, mismeasurement will actually lead
to estimates of the intergenerational
elasticity that are biased downwards.
In the early 1990s, the first studies to
use nationally representative longitu-
dinal datasets, such as the Panel Study
of Income Dynamics (PSID) and the
National Longitudinal Surveys (NLS),
found that averaging a few years of
income made a dramatic difference to
the results. These studies found the
intergenerational elasticity to be about
0.4, roughly twice the estimates of pre-
vious studies that had only used single
measures of income on unrepresenta-
tive samples.
These datasets, however, are still far
from ideal for measuring the inter-
generational elasticity. The
key problem is that many
individuals in these surveys
tend to drop out of the sam-
ple over time for various
reasons. This not only re-
duces the sample size but
also requires researchers to
use relatively short windows
of time over which to mea-
sure lifetime economic sta-
tus. Typically, researchers
have used only up to five-
year averages of fathers’ in-
come in estimating the
Galton model. But does
this really make such a big
difference? There is reason
to believe that it does. This is because
many transitory shocks to income, say
due to a recession or a health problem,
tend to persist for a few years. If averag-
es are taken over short time horizons,
then these shocks are not averaged away.
In order to get a sense of how this might
affect estimates of ρ, I conducted simu-
lations using assumptions about the “time
series” properties of earnings. Since the
1970s, labor economists have conduct-
ed studies on earnings dynamics where
they have identified how much of the
variance of earnings in a single year is
transitory versus permanent and how
persistent these transitory fluctuations
tend to be from year to year. I incorpo-
rated the estimates from these models
to determine the amount of downward
bias that results from using a short-term
average of income as a proxy for life-
time earnings.
The results are shown in figure 1. The
horizontal axis represents the number
of years over which a father’s earnings
are averaged and the vertical axis plots
the amount of downward bias in the es-
timate of the intergenerational elastici-
ty. So, for example, using just a single
year of earnings results in a coefficient
that is biased down by about 45%. As
averages are taken over longer periods
this bias drops considerably. However,
it is clear that even a five-year average
can result in an estimate that is biased
downward by about 27%. Therefore, an
estimate of 0.4 obtained using a five-year
average implies that the “true” ρ is
NOTE: Number of years averaged is the number of years used to average
the father’s earnings.
0.0
0.2
0.4
0.6
0.8
13 57 9 1 1 1 3 1 5Michael H. Moskow, President; William C. Hunter,
Senior Vice President and Director of Research;  Douglas
Evanoff, Vice President, financial studies; Charles
Evans, Vice President, macroeconomic policy research;
Daniel Sullivan, Vice President, microeconomic policy
research;  William Testa, Vice President, regional
programs and Economics Editor; Helen O’D. Koshy,
Editor; Kathryn Moran, Associate Editor.
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3. Lifecycle pattern of variance of transitory shocks
between 0.5 and 0.6 —suggesting sub-
stantial intergenerational immobility.
New estimates of intergenerational
inequality
Ideally, the most direct way to obtain
accurate estimates of the intergenera-
tional elasticity would be to actually use
a sample that has the long-term earn-
ings histories of fathers and sons. In
fact, a confidential dataset that matches
fathers and sons in the Census Bureau’s
1984 Survey of Income and Program Par-
ticipation (SIPP) to their social security
earnings records from 1951 to 1998
was used for exactly this purpose.3 The
earnings of sons were averaged from
1995 to 1998 when they were in their
early thirties and the earnings of the
fathers were averaged over various pe-
riods ending in 1985. The results are
shown in figure 2.
As was the case in earlier studies, the es-
timate of ρ is close to 0.4 when using only
four-year averages of fathers’ earnings.
However, when earnings are averaged
over as many as 16 years, the estimate
is slightly greater than 0.6. It appears
that it is the greater window over which
the lifetime economic status of fathers
is measured that is the key factor.
Another possible explanation for this
result is that the age at which fathers’
earnings are measured might matter.
If younger or older fathers have espe-
cially volatile earnings, then averaging
their earnings over periods in which
their earnings are more
stable might lead to less
biased estimates. In order
to test this hypothesis, I es-
timated an earnings dynam-
ics model that incorporated
age effects to uncover the
lifecycle pattern of the
transitory variance in log
earnings. The results do,
in fact, show a pronounced
U-shaped pattern to the
variance of transitory fluc-
tuations, as we see in
figure 3.
Given their relatively small
samples, previous research
that used the PSID and NLS
might have relied too heavily on families
with fathers that were especially young
or old. Therefore, I reexamined the re-
sults from one highly influential study
using the PSID (Solon, 1992) employ-
ing a new econometric procedure that
essentially weights observations by their
estimated reliability based on the age
of the fathers.4 The effect of incorpo-
rating these age effects was to change
the estimate of ρ from 0.413 to 0.620.
Given that three different approaches
have all produced the same result—
that the intergenerational elasticity in
earnings is about 0.6—strongly suggests
that the previous consensus view of 0.4
should be revised upwards. Although
it is difficult to make comparisons across
countries in intergenerational mobili-
ty due to methodological differences,
the results for the U.S. appear to be sig-
nificantly higher than what has been
found in other industrialized countries.
For example, a similar study using tax
records for a very large sample in
Canada found an intergenerational
elasticity of about 0.2.5 This suggests that
the U.S. is not very economically mobile
and that further policies might be in
order to promote equal opportunity.
Does money matter?
Although the intergenerational elastic-
ity in earnings appears to be quite high,
the underlying channels through which
economic advantages are transmitted
from parents to children are not well
understood. Social scientists have pro-
posed a number of explanations in-
cluding: genetically transmitted ability,
parents’ investment in their children’s
human capital, the implicit or explicit
transmission of valuable social networks
and social capital, or the high propen-
sity of sons to have the same occupation
as fathers. Obviously, it will be difficult
to design appropriate policies without
a better understanding of which factors
are at work.
For economists, the well-developed
theory of human capital is an obvious
starting point. These theoretical models
typically predict that under ideal mar-
ket conditions the intergenerational
elasticity should be quite low, since
parents will optimally choose the ap-
propriate level of “investment” in their
child’s schooling irrespective of their
own financial conditions. However, in
the presence of credit constraints, low-
income families with “high-potential”
children might underinvest in their
children’s schooling, thereby inducing
a sizable correlation in economic status
across generations.
Using the intergenerational sample
drawn from the SIPP described earlier,
I tested this hypothesis by comparing
the intergenerational elasticity for fami-
lies from different parts of the wealth
distribution. Indeed, those in the bot-
tom quartile of net worth had a sharp-
ly higher estimated coefficient than
 .00
 .05
 .10
 .15
 .20
 .25
 .30
26 28 30 32 36 38 40 42 44 46 48 50 52 54 56 58 60
Age
NOTE: Variance is the variance of transitory shocks to log earnings.
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those in the top quartile, and the dif-
ference was statistically significant. This
provides some preliminary evidence
that borrowing constraints may be an
important factor in the intergenera-
tional persistence of income.
This is an important result because a
number of studies have been unable to
identify any causal effect of family in-
come on children’s future success. This
has led some to argue that money itself
does not matter but rather it is other
family characteristics associated with in-
come, such as motivation, that are driv-
ing the intergenerational association
in income. However, these studies typ-
ically have not focused on families with
little or no wealth. If money matters, but
primarily for families that are unable
to borrow against future income, then
this might help explain the puzzle.
Still, there is considerably more that we
need to understand about borrowing
constraints before successful policies
can be developed. For example, is the
lack of access to credit mainly a problem
for students at the time of going to col-
lege, or is it a deeper problem that af-
fects the quality of schooling at much
younger ages? It might be that families
with limited financial resources are un-
able to “buy” into the neighborhoods
with the best schools.
Conclusion
Recent research that has measured the
intergenerational elasticity in earnings
between fathers and their children shows
that there is a substantial degree of per-
sistence in income among families over
generations. These studies suggest that
the rise in income inequality in recent
decades may persist for several gener-
ations. The underlying mechanisms that
enable this persistence are not well
understood. However, recent research
suggests that the existence of borrow-
ing constraints among those with little
wealth is a plausible candidate to ex-
plain the high intergenerational elas-
ticity. Families that are unable to access
credit may not optimally invest in their
children’s schooling. Gaining a better
understanding of the nature of these
borrowing constraints is a necessary
step in designing the appropriate poli-
cies to foster greater income mobility.
1 Francis Galton, 1889, Natural Inheritance,
London: Macmillan, p. 97.
2 This example assumes a common inter-
generational elasticity for both groups
and no other group-specific effects. For
example, a number of factors such as
skill-biased technical change or declin-
ing unionism could affect each group
differently and temporarily widen the
gap further.
3 See Bhashkar Mazumder, 2001, “Earnings
mobility in the US: A new look at intergen-
erational inequality,” Federal Reserve Bank
of Chicago, working paper, No. 2001-18.
4 See Gary Solon, 1992, “Intergenerational
income mobility in the United States,”
American Economic Review, Vol. 82, pp. 393–
408. See also Daniel G. Sullivan, 2001, “A
note on the estimation of linear regression
models with heteroscedastic measurement
errors,” Federal Reserve Bank of Chicago,
working paper, No. 2001-23, for more de-
tail on the econometric procedure that
was used.
5 See Miles Corak and Andrew Heisz, 1999,
“The intergenerational earnings and in-
come mobility of Canadian men: Evidence
from longitudinal income tax data,” Jour-
nal of Human Resources, Vol. 34, No. 3,
pp. 504–533.

Analyzing income mobility over generations

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Analyzing income mobility over generations

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