PRELIMINARY AND INCOMPLETE
[DO NOT CITE WITHOUT PERMISSION]
Estimating the Intergenerational Elasticity and Rank Association in the US:
Overcoming the Current Limitations of Tax Data
Bhashkar Mazumder*
Federal Reserve Bank of Chicago
and University of Bergen
March, 2015
Abstract:
The intergenerational economic mobility literature has begun to use estimators of rank mobility
in addition to the intergenerational elasticity (IGE). I argue that both estimators are useful for
providing insight but for different mobility concepts. The influential work by Chetty et al (2014)
focuses on rank mobility estimators and their choice is primarily motivated by measurement
concerns with the IGE rather than for conceptual reasons. I argue that those measurement
concerns are largely misplaced and instead reflect fundamental limitations of the
intergenerational samples that can currently be constructed with U.S. administrative tax data
from the IRS. Despite the seeming advantages of extremely large samples of administrative
data, I use small samples of survey data from the PSID to demonstrate that it is the age structure,
limited panel dimension, and measurement error in administrative data rather than the use of the
IGE that leads to the measurement problems encountered by Chetty et al. Using the PSID data I
also demonstrate that the national estimates of the IGE in family income in the U.S. are greater
than 0.7 and are vastly higher than virtually all current estimates and substantially higher than
those produced by Chetty et al. The father-son income elasticity estimates are consistent with
those of Mazumder (2005) and suggest that those earlier estimates were not driven by
imputations but rather by the availability of longer time spans to measure permanent economic
status of parents. I also highlight several other lesser-known studies that find evidence consistent
with Mazumder (2005) that are imputation-free. Finally, I show that when using a more ideal
sample in the PSID, that the rank-rank slope estimates are around 0.5 and significantly higher
than the estimate of 0.341 found by Chetty et al using the IRS data.
*I thank Andy Jordan for outstanding research assistance. The views expressed here do not
reflect those of the Federal Reserve Bank of Chicago or the Federal Reserve system.
I.
Introduction
Inequality of opportunity has become a tremendously salient issue for policy makers
across many countries in recent years. The sharp rise in inequality has given rise to fears that
economic disparities will persist into future generations. This has resulted in a heightened focus
on the literature on intergenerational economic mobility. This body of research which is now
several decades old seeks to understand the degree to which economic status is transmitted
across generations. Of course, a critical first step in understanding this literature and correctly
interpreting its findings is having a sound understanding of the measures that are being used and
what they do and do not measure.
This paper will focus on two prominent measures of
intergenerational mobility: the intergenerational elasticity (IGE) and the rank-rank slope and
discuss several key conceptual and measurement issues related to these estimators in the context
of the U.S.
The IGE has a fairly long history of use in economics dating back to papers from the
1980s (add cites) and many notable advances have been made in terms of measurement and
issues concerning life-cycle bias (e.g. Solon, 1992; Mazumder, 2005a; Haider and Solon, 2006).1
In recent years a number of papers have started to use rank based measures of intergenerational
mobility (Dahl and Deliere, 2009; Bhattacharya and Mazumder, 2011, Corak et al., 2014, Chetty
et al, 2014, Mazumder, 2014 and Bratberg et al., 2015). However, the motivation for using rankbased measures has differed among these studies. Dahl and Deliere (2009) and Chetty et al.
(2014) have emphasized measurement problems with the IGE as their reason for shifting to
ranks. The other studies, in contrast, have generally emphasized other conceptual aspects of the
rank based measures such as the ability to: distinguish upward versus downward movements,
make subgroup comparisons, and identify nonlinearities in intergenerational mobility.
1
Reviews of this literature can be found in Solon (1999) and Black and Devereaux (2011).
Given the recent shift in the literature, it would be useful to better understand the recent
criticisms of the IGE and to see what they imply for their use going forward. To address this, I
first discuss the conceptual differences between the estimators and separate this discussion from
the measurement concerns. In short, I argue that conceptually, both measures can provide useful
insights about different aspects of mobility. I argue that there are clearly certain questions that
are best answered by the IGE and for that reason researchers should continue to use the IGE as at
least one tool for measuring intergenerational mobility.
Rank estimators are also valuable
because they can be used to examine other aspects of mobility such as geographic differences
within a country or racial differences in a way that the IGE cannot (Mazumder, 2014).
In terms of measurement, I argue that the criticisms of the IGE are context specific.
When the structure of an intergenerational dataset is limited in terms of the observed age ranges
of parents or children, or if the panel dimension for the data is relatively small, then the IGE
estimates are likely to less robust than rank-based estimates. We should be clear, though that this
is a function of the available data and is not an intrinsic problem with the estimator in all
contexts. Further, the various measurement studies over the last 25 years provide tremendous
insight and various tools that can be used to appropriately adjust the estimates.
This is particularly important when evaluating some of the claims made in the very
influential paper by Chetty et al (2014). They argue that using the IGE leads to dramatically
different results depending on how they code instances of zero earnings among the children in
their sample. They suggest that this is due to nonlinearities in the log-log relationship. They
show that their rank mobility estimates do not suffer from this issue and in large part it is for this
greater robustness that they prefer those estimates for characterizing intergenerational mobility at
the national level. I will argue that this apparent sensitivity of the IGE estimates is due to the
limitations of the tax data that is currently available rather than an intrinsic feature of the
estimator. For all of its tremendous advantages such as having huge sample sizes, the IRS data is
fundamentally limited in a few key respects. First, children’s income is only measured over 2
years at a relatively early point in the life cycle (around age 30) at a time in which
unemployment was quite high. Second, parents’ income is measured relatively late in life
(around age 50) and only for up to 5 years.
Third, recent research has established that
administrative data can be worse than survey data, particularly at the bottom end of the income
distribution and can actually introduce measurement error (e.g. Abowd and Stinson, 2013 and
Hokayem et al., 2012, 2015).
I use the PSID to demonstrate the implications of these data limitations, empirically.
First, I use the PSID to construct an intergenerational sample where both kids and parents
income is observed over many years and is centered over the prime working years in both
generations. The time span also covers a much larger portion of the lifecycle than the IRS
records. I estimate the IGE using this close to “ideal” sample and then show how the estimates
change if I impose the same kinds of data limitations that exist in the IRS data. The results of
this exercise show that the data limitations lead to very dramatic differences in estimates. For
example, imposing the data restrictions in the IRS data leads to IGE estimates from the PSID
with respect to family income that are about 50 to 60 percent of the size of the estimates with the
complete data. Moreover, even when I impose the same data limitations found in the IRS data in
the PSID I find that the estimates are significantly higher in the PSID than in the tax data –which
runs exactly counter to what one would expect if measurement error was reduced with
administrative data. This suggests that researchers should use caution when interpreting the
results only from U.S. administrative tax data and look to compare them to results with survey
data.
Perhaps the most significant contribution of the paper is to show that the magnitude of
the IGE estimates when using many years of income data centered over the prime working years
in both generations are vastly higher than almost all previous estimates in the literature. For
example, the estimates of the IGE with respect to family income are centered at 0.7 and are
consistently in the 0.6 to 0.8 range. Surprisingly, only one prior study has constructed a PSID
sample centered over the prime working years and covering long time spans to directly estimate
the IGE.2 Although Chetty et al emphasize their national rank mobility estimates, they argue that
their estimates of the IGE in family income of 0.344 are preferable to previous estimates. For
example, they argue that the estimate of the IGE in father-son earnings of 0.6 in Mazumder
(2005) is likely due to imputations imposed in Mazumder’s data. The analysis here suggests that
the findings in Mazumder (2005) can easily be replicated using publicly available survey data
that requires no imputations. Obtaining these estimates simply requires using samples with the
appropriate ages and long time spans of available income data centered around the prime
working ages in both generations. I also point to other studies in the literature that yield findings
consistent with Mazumder (2005) that do not require imputations (e.g. Mazumder, 2005b; Nilsen
et al (2012); and Mazumder and Acosta, 2014).
A final exercise uses the PSID data to estimate the rank-rank slope which is one of the
measures used by Chetty et al (2014). Once again the estimates are significantly larger with the
PSID (around 0.5) than what one obtains when using the IRS data (0.341). This suggests that
while the rank-rank slope may be more relatively robust to the data limitations of the IRS sample
2
See Mazumder and Acosta (2014).
than the IGE, it is still far from ideal and suggests that the intergenerational mobility even by
rank-based measures may be overstated by the tax data.
One clear conclusion to be drawn from this paper is that researchers should continue to
use the IGE if that is the conceptual parameter of interest and when their intergenerational
samples have the appropriate panel lengths and age structure. Even when the ideal data is not
available, researchers can still attempt to assess the extent of the bias based on prior papers in the
literature that propose methodological fixes. Substantively, the results of this paper show that
intergenerational mobility in the US is substantially lower than what one would think based on
using the currently available IRS data irrespective of which measure is used.
The rest of the paper proceeds as follows. Section 2 describes the conceptual differences
between the estimators.
Section 3 describes measurement issues with IGE estimation and
describes the structure of an “ideal” dataset. It then compares this ideal dataset with the IRSbased intergenerational sample used by Chetty et al (2014) and a close to ideal sample that can
be constructed with publicly available PSID survey data. Section 4 presents the results when
using the PSID to show the effects of imposing the limitations with the tax data. Section 5
concludes.
II.
Conceptual Issues
The concept of regression to the mean over generations has a long and notable tradition
going back to the Victorian era social scientist Sir Francis Galton who studied among other
things the rate of regression to the mean in height between parents and children. Modern social
scientists have continued to find this concept insightful as a way of describing the rate of
intergenerational persistence in a particular outcome and to infer the rate of mobility as the flip
side of persistence. In particular economists have focused on the intergenerational elasticity
(IGE). The IGE is the estimate of  obtained from the following regression:
(1)
y1i =  + y0i + i
where y1i is the log income of the child generation and y0i is the log of income in the parent
generation.3 The estimate of  provides a measure of intergenerational persistence and 1 -  can
be used as a measure of mobility. One way to interpret the elasticity in practical terms is to
consider what it implies about how many generations it would take for a family living in poverty
to attain close to the national average household income level. If for example, the IGE is around
0.60 as claimed by Mazumder (2005a) then it would take 6 generations (150 years). On the
other hand if the IGE is around 0.34 as claimed by Chetty et al (2014) then it would take just 3
generations.4 Clearly, the two estimates have profoundly different implications on the rate of
intergenerational mobility and if the rate of regression to the mean is what we are interested in
knowing then the IGE is what we estimate. The concept of regression to the mean is also widely
used in other aspects of economics such as the macroeconomic literature on differences in percapita income across countries (e.g. Barro and Sala-i-Martin, 1992).
The rank–rank slope on the other hand is about a different concept of mobility, positional
mobility. It asks, for example, what the expected difference in ranks between members of two
different families would be if the families differed in the parent generation by 10 percentiles.
One can imagine that depending on the shape of the income distribution the descendants of a
family in poverty might experience relatively rapid positional mobility but slower regression to
Often the regression will include age controls but few other covariates since  is not given a causal interpretation
but rather reflects all factors correlated with parent income
4
This exercise is based on Mazumder (2005) and considers a family of four with two children under the age of 18
whose income is $18,000 (under the poverty threshold in 2013 of around $24,000). Mean household income in
2013 was approximately $73,000. The calculation specifically examines how many generations before the
expected income of the descendants of this family would be within 5% of the national average.
3
the mean.5 How are the two measures related? Chetty et al (2014) point out that that the rankrank slope is very closely related to the intergenerational correlation (IGC) in log income. They
and many others have also shown that the IGE is equal to the IGC times the ratio of the standard
deviation of log income in the child generation to the standard deviation of log income in the
parent generation:
(2)
This relationship is sometimes taken to imply that a rise in inequality would lead the IGE
to rise but not affect the IGC and that therefore, the IGC may be a preferred measure that avoids
a “mechanical” effect of inequality. By extension one might also prefer the rank-rank slope if
one accepts this argument. Several comments are worth making here. First, in reality the
parameters are all jointly determined by various economic forces. In the absence of a structural
model one cannot meaningfully talk about holding “inequality” fixed. For example, a change in
 might cause inequality to rise, rather than the reverse, or both might be altered by some third
force such as rising returns to skill. The mathematical relationship shown in (2) does not
substitute for a behavioral relationship and so it does not make sense to pretend that we can
separately isolate inequality from the IGE. Second, even if it was the case that the IGC or rankrank slope was a measure that was independent of inequality, that doesn’t mean that society
shouldn’t continue to be interested in the rate of regression to the mean. I would argue that it is
precisely because of the rise in inequality that societies are increasingly concerned about
intergenerational persistence and so incorporating the effects of inequality may actually be
critical to understanding the rates of mobility that policy makers want to address.
5
In the example above, one can imagine that it may take significantly longer for the family with income of $18,000
to attain the mean income level of $73,000 than the median income level of $52,000.
In addition to providing useful information about positional mobility the rank-rank slope
has other attractive features. Perhaps it’s most useful advantage over the IGE is that it can be
used to measure mobility differences across subgroups of the population. This is because the
IGE estimated within groups is only informative about persistence or mobility with respect to the
group specific mean whereas the rank-rank slope can be estimated based on ranks calculated
based on the national distribution. Chetty et al (2014) were able to use this to characterize
mobility for the first time at an incredibly fine geographic level. Mazumder (2014) used other
“directional” rank mobility measures to compare racial differences in intergenerational mobility
between blacks and whites in the U.S. However, for characterizing intergenerational mobility at
the national level both the IGE and the rank-rank slope are suitable depending on which concept
of mobility the researcher is interested in studying.
III.
Measurement Issues and the Ideal Intergenerational Sample
Measurement Issues
The prior literature on intergenerational mobility has highlighted two key measurement
concerns that I will briefly review here. The first issue is regarding measurement error or
transitory fluctuations in income. In an ideal setting the measures of y1 and y0 in equation (1)
would be measures of lifetime or permanent income but in most datasets we only have short
snapshots of income that can contain noise and attenuate estimates of the IGE. Solon (1992)
showed that using a single year of income as a proxy for lifetime income of fathers can lead to
considerable bias relative to using a 5 year average of income. Using the PSID, Solon concluded
that the IGE was 0.4 “or higher”. Mazumder (2005a) used the SIPP matched to social security
earnings records and showed that using even a 5-year average can lead to considerable bias and
estimated the IGE to be around 0.6 when using longer time averages of fathers earnings (up to 16
years). Mazumder argues that the key reason that a 5-year average is insufficient is that the
transitory variance in earnings tends to be highly persistent and appeals to the findings of U.S.
studies of earnings dynamics that support this point. Using simulations based on parameters
from these other studies, Mazumder shows that the attenuation bias from using a 5-year average
in the data is close to what one would expect to find based on the simulations. In a separate
paper, that is less well known, Mazumder (2005b) showed that if one uses short term averages in
the PSID and uses a Hetereoscedastic Errors in Variables (HEIV) estimator that adjusts for the
amount of measurement error or transitory variance contained in each observation, then that the
PSID adjusted estimate of the IGE is also around 0.6. This latter paper is a useful complement
because unlike the social security earnings data used by Mazumder (2005a) the PSID data is not
topcoded and doesn’t require imputations. Chetty et al (2014) has contended that the larger
estimates of the IGE in Mazumder (2005a) was due to the nature of the imputation process rather
than due to larger time averages of fathers’ earnings.
The second critical measurement concern in the literature concerns lifecycle bias best
encapsulated by Haider and Solon (2006). One aspect of this critique concerns the effects of
measuring children’s income when they are too young. Children who end up having high
lifetime income often have steeper income trajectories than children who have lower lifetime
incomes. Therefore if income is measured at too young an age it can lead to an attenuated
estimate of the IGE. Haider and Solon show that this bias can be considerable and is minimized
when income is measured at around age 40. A related issue is that transitory fluctuations are not
constant over the lifecycle but instead follow a u-shaped pattern over the lifecycle (Baker and
Solon, 2003; Mazumder, 2005). This implies that measuring parent income when they are either
too young or (especially) when they are too old can also attenuate estimates of the IGE. While
there are econometric approaches one can use to correct for lifecycle bias, one simple approach
would be to simply center the time averages of both children’s and parents income around the
age of 40. Using this approach with the PSID, Mazumder and Acosta estimate the IGE to be
around 0.6. Further, Nilson et al (2012), using Norweigian data show that both time averaging
and life-cycle bias play a role in attenuating IGE coefficients. It should be noted that Nilsen et al
find that these biases matters despite using administrative data like Chetty et al.6
Comparisons of Intergenerational Samples
To better understand the limitations with currently available intergenerational samples in
the US with respect to these measurement issues, it is useful to think about what an ideal sample
would look like. In an ideal setting we would want to construct an intergenerational sample
where income is measured for both generations throughout the entire working life cycle, say
between the ages of 25 and 55.7 If we take 2012 as an end point that would be mean that for the
children’s generation we would want cohorts of children who were born in 1957 or earlier for
full lifecycle coverage. For the 1957 cohort we would measure their income between 1982 and
2012. For the 1956 cohort we would measure income between 1981 and 2011. We could then
continue to work backwards to collect data on earlier cohorts. Suppose that for the parent
generation, the mean age at the time the child is born is 25. Then for the 1957 cohort we would
collect income data from 1957 to 1987 and from 1956 to 1986 for the parents of the earlier birth
cohorts, and so on. With such a dataset in hand we would be confident that we would have
measures of lifetime income that are error-free and would also be free of lifecycle bias. The top
portion of Figure 1 shows a visual representation of this ideal dataset.
6
Chetty et al speculate that perhaps time averaging and life cycle bias don’t matter in their robustness checks
because of their use of administrative data. I discuss later why their robustness checks are of limited value.
7
The precise end points are debatable but one might want to ensure that most sample members have finished
schooling and that most sample members have not yet retired.
Unfortunately, for most countries, including the US, it is difficult to construct an
intergenerational dataset with income data going back to the 1950s.8
Still, we can come
somewhat close to this ideal sample with publicly available survey data in the Panel Study of
Income Dynamics (PSID).
The PSID began in 1968 and started collecting income data
beginning with 1967 for a nationally representative sample of about 5000 families. The 1957
cohort would have been 11 years old at the time the PSID began so this cohort along with those
born as early as 1951 would have been under the age of 18 at the beginning of the survey. The
approach I take in this paper is to construct time averages of both parent and child income
centered around the age of 40. For parents, these averages include income obtained between the
ages of 25 and 55 and for children these averages include income obtained between the ages of
35 and 45. The middle portion of Figure 1 shows a rough approximation of the PSID sample
that I will use.9
Relative to the ideal sample, the PSID sample is close in several regards. Since it covers
the 1967 to 2010 period it is able cover vast stretches of the lifecycle for both generations. For
example, for the 16 cohorts born between 1951 and 1965, income can be measured for all years
that cover the age range between 35 and 45. For the cohorts born between 1967 and 1975, their
parent’s income can also be measured through the ages of 25 and 55.
Now let us contrast this with the limitations faced by Chetty et al (2014) in their analysis
of currently available IRS data. First the tax data is currently only digitized going back to 1996,
which is nowhere near as far back as the ideal dataset would require (1957), or even what is
available in the PSID (1967). Therefore, there is no birth cohort for whom the income of parents
8
The SIPP-SER data used by Mazumder (2005) and Dahl and Deliere (2008) meets some but not all of these
requirements.
9
Currently I am not restricting all of the assumptions shown in Figure 1. For example cohorts born before 1951 are
being included.
can be measured for the entire 31 year time span between the ages of 25 and 55. Furthermore,
the authors chose to limit the analysis to just a 5-year average between 1996 and 2000. This is
likely due to the skewed age structure of parent income. The mean age of fathers in their sample
in 1996 is reported to be 43.5 with a standard deviation of 6.3 years. This implies that over the 5
years from 1996 through 2000, roughly 24 percent of the father-year observations used in
constructing the average would be when fathers are over the age of 50.10 This is an age at which
the transitory variance in income is quite high. They also report that prior to 1999 they record
the income of non-filers to be zero. Therefore for about 3 percent of observations in three of the
five years used in their average they impute zeroes to the missing observations.11
For the children in the sample, the data limitations are even more severe. Chetty et al use
cohorts born between 1980 and 1982 and measure their income in 2011 and 2012 when they are
between the ages of 29 and 32. For this age range, simulations from Haider and Solon (2006)
suggest that there would be around a 20 percent bias in the estimated IGE compared to having
the full lifecycle. A further complication is that their measures are taken in 2011 and 2012 when
unemployment was relatively high and labor force participation quite low. They report that they
throw out about 17 percent of observations from the poorest families due to their having zero
income over those 2 years. If their sample also included 29 to 32 year olds over several decades
which also included many boom years then this would be less of a concern. Finally, there is a
concern about whether administrative income data adequately captures true income, particularly
at the low and the high ends of the income distribution. For example, at the lower end of the
10
This example assumes the data is normally distributed. In 2000, more than a third of the observations would be
when fathers are over the age of 50.
11
See footnote 14 of Chetty et al. (2014). They show that this has no effect on their rank mobility estimates but
they do not show how the IGE estimates change. Further, measuring income from 1999 to 2003 only worsens the
attenuation bias in the IGE resulting from measuring fathers at late ages.
distribution, tax data could miss forms of income that go unreported to the IRS such as black
market income. At the higher end, tax avoidance behavior could lead to an under-reporting of
income. Hoyakem et al (2012, 2015) find that administrative tax data does a worse job than
survey data in measuring poverty. Abowd and Stinson (2013) argue that it is preferable to treat
both survey data and administrative data as containing error.
To their credit, Chetty et al (2014) attempt to conduct some sensitivity checks to these
issues, but as discussed above, their data are not well suited to doing effective robustness checks
for the IGE measure, because the panel length of the data relative to the lifecycle in each
generation is poorly matched. For example, when they increase the length of the time average of
parent income by using more years after 2000, they must necessarily increase the attenuation
bias from using later ages in the lifecycle. In one specification, they restrict their sample to just
look at parents whose income is measured before the age of 50 but then they can only look at 5
year averages. They also try to measure the effects of parent income on children whose income
is measured at a later age by using a separate set of tax data derived from much smaller crosssections of data from the IRS’ SOI data which covers cohorts born as far back as 1970.
Unfortunately, these cross-sections only contain single year measures of parent income which
are of course heavily attenuated. One also has to make heavy parametric assumptions in order to
infer that the bias from using income from this short-panel data would necessarily apply when
considering lifetime income.
In their appendix, Chetty et al (2014) also argue that if they conduct simulations like
Mazumder (2005a) but instead use a smaller share of earnings variance due to transitory
fluctuations, then they do not find estimates of attenuation bias that are consistent with
Mazumder’s results. However, Chetty et al do not provide evidence explaining what parameter
values they use and how they are derived. In principle, Chetty et al could have directly estimated
a model of earnings dynamics with their IRS data using a large sample covering men of all ages
to directly provide evidence on this point.
IV.
PSID Data
I restrict the analysis to father-son pairs as identified by the PSID’s Family Identification
Mapping System (FIMS). I construct two parallel sets of samples. The first considers the labor
income of the household head and the second considers the labor income of the entire family.
Labor income is not simply wage income but also incorporates other sources of income such as
self-employment. Observations marked as being generated by a ‘major’ imputation are set to
missing. Yearly income observations are deflated to real terms using the CPI. In the PSID the
household head is recorded as having zero income if their income was actually zero or if their
income is missing, so one cannot cleanly distinguish true zeroes. For the analysis using the
income of household heads, I use only years of non-zero income when constructing time
averages of income. When using the PSID constructed measures of family income this problem
does not arise as we found no instances of zero family income for the samples we constructed.
The approach to estimation in this study is slightly different than in most previous PSID
studies of intergenerational mobility. Rather than relying on any one fixed length time average
for each generation and relying on parametric assumptions to deal with lifecycle bias (e.g. Lee
and Solon, 2009), instead I measure an entire matrix of IGE’s for many combinations of lengths
of time averages that are all centered around age 40. I will present the full matrix of estimates
along with weighted averages across entire rows and columns representing the effects of a
particular length of the time average for a given generation. For example, rather than simply
comparing the IGE from using a ten-year average of fathers income to using a five year average
of fathers’ income for one particular time average of sons income, I can show how it is affected
for every combination of time average of sons’ income and for the weighted average across these
combinations.
V.
Results
IGE Estimates
Table 1 shows the estimates of the IGE between fathers and sons when using the income
of household heads. The first entry of the table at the upper left shows the estimate if we use just
one year of income of fathers and one year of income for the sons when they are closest to age
40 and also are within the age-range constraints described earlier. This estimate of the IGE is
0.376 with a standard error of (0.043) and utilizes a sample of 2189 father-son pairs. One point
immediately worth noting is that this estimate using the smallest possible time average centered
around age 40 is higher than the 0.344 found by Chetty et al (2014). Moving across the row, the
estimates gradually include more years of income between the ages of 35 and 45 for the sons.
For the most part the estimates don’t change much and are all in the range of 0.34 and 0.39
except when using a 10 year average. Moving across the rows, the sample size gradually
diminishes as enlarging the time average for the sons comes at the expense of sample size as an
increasingly fewer number of sons have will income available for a higher length of required
years. At the end of the row I display the weighted average across the columns, where the
estimates are weighted by the sample size. For the first row the weighted average is 0.357.
Moving down the rows for a given column, the estimates gradually increase the time
average used to measure fathers’ income and as a consequence also reduces the sample size. For
example, if we move down the first column and continue to just use the sons’ income in one year
measured closet to age 40 and now increase the time average of fathers’ income to 2 years, the
estimate rises to 0.454 as the sample falls to 2143. Using a five year average raises the estimate
to 0.619 (N=1926).
Increasing the time average to 10 years increases the estimate 0.690
(N=1502). Using a 15 year average raises the estimate further to 0.706 (N=1041). This pattern
of rising estimates with a rising time average of fathers’ income, however, is not monotonic and
is not true for every column. For most columns, in fact the time average tends to plateau quite
quickly with time averages of around 5 to 10 years. The weighted average for each column is
displayed in the bottom row. For example, the weighted average for first column is 0.599.
A few points are worth making. Since expanding the time average in either dimension
reduces the sample size it risks making the sample less representative. The implications on the
estimates, however, are quite different for whether we increase the time average for the sons’
generation or for the fathers. For the fathers, increasing the time average tends to raise estimates.
This is a consistent with a story in which larger time averages reduce attenuation bias stemming
from mis-measurement of parent income (Solon, 1992; Mazumder, 2005). This also accords
with standard econometric theory concerning mis-measurement of the right hand side variable.
On the other hand, econometric theory posits that mis-measurement in the dependent variable
typically should not cause attenuation bias. Indeed, increasing the time average of sons’ income
has little effect. But crucially, this is because we have centered the time average of income in
each generation so that the lifecycle bias which induces “non-classical” measurement error in the
dependent variable (Haider and Solon, 2006) may already be accounted for.
By this reasoning one might consider the estimates in the first column to be the most
useful since they allow one to see how a reduction in measurement error in the father’s income
affects the estimates while simultaneously minimizing life cycle bias and keeping the sample as
large as possible. A more conservative view would be to use the weighted average in the final
column that takes into account the possible effects of incorporating more years of data on sons’
income while also giving greater weight to estimates with larger samples. Using the first
approach would suggest that the father-son IGE in own income may be as high as 0.7, while the
latter approach would suggest that it is closer to 0.6. In either case the estimates are similar to
those found in Mazumder (2005) without requiring imputation.
It is important to note that in estimating the IGE, estimates may differ based on the
concept of income being used. For example, in the landmark study by Solon (1992) using the
PSID, Solon estimates the IGE in income to be 0.413 but the IGE in family income to be 0.483.
More generally, estimates of the IGE in family income have tended to be larger than similar
estimates that only use the labor income of one individual in each generation.12 Table 2 presents
an analogous set of results as Table 1 using family income.
[Add discussion of Table 2]
Rank-Rank Slope Estimates
12
Examples include:
References
Chetty, Raj, Nathaniel Hendren, Patrick Kline, and Emmanuel Saez. 2014. “Where is the land of
Opportunity? The Geography of Intergenerational Mobility in the United States”. Quarterly
Journal of Economics, 129(4): 1553-1623.
Dahl, Molly and Thomas DeLeire. 2008. “The Association between Children’s Earnings and
Fathers’ Lifetime Earnings: Estimates Using Administrative Data.” Institute for Research on
Poverty, University of Wisconsin-Madison.
Mazumder, Bhashkar. 2014. “Black-white differences in intergenerational economic mobility in
the United States.” Economic Perspectives, 38(1).
Nybom, Martin amd Jan Stuhler. 2015. “Biases in Standard Measures of Intergenerational
Dependence.”
Table 1: Estimates of the father-son IGE in household head income
Time Average of Sons' Income (years)
Time Avg.
Fath. Inc.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
wgt avg.
1
0.376
2
0.343
3
0.350
4
0.341
5
0.355
6
0.357
7
0.332
8
0.344
9
0.387
10
0.468
(0.043)
(0.037)
(0.040)
(0.042)
(0.044)
(0.052)
(0.052)
(0.046)
(0.049)
(0.050)
2189
0.454
1867
0.405
1611
0.399
1381
0.392
1137
0.399
877
0.391
620
0.374
488
0.400
374
0.429
255
0.518
(0.056)
(0.049)
(0.050)
(0.052)
(0.058)
(0.066)
(0.066)
(0.050)
(0.063)
(0.054)
2143
0.536
1826
0.482
1581
0.482
1358
0.480
1118
0.501
862
0.507
607
0.502
478
0.508
369
0.552
251
0.610
(0.051)
(0.038)
(0.039)
(0.036)
(0.036)
(0.038)
(0.046)
(0.047)
(0.052)
(0.063)
2078
0.607
1768
0.529
1534
0.530
1315
0.505
1081
0.528
829
0.521
579
0.515
458
0.516
352
0.563
238
0.601
(0.044)
(0.039)
(0.040)
(0.039)
(0.040)
(0.042)
(0.049)
(0.053)
(0.058)
(0.067)
2003
0.619
1710
0.547
1480
0.556
1265
0.525
1035
0.542
790
0.530
550
0.538
436
0.541
334
0.591
225
0.609
(0.046)
(0.040)
(0.042)
(0.041)
(0.043)
(0.045)
(0.050)
(0.054)
(0.062)
(0.073)
1926
0.632
1644
0.562
1419
0.570
1209
0.536
984
0.548
746
0.526
514
0.529
402
0.535
304
0.579
201
0.617
(0.046)
(0.041)
(0.043)
(0.042)
(0.044)
(0.045)
(0.049)
(0.051)
(0.058)
(0.076)
1866
0.659
1592
0.589
1372
0.592
1164
0.552
942
0.566
710
0.543
485
0.549
380
0.549
287
0.578
189
0.622
(0.050)
(0.044)
(0.046)
(0.045)
(0.047)
(0.049)
(0.052)
(0.053)
(0.061)
(0.084)
1783
0.646
1521
0.565
1313
0.575
1111
0.536
894
0.549
669
0.518
451
0.501
352
0.509
264
0.557
169
0.600
(0.052)
(0.046)
(0.047)
(0.048)
(0.050)
(0.052)
(0.056)
(0.058)
(0.069)
(0.098)
1685
0.660
1431
0.572
1234
0.572
1035
0.527
828
0.531
606
0.503
403
0.512
313
0.528
232
0.589
148
0.664
(0.056)
(0.046)
(0.047)
(0.047)
(0.047)
(0.051)
(0.061)
(0.064)
(0.074)
(0.103)
1611
0.690
1369
0.596
1178
0.604
985
0.554
783
0.543
569
0.514
373
0.535
286
0.569
213
0.627
136
0.713
(0.062)
(0.049)
(0.050)
(0.050)
(0.051)
(0.055)
(0.066)
(0.069)
(0.083)
(0.116)
1502
0.654
1269
0.566
1081
0.575
900
0.524
712
0.528
507
0.501
325
0.516
243
0.523
180
0.565
110
0.676
(0.063)
(0.048)
(0.049)
(0.050)
(0.052)
(0.057)
(0.068)
(0.073)
(0.087)
(0.121)
1411
0.635
1193
0.561
1012
0.573
839
0.510
665
0.515
469
0.474
296
0.452
220
0.448
158
0.491
98
0.626
(0.059)
(0.053)
(0.053)
(0.055)
(0.058)
(0.062)
(0.076)
(0.082)
(0.099)
(0.125)
1335
0.652
1123
0.564
949
0.571
779
0.502
611
0.506
423
0.465
258
0.459
186
0.427
131
0.477
81
0.570
(0.061)
(0.053)
(0.053)
(0.054)
(0.056)
(0.062)
(0.074)
(0.080)
(0.097)
(0.104)
1248
0.674
1050
0.583
884
0.602
720
0.535
558
0.537
379
0.476
222
0.474
156
0.438
107
0.493
64
0.635
(0.063)
(0.056)
(0.055)
(0.057)
(0.060)
(0.066)
(0.081)
(0.084)
(0.103)
(0.103)
1171
0.706
987
0.589
828
0.606
667
0.545
510
0.536
341
0.453
192
0.423
134
0.376
93
0.422
55
0.518
(0.069)
(0.059)
(0.058)
(0.059)
(0.062)
(0.070)
(0.092)
(0.097)
(0.126)
(0.114)
1041
879
730
587
444
287
151
98
62
31
0.599
0.526
0.531
0.496
0.505
0.483
0.478
0.484
0.528
0.593
Wgt.
Avg.
0.357
0.412
0.505
0.543
0.560
0.569
0.590
0.570
0.573
0.600
0.571
0.553
0.554
0.580
0.586
Table 2: Estimates of the father-son IGE in family income
Time Average of Sons' Income (years)
Time Avg.
Fath. Inc.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
wgt avg.
1
0.579
2
0.659
3
0.650
4
0.644
5
0.640
6
0.641
7
0.630
8
0.639
9
0.619
10
0.566
(0.042)
(0.043)
(0.038)
(0.039)
(0.038)
(0.040)
(0.040)
(0.047)
(0.048)
(0.056)
2290
0.613
2031
0.688
1806
0.675
1577
0.672
1359
0.675
1108
0.681
864
0.671
667
0.675
533
0.663
392
0.607
(0.047)
(0.048)
(0.043)
(0.045)
(0.044)
(0.045)
(0.045)
(0.049)
(0.048)
(0.063)
2234
0.662
1982
0.727
1762
0.716
1538
0.713
1323
0.698
1076
0.702
835
0.693
640
0.710
515
0.685
379
0.629
(0.048)
(0.050)
(0.045)
(0.047)
(0.046)
(0.047)
(0.049)
(0.053)
(0.052)
(0.069)
2194
0.686
1944
0.720
1731
0.701
1508
0.707
1296
0.683
1049
0.709
810
0.719
617
0.724
494
0.692
364
0.671
(0.046)
(0.054)
(0.048)
(0.048)
(0.046)
(0.052)
(0.053)
(0.058)
(0.062)
(0.077)
2099
0.708
1856
0.745
1645
0.722
1433
0.730
1229
0.706
992
0.727
760
0.730
573
0.729
457
0.679
333
0.668
(0.047)
(0.058)
(0.050)
(0.051)
(0.048)
(0.054)
(0.054)
(0.060)
(0.061)
(0.077)
2043
0.719
1802
0.725
1594
0.732
1383
0.742
1182
0.721
950
0.752
720
0.751
540
0.756
433
0.701
314
0.688
(0.050)
(0.053)
(0.055)
(0.054)
(0.052)
(0.059)
(0.057)
(0.064)
(0.067)
(0.084)
1964
0.709
1726
0.704
1523
0.710
1315
0.727
1122
0.719
896
0.743
675
0.747
503
0.760
399
0.687
285
0.688
(0.052)
(0.055)
(0.057)
(0.056)
(0.054)
(0.061)
(0.059)
(0.068)
(0.071)
(0.092)
1861
0.709
1631
0.697
1436
0.703
1236
0.723
1048
0.714
829
0.743
620
0.746
457
0.765
360
0.691
255
0.710
(0.055)
(0.058)
(0.060)
(0.059)
(0.056)
(0.064)
(0.061)
(0.071)
(0.076)
(0.099)
1792
0.723
1573
0.697
1383
0.710
1185
0.727
1000
0.721
786
0.752
584
0.750
426
0.757
332
0.696
234
0.719
(0.057)
(0.062)
(0.066)
(0.064)
(0.060)
(0.071)
(0.066)
(0.074)
(0.082)
(0.106)
1683
0.743
1468
0.718
1283
0.733
1097
0.737
918
0.737
715
0.776
522
0.772
382
0.800
295
0.772
207
0.815
(0.055)
(0.059)
(0.064)
(0.064)
(0.061)
(0.073)
(0.067)
(0.074)
(0.085)
(0.105)
1580
0.748
1376
0.730
1196
0.738
1015
0.754
847
0.751
655
0.802
473
0.773
339
0.813
257
0.761
179
0.784
(0.059)
(0.064)
(0.068)
(0.070)
(0.064)
(0.076)
(0.075)
(0.081)
(0.093)
(0.108)
1501
0.774
1301
0.753
1123
0.754
945
0.769
782
0.764
599
0.828
421
0.785
297
0.831
221
0.817
156
0.865
(0.061)
(0.066)
(0.070)
(0.072)
(0.066)
(0.080)
(0.077)
(0.083)
(0.093)
(0.110)
1418
0.766
1226
0.742
1056
0.759
882
0.777
725
0.770
547
0.838
374
0.780
258
0.802
193
0.792
133
0.853
(0.064)
(0.069)
(0.074)
(0.075)
(0.069)
(0.083)
(0.079)
(0.087)
(0.100)
(0.118)
1341
0.796
1159
0.766
993
0.777
821
0.798
668
0.773
497
0.853
330
0.778
221
0.786
164
0.770
110
0.822
(0.070)
(0.075)
(0.080)
(0.083)
(0.075)
(0.093)
(0.087)
(0.100)
(0.117)
(0.138)
1207
0.825
1040
0.789
884
0.803
718
0.812
579
0.767
419
0.871
267
0.782
171
0.755
125
0.739
81
0.754
(0.073)
(0.079)
(0.086)
(0.089)
(0.083)
(0.104)
(0.100)
(0.108)
(0.122)
(0.145)
1084
930
784
632
509
359
219
137
95
60
0.705
0.719
0.718
0.725
0.713
0.742
0.726
0.737
0.698
0.686
Wgt.
Avg.
0.630
0.663
0.699
0.702
0.720
0.730
0.718
0.716
0.722
0.745
0.754
0.775
0.772
0.788
0.804
Table 3: Estimates of the father-son IGE in family income imposing data limitations
Time Average of Sons' Income (years)
Time Avg.
Fath. Inc.
1
2
3
4
5
6
7
8
9
10
wgt avg.
1
0.351
2
0.383
3
0.404
4
0.413
5
0.427
6
0.423
7
0.433
8
0.453
9
0.428
10
0.477
(0.033)
(0.027)
(0.027)
(0.029)
(0.031)
(0.033)
(0.037)
(0.042)
(0.042)
(0.039)
3481
0.438
3058
0.442
2705
0.462
2386
0.468
2122
0.488
1854
0.488
1622
0.499
1403
0.521
1215
0.495
1030
0.515
(0.028)
(0.029)
(0.030)
(0.032)
(0.032)
(0.033)
(0.036)
(0.040)
(0.040)
(0.042)
3391
0.466
2986
0.466
2645
0.485
2333
0.489
2075
0.504
1813
0.511
1589
0.520
1373
0.547
1189
0.516
1011
0.534
(0.029)
(0.029)
(0.031)
(0.033)
(0.033)
(0.035)
(0.037)
(0.041)
(0.041)
(0.044)
3285
0.462
2896
0.460
2574
0.484
2270
0.487
2019
0.501
1764
0.503
1549
0.518
1339
0.546
1158
0.518
984
0.536
(0.032)
(0.031)
(0.032)
(0.034)
(0.034)
(0.035)
(0.037)
(0.041)
(0.041)
(0.043)
3109
0.456
2754
0.470
2451
0.483
2171
0.485
1934
0.485
1690
0.492
1487
0.497
1286
0.550
1111
0.515
941
0.517
(0.042)
(0.036)
(0.037)
(0.038)
(0.041)
(0.045)
(0.051)
(0.046)
(0.047)
(0.051)
2923
0.498
2613
0.508
2335
0.521
2081
0.522
1857
0.523
1628
0.531
1431
0.538
1235
0.579
1064
0.551
902
0.561
(0.037)
(0.035)
(0.034)
(0.035)
(0.036)
(0.037)
(0.039)
(0.044)
(0.044)
(0.047)
2725
0.513
2448
0.516
2208
0.524
1975
0.529
1771
0.529
1556
0.537
1369
0.537
1177
0.581
1013
0.552
855
0.557
(0.042)
(0.038)
(0.038)
(0.038)
(0.039)
(0.040)
(0.042)
(0.047)
(0.048)
(0.050)
2476
0.540
2234
0.535
2032
0.538
1832
0.534
1644
0.534
1452
0.546
1282
0.544
1094
0.583
935
0.553
786
0.559
(0.045)
(0.041)
(0.040)
(0.040)
(0.041)
(0.042)
(0.043)
(0.049)
(0.050)
(0.053)
2278
0.552
2070
0.549
1895
0.542
1719
0.546
1556
0.546
1384
0.556
1223
0.550
1039
0.590
889
0.562
750
0.557
(0.042)
(0.042)
(0.039)
(0.042)
(0.043)
(0.043)
(0.044)
(0.049)
(0.051)
(0.054)
2051
0.558
1876
0.550
1724
0.540
1563
0.545
1422
0.544
1263
0.553
1113
0.544
948
0.588
808
0.565
676
0.552
(0.045)
(0.045)
(0.042)
(0.045)
(0.047)
(0.047)
(0.047)
(0.051)
(0.051)
(0.055)
1829
1679
1554
1407
1286
1145
1010
861
743
620
0.472
0.479
0.492
0.496
0.504
0.509
0.514
0.549
0.520
0.534
Wgt.
Avg.
0.408
0.472
0.495
0.492
0.487
0.526
0.532
0.543
0.553
0.552
Table 4: Estimates of the father-son rank-rank slope in family income
Time Average of Sons' Income (years)
Time Avg.
Fath. Inc.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
wgt avg.
1
0.453
2
0.489
3
0.502
4
0.512
5
0.533
6
0.550
7
0.576
8
0.572
9
0.546
10
0.526
(0.022)
(0.023)
(0.024)
(0.025)
(0.026)
(0.028)
(0.030)
(0.033)
(0.037)
(0.044)
2290
0.454
2031
0.486
1806
0.502
1577
0.513
1359
0.535
1108
0.555
864
0.576
667
0.567
533
0.550
392
0.526
(0.022)
(0.024)
(0.025)
(0.026)
(0.027)
(0.028)
(0.031)
(0.034)
(0.037)
(0.044)
2234
0.457
1982
0.484
1762
0.502
1538
0.513
1323
0.532
1076
0.554
835
0.574
640
0.564
515
0.538
379
0.517
(0.022)
(0.024)
(0.025)
(0.026)
(0.027)
(0.028)
(0.031)
(0.035)
(0.039)
(0.047)
2194
0.450
1944
0.465
1731
0.478
1508
0.491
1296
0.507
1049
0.535
810
0.556
617
0.546
494
0.521
364
0.508
(0.023)
(0.024)
(0.025)
(0.026)
(0.027)
(0.029)
(0.032)
(0.036)
(0.041)
(0.050)
2099
0.452
1856
0.469
1645
0.482
1433
0.495
1229
0.510
992
0.536
760
0.552
573
0.546
457
0.519
333
0.502
(0.023)
(0.024)
(0.026)
(0.027)
(0.027)
(0.030)
(0.033)
(0.037)
(0.041)
(0.051)
2043
0.458
1802
0.471
1594
0.486
1383
0.499
1182
0.516
950
0.541
720
0.554
540
0.550
433
0.524
314
0.513
(0.024)
(0.025)
(0.027)
(0.028)
(0.028)
(0.031)
(0.034)
(0.038)
(0.042)
(0.052)
1964
0.451
1726
0.461
1523
0.474
1315
0.490
1122
0.511
896
0.534
675
0.549
503
0.548
399
0.514
285
0.504
(0.024)
(0.026)
(0.028)
(0.029)
(0.029)
(0.032)
(0.036)
(0.039)
(0.045)
(0.056)
1861
0.451
1631
0.456
1436
0.468
1236
0.485
1048
0.506
829
0.530
620
0.544
457
0.544
360
0.508
255
0.514
(0.025)
(0.027)
(0.029)
(0.030)
(0.031)
(0.033)
(0.037)
(0.041)
(0.047)
(0.058)
1792
0.451
1573
0.449
1383
0.464
1185
0.477
1000
0.497
786
0.520
584
0.540
426
0.547
332
0.516
234
0.532
(0.025)
(0.028)
(0.030)
(0.031)
(0.032)
(0.035)
(0.039)
(0.042)
(0.048)
(0.058)
1683
0.443
1468
0.439
1283
0.451
1097
0.460
918
0.484
715
0.506
522
0.527
382
0.538
295
0.513
207
0.533
(0.026)
(0.029)
(0.031)
(0.033)
(0.034)
(0.037)
(0.042)
(0.046)
(0.053)
(0.063)
1580
0.436
1376
0.432
1196
0.442
1015
0.453
847
0.474
655
0.497
473
0.510
339
0.525
257
0.508
179
0.519
(0.027)
(0.030)
(0.033)
(0.034)
(0.036)
(0.039)
(0.045)
(0.049)
(0.057)
(0.068)
1501
0.448
1301
0.445
1123
0.454
945
0.464
782
0.485
599
0.509
421
0.536
297
0.567
221
0.579
156
0.611
(0.028)
(0.031)
(0.034)
(0.035)
(0.036)
(0.040)
(0.046)
(0.049)
(0.054)
(0.065)
1418
0.446
1226
0.443
1056
0.455
882
0.467
725
0.487
547
0.518
374
0.546
258
0.560
193
0.594
133
0.641
(0.029)
(0.032)
(0.035)
(0.036)
(0.038)
(0.041)
(0.047)
(0.053)
(0.058)
(0.072)
1341
0.457
1159
0.451
993
0.456
821
0.466
668
0.480
497
0.516
330
0.549
221
0.537
164
0.580
110
0.639
(0.030)
(0.034)
(0.037)
(0.039)
(0.040)
(0.044)
(0.050)
(0.059)
(0.065)
(0.084)
1207
0.460
1040
0.448
884
0.450
718
0.452
579
0.455
419
0.492
267
0.502
171
0.454
125
0.495
81
0.552
(0.032)
(0.036)
(0.039)
(0.042)
(0.045)
(0.050)
(0.058)
(0.070)
(0.077)
(0.100)
1084
930
784
632
509
359
219
137
95
60
0.451
0.462
0.475
0.487
0.507
0.532
0.552
0.551
0.532
0.528
Wgt.
Avg.
0.511
0.511
0.510
0.492
0.494
0.497
0.489
0.485
0.481
0.469
0.459
0.475
0.476
0.476
0.461
Table 5: Estimates of the father-son rank-rank slope in family income imposing data limitations
Time Average of Sons' Income (years)
Time Avg.
Fath. Inc.
1
2
3
4
5
6
7
8
9
10
wgt avg.
1
0.371
2
0.394
3
0.430
4
0.442
5
0.452
6
0.453
7
0.470
8
0.483
9
0.478
10
0.493
(0.018)
(0.020)
(0.021)
(0.022)
(0.023)
(0.024)
(0.025)
(0.026)
(0.028)
(0.029)
3481
0.383
3058
0.406
2705
0.441
2386
0.455
2122
0.465
1854
0.466
1622
0.482
1403
0.493
1215
0.490
1030
0.503
(0.018)
(0.020)
(0.021)
(0.022)
(0.023)
(0.024)
(0.025)
(0.027)
(0.028)
(0.030)
3391
0.387
2986
0.409
2645
0.444
2333
0.458
2075
0.467
1813
0.470
1589
0.488
1373
0.500
1189
0.494
1011
0.509
(0.018)
(0.020)
(0.021)
(0.022)
(0.023)
(0.024)
(0.025)
(0.026)
(0.028)
(0.030)
3285
0.380
2896
0.400
2574
0.436
2270
0.449
2019
0.457
1764
0.459
1549
0.479
1339
0.488
1158
0.485
984
0.493
(0.019)
(0.020)
(0.021)
(0.023)
(0.023)
(0.024)
(0.025)
(0.027)
(0.028)
(0.031)
3109
0.388
2754
0.407
2451
0.442
2171
0.456
1934
0.463
1690
0.468
1487
0.491
1286
0.501
1111
0.496
941
0.504
(0.019)
(0.021)
(0.022)
(0.023)
(0.024)
(0.025)
(0.026)
(0.027)
(0.029)
(0.031)
2923
0.400
2613
0.419
2335
0.453
2081
0.464
1857
0.472
1628
0.474
1431
0.496
1235
0.505
1064
0.504
902
0.513
(0.020)
(0.022)
(0.023)
(0.024)
(0.024)
(0.025)
(0.026)
(0.028)
(0.029)
(0.032)
2725
0.394
2448
0.411
2208
0.442
1975
0.457
1771
0.463
1556
0.466
1369
0.484
1177
0.495
1013
0.495
855
0.504
(0.021)
(0.023)
(0.024)
(0.025)
(0.026)
(0.026)
(0.027)
(0.029)
(0.031)
(0.033)
2476
0.396
2234
0.412
2032
0.439
1832
0.448
1644
0.453
1452
0.458
1282
0.476
1094
0.484
935
0.479
786
0.491
(0.022)
(0.024)
(0.025)
(0.026)
(0.026)
(0.027)
(0.028)
(0.031)
(0.032)
(0.035)
2278
0.407
2070
0.418
1895
0.440
1719
0.452
1556
0.457
1384
0.464
1223
0.482
1039
0.488
889
0.483
750
0.490
(0.023)
(0.024)
(0.025)
(0.027)
(0.027)
(0.028)
(0.029)
(0.031)
(0.033)
(0.036)
2051
0.408
1876
0.420
1724
0.436
1563
0.443
1422
0.447
1263
0.452
1113
0.468
948
0.474
808
0.472
676
0.474
(0.024)
(0.026)
(0.027)
(0.029)
(0.029)
(0.029)
(0.031)
(0.033)
(0.034)
(0.037)
1829
1679
1554
1407
1286
1145
1010
861
743
620
0.389
0.408
0.440
0.453
0.460
0.463
0.482
0.492
0.488
0.498
Wgt.
Avg.
0.433
0.445
0.449
0.440
0.448
0.458
0.450
0.444
0.449
0.443
Figure 1: Comparison of Intergenerational Samples
Parent Income
“Ideal”
PSID
1987, age 55
1986, age 54
.
.
.
1958, age 26
1957, age 25
2005, age 55
2004, ages 54-55
.
.
.
1968, ages 25-42
1967, ages 25-41
Child Cohort
1957
Child Income
2012, age 55
2011, age 54
.
.
.
1983, age 26
1982, age 25
1951-1975
2010, ages 35-45
2009, ages 35-45
.
.
1988, ages 35-37
1987, ages 35-36
1986, age 35
1980-82
2012, ages 30-32
2011, ages 29-31
IRS
Figure 2: Effects of time averaging on father-son IGE in household head
income
0.8
0.7
0.6
IGE
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Length of Time Average of Father's Income
Weighted Average
One year of Sons' Income
Figure 3: Effects of time averaging on father-son IGE in Family income
0.900
0.800
0.700
IGE
0.600
0.500
0.400
0.300
0.200
0.100
0.000
1
2
3
4
5
6
7
8
9
10
11
Length of Time Average of Father's Income
Weighted Average
One year of Sons' Income
12
13
14
15