Full text of Working Papers (Federal Reserve Bank of Chicago) : The Mis-Measurement of Permanent Earnings : New Evidence From Social Security Earnings Data, Working Paper 2001-24

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

Federal Reserve Bank of Chicago

The Mis-Measurement of Permanent
Earnings: New evidence from Social
Security Earnings Data

By: Bhashkar Mazumder

WP 2001-24

The Mis-Measurement of Permanent Earnings:
New evidence from Social Security Earnings Data

Bhashkar Mazumder
Federal Reserve Bank of Chicago
October, 2001

Abstract
This study investigates the reliability of using short-term averages of earnings as a proxy for
permanent earnings in empirical research. An earnings dynamics model is estimated on a large
sample of men covering the period from 1983 to 1997 following the cohort-based methodology of
Baker and Solon (1999). The analysis uses a unique dataset that matches men in the 1984, 1990
and 1996 Surveys of Income and Program Participation (SIPP) to the Social Security
Administartion’s Summary Earnings Records (SER). The results confirm that using a short-term
average of earnings can lead to spurious estimates of the effect of lifetime earnings on a particular
outcome. In addition, the transitory variance appears to vary considerably over the lifecycle. The
share of earnings variance due to transitory factors is higher among blacks and the persistence of
transitory shocks appears to be greater for this group as well. Finally, the transitory variance
appears to be a more important factor in explaining the overall earnings variance of college
educated men than those without college.

I am grateful to David Card and David Levine for their helpful advice and comments. I greatly
appreciated the help of Andrew Hildreth, Julia Lane and Susan Grad in helping me gain access to
the data. The views presented here do not reflect the views of the Federal Reserve System.

I. Introduction
In recent years, numerous studies on a wide variety of topics have tried to incorporate
measures of lifetime earnings or income into empirical economic research. Typically, researchers
have used nationally representative longitudinal household survey data such as the Panel Study of
Income Dynamics (PSID) and the National Longitudinal Survey (NLS) in order to calculate the
earnings stream of individuals and families over time. Unfortunately, for many purposes, the
longitudinal samples that can be constructed from these sources are relatively small, due in part to
attrition. As a result, researchers have often been forced to rely on relatively short windows of
time over which to measure lifetime economic status. This is particularly true in studies on
intergenerational earnings mobility (e.g. Solon 1992; Zimmerman 1992; Mulligan 1997), where
acquiring meaningful data for family members in two generations is an important limitation.
Therefore, these studies have typically used only up to five years of data on fathers’ earnings or
income to proxy for lifetime earnings.
When researchers observe only a few years of an individual’s lifetime earnings, exactly
how good a reading does it provide of permanent economic status? While at first glance this
might appear to be a somewhat narrow technical question, recent studies have found that the
degree of the mis-measurement of lifetime earnings may have important ramifications on our
understanding of long-term earnings dynamics and inequality. In the case of intergenerational
earnings mobility, for example, due to the high persistence of transitory fluctuations in earnings,
the bias from using even a five-year average of earnings may be quite substantial –in the order of
30 percent (Mazumder 2001). In addition, there is strong reason to suspect, based on both theory
and empirical evidence that the variance in the transitory component of earnings changes
considerably over the course of the lifecycle. Using an extraordinarily large database of
Canadian taxpayers and a highly structured earnings dynamics model, Baker and Solon (1999)
found that the transitory variance follows a U-shaped pattern over the lifecycle. This implies that
the age at which fathers’ earnings are measured may have a sizable effect on estimates of the

1

intergenerational elasticity of earnings. Grawe (2000), building on the findings of Jenkins (1987)
has estimated that lifecycle bias in intergenerational mobility studies may be of the order of 25
percent or more. Age-related heteroscedasticity in earnings is obviously an important issue for
many other areas of empirical economic research as well. For example, recent studies that have
tried to identify the causal effect of family income on children’s outcomes, typically have ignored
the age at which parent income is measured (e.g. Cameron and Heckman 2001; Duncan and
Brooks-Gunn 1997; Mayer 1997 and Blau 1999).
Due to data limitations, however, a detailed empirical analysis of the variance of earnings
comparable to Baker and Solon’s work has not yet been attempted for the US. Such an analysis
would provide greater insight into the nature and extent of bias in existing studies that use shortterm proxies for permanent earnings. In addition, other dimensions of earnings instability have
largely not been explored. It would be useful, for example, to document whether there are
important differences in earnings dynamics by race, sex, income or education. 1 Recent studies
that have failed to uncover differences in intergenerational mobility by groups with differential
access to credit, (e.g. Mulligan 1997) might not have properly accounted for differences in
transitory variance among these groups. Other research has also found that there has been a sharp
rise in the variance of transitory earnings in the US during the 1980s (Gottschalk and Moffitt
1994; Moffitt and Gottschalk 1995; Gittleman and Joyce 1996; Haider 1998), and that this
increase is an important factor in explaining growing inequality. It would obviously be important
to know whether this trend has continued into the 1990s.
Following Baker and Solon, this study uses a new source of data that is able to identify a
very rich model of earnings dynamics for the U.S. Specifically, the analysis uses the 1984, 1990
and 1996 Survey of Income and Program Participation (SIPP) matched to Social Security
earnings records (SER). By pooling several SIPPs, a very large sample size is generated,

1

An exception is Gittleman and Joyce (1996) but their analysis was limited to short-term changes in
inequality.

2

allowing for a highly detailed analysis. The match to individuals’ social security earnings
histories, prevents attrition from dissipating the sample size. The methodology uses minimum
distance techniques and a cohort-based estimation strategy that has not yet employed on U.S.
data. Among other things, the study documents the lifecycle patterns in the variance of earnings
as well as recent trends in the decomposition of earnings inequality between its permanent and
transitory components. In addition, differences in earnings dynamics among subgroups of the
population are also explored. The results of this analysis are then used to gauge the degree of bias
in studies that use short-term proxies in place of true permanent earnings.
The paper proceeds as follows: section II briefly describes the measurement issues
involved in using short-term averages of earnings to proxy for permanent earnings in regression
models. Section III discusses the data and methodology used in the analysis. Section IV presents
the results and their implications. Section V concludes.

3

II. Measurement Issues
In many economic studies, permanent earnings is used as a right hand side variable in a
regression either as a control or as an explanatory variable. The problem with using short-term
averages of earnings as a proxy for permanent earnings can be easily understood in the following
simplified framework.
yi = βxpi + ε

(1)
(2)

xit = x pi + wit + vit
wit = ρwit-1+ ξit

(3)

Here yi is the dependent variable. In studies of intergenerational transmission of earnings this
would be a measure of the child’s earnings as an adult. xpi represents permanent earnings and has
typically referred to fathers’ earnings in intergenerational studies. Of course, what is actually
used in empirical work is not xpi , but instead a proxy based on averaging annual earnings, xit , over
T number of years. As shown in (2), xit can be decomposed into a permanent component, xpi , a
transitory component; wit , and a measurement error term, vit . In addition, wit , follows a first order
autoregressive process with ρ representing the autocorrelation coefficient. If , xit is averaged over
T years, the estimate of β derived from OLS will be biased down by an attenuation factor, λt , as
shown below in (4).
∧

β OLS = βλt

(4)
where,

λT =

σ x2
1
1
σ + ασ w2 + σ v2
T
T

,

2
x

(

)


 1− ρT  

T − 
(1 − ρ )  


α = 1 + 2ρ 
,
 T (1 − ρ ) 





4

var (xp ) = σ2 x , var (w) = σ2 w and var (v) = σ2 v
Essentially, (4) demonstrates that as more years of data are used, the attenuation factor
will rise and the attenuation bias will decline, since the transitory shocks and measurement errors
are averaged away. On the other hand, the larger ρ is, the larger α will be, which will, to some
extent, offset the benefits of averaging earnings. Using some estimates of the key parameters
from previous earnings dynamics models, it can be shown that when using a five-year average of
earnings, a reasonable value for λ5 is about 0.67. 2 This suggests that the resulting estimate of β
may be biased down by 33 percent. In studies of intergenerational earnings mobility, where
consensus estimates have pointed to an elasticity of 0.4 (Solon, 1999), the actual value may be
closer to 0.6.
While this exercise suggests that there is likely to be significant downward bias, there are
dimensions to this problem that have been simplified. For example, these calculations have
assumed that the variance in the transitory component of earnings represents about 30 percent of
the total variance in annual earnings and is constant over time and over the lifecycle. A number
of studies (Gottschalk and Moffitt 1994; Moffitt and Gottschalk 1995; Gittleman and Joyce 1996,
Haider 1998), have documented that transitory earnings variance has increased during the 1980s
and has been an important cause of rising inequality in the US. In addition, Baker and Solon,
using Canadian data, have documented that the transitory variance follows a U-shaped pattern
over the lifecycle. This suggests that results from studies of the intergenerational earnings
elasticity may be sensitive to the age composition of the particular sample. This point was first
emphasized by Jenkins (1987) and refined by Grawe (2001) who has argued that this is a key
factor in explaining some of the differences in results obtained by various studies. Gittleman and
Joyce found evidence of greater earnings instability among blacks and those who are less

2

Specifically, estimates are needed for ρ, the share of the variance in annual earnings accounted for by
permanent earnings, transitory earnings and measurement error. This exercise uses parameter estimates
drawn from Card (1994) and Hyslop (2001). See Mazumder (2001) for a more detailed description of the
calculations.

5

educated, suggesting even greater downward bias in estimates for these groups. This suggests
that attempts to uncover differences in the effects of family income among subgroups of the
population might be biased away from finding large differences, even if they might actually exist
for reasons such as borrowing constraints. Gittleman and Joyce’s results, however, were based
on a series of two-year panels. Finally, the model has also omitted a random-walk component to
individual earnings which several empirical studies have found to be important (e.g. MacCurdy
1982; Abowd and Card 1989; Moffitt and Gottschalk 1995; Baker and Solon 1999).

6

III. Data and Methodology
This analysis pools data from the 1984, 1990 and 1996 Surveys of Income and Program
Participation (SIPP). In each SIPP year, individuals are matched to their social security earnings
records (SER) from 1951 to 1998. The relevant period of analysis for this study is 1983 through
1997. The time period is restricted to begin in 1983 because in earlier years, the maximum level
of earnings that were taxed for Social Security was quite low in real terms. This is important
because the SER data is censored at the taxable maximum. In section IV the issues that might
arise from this topcoding are addressed. The match rate from the SIPPs to the SER is quite high
at over 90 percent and does not appear to present any selection issues.3
The methodology closely follows that used by Baker and Solon, for ease of comparison.
The sample is restricted to cohorts of men who were between the ages of 24 and 59 for at least
nine years from 1982 to 1998. The sample is further divided into two-year birth cohorts
beginning with 1931/32 and ending with 1965/66 yielding a total of 18 cohorts. Only men with
positive earnings in all of the years that they meet the age requirement are included, thereby
restricting the sample to those with a high attachment to the workforce.4 In order to account for
any peculiarities in the earnings variance arising from those entering or exiting the workforce, the
first and last years of earnings are excluded. The actual working sample, therefore, consists of
men aged between 25 and 58 and spans the years from 1983 and 1997. For 10 of the cohorts,
starting with 1939/1940 and up to 1956/57, earnings information is used for all 15 years, allowing
for estimates of the autocovariance at lags from 1 to 14 years. On the other hand, the 1931/32
cohort and the 1965/66 cohorts are restricted to earnings information for just 7 years with a
maximum autocovariance lag of only 6 years. Some key features of the data are described in
Table 1.

3

See Mazumder (2001) for more detail.
This is a standard practice in the literature and suggests that, if anything, the selection rule results in
understating the degree of instability in earnings
4

7

The most obvious drawback with the selection rule is that it eliminates all men who do
not have at least nine consecutive years of positive earnings, thereby excluding those with long
spells of unemployment. 5 On the other hand, dropping men with years of zero earnings is
preferable with this particular dataset because the SER data records a zero either because the
individual did not work or because he did not work in a job covered by the Social Security
system. Roughly 60 percent of the recorded zeroes for men are due to non-covered status.6
Baker and Solon found that without the selection rule of consecutive years of positive earnings,
the variances would be considerably larger but that the year-to-year movements would be
unaffected. Therefore, for the purpose of identifying trends and relative differences in variance
parameters, this selection rule is probably not a problem.
On important advance compared to previous research on earnings dynamics in the US is
the sample size. This study uses a total of 23837 men with an average of 1324 in each cohort.
This compares to samples of 2730 used by Gottschalk and Moffitt (1994) and 534 used by Baker
(1997). It is also nearly three quarters the size of the working sample of 32,105 used by Baker
and Solon.
The analysis in this paper estimates two sets of models. First, a fairly straightforward
model of earnings dynamics is presented that allows estimation of a few parameters that would
allow for a simple assessment of the bias from averaging earnings over a short span as was done
in section II. At this point the estimation simply uses the empirical moments from the variancecovariance matrix of log earnings residuals for the entire sample following most of the earlier
literature. The actual moments used for estimation are shown in Appendix Table A1. Like most
previous studies, the sample is also restricted to be a balanced panel. 7 In the second set of results

5

Since annual earnings are used, an individual would have to have no earnings for an entire calendar year
to be excluded.
6
See Mazumder (2001).
7
This is equivalent to simply using the ten cohorts that are in the sample for all 15 years. Some
experimentation was done using an unbalanced panel, but for the most part, results were not very different.

8

a more complex model is estimated that tries to identify, among other things, lifecycle and time
effects and exploits a cohort-based estimation strategy. In this latter case, the set of empirical
moments from the variance-covariance matrix of each of the cohorts is stacked and used for
estimation of the model. For the ten cohorts with earnings data for all 15 years, a total of 120
moments (15 × 16 ÷ 2) are calculated. For the other cohorts, obviously, fewer moments are
available for the analysis although within each cohort, there is a balanced panel. In total, there
are 1660 empirical moments that are used for estimation in the second set of results.
An advantage of using a revolving balanced panel design is that it largely removes the
direct link between time and age so that both year and age effects can be separately identified.
There is still some aging of the panel over time, however, that is most pronounced during the
early 1980s and late 1990s (see Table 2).
The methodology for the first approach follows previous studies (e.g. Abowd and Card
1989; Baker 1997) that first “demean” log earnings by using a regression that also adjusts for age,
with a quartic function, and year effects, by using dummy variables. The resulting deviations of
log earnings, yit , are then modeled as follows:
(5)

yit = αi + εit + ζit
where
εit = ρεit-1 + uit ,

var(αi ) = σ2 α , var(ζit ) = σ2 ζ, var(u it) = σ2ut ,
cov(ζit, ζis ) = 0, t≠ s; cov(ζit, α i ) = cov(ζit, u i) = cov(u it, αi ) = 0
In this setup, α i is the permanent component of earnings that varies across individuals; ε it is a
transitory component which follows a first-order autoregressive process with a time-varying
variance and ζit is a white noise component. The final term, ζit , represents measurement error and

There are also some complexities involved in calculating standard errors that are avoided by using a
balanced panel.

9

is identified by virtue of the fact that it is only contained in the variances not the covariances.8
This implies, for example, that the variance of earnings in 1990 is as follows:
(6)

var(y1990 ) = σ2 α + ρ2 σ2 ε1989 + σ2 ε1990 + σ2 ζ

One point that is immediately evident is that the transitory variance follows a recursive structure.
Following previous research, it is assumed that the initial variance, σ2 ε1983 captures all
accumulated shocks up to 1983, and that this variance will be common to all individuals in the
sample. Using this simple framework, all 120 moments from the variance-covariance matrix of
the entire working sample are calculated and then used to estimate the parameters of the model
using equally weighted minimum distance (EWMD) –which is equivalent to nonlinear least
squares.9 This approach is then used to estimate the parameters separately for various subgroups
of the population.
In the second part of the study, the earnings model closely follows Baker and Solon and
borrows their notation. Instead of using a regression to calculate age- and year-adjusted
deviations, a more general procedure is now used:
(7)

Yibt = µbt + y ibt

Let Yibt represent the log earnings of individual i, in birth cohort b, in year t; µbt be the cohortspecific mean for that year; and yibt be the individual-specific deviation from that mean. Then yibt
can simply be calculated by subtracting the sample average log earnings for cohort b in year t
from the observed earnings, Yibt . The deviations from the mean are then modeled as follows:
(8)

yibt = p t [αib + βib (t-b-26) + u ibt] + εibt
where

8

Although one might expect that there would not be substantial measurement error in administrative data
one problem that does arise with social security earnings data is that only covered earnings are reported
when in fact, individuals may have non-covered earnings as well. See Mazumder (2001) for a discussion
of this problem. In addition, there could be mismeasurement due to employer recording errors or changes
in the timing of paychecks and bonuses.
9
See the appendix of Abowd and Card (1989) for a description of the technique. Evidence from Altonji
and Segal (1996) and Clark (1996) suggest that using the theoretically derived optimal weighting matrix

10

(9)
(10)

u ibt = u ibt-1 + ribt
εibt = ρεibt-1 + λt vibt
and

(11)

var(vibt) = γ0 + γ1 (t-b-26) + γ2 (t-b-26)2 + γ3 (t-b-26)3 + γ4 (t-b-26) 4

Deviations in log earnings have both a permanent and transitory component. The
expression in brackets shown in the right hand side of (8) breaks down the permanent component
into three parts. As before, α ib , with variance σ2 α, is a fixed effect that varies across individuals.
The βib term, with variance σ2 β, corresponds to Baker’s (1997) finding of heterogeneity in the
growth rate of earnings over time and captures the deviation of the individual’s idiosyncratic
growth rate from his cohort’s, after age 26. In addition, since human capital theory typically
implies a tradeoff between initial earnings and future earnings growth, σαβ is included to
represent the covariance between α and β and is expected to be negative.10 The uibt term is a
random walk component as shown in (9). Here ribt is “white noise” with variance σ2 r. Various
studies (MacCurdy 1982; Abowd and Card 1989; Moffitt and Gottschalk 1995; Baker and Solon
1999) have found evidence of a random walk component to earnings. As Baker and Solon point
out, the random-walk component can be separately identified from the idiosyncratic growth
parameter since the former implies a linear growth pattern in log earnings variance, whereas the
latter implies a quadratic pattern. In order to capture changes over time in the permanent effect, a
factor loading term represented by p t is also included.

can produce serious bias in finite samples. Recent studies therefore, have used the identity matrix as the
weighting matrix.
10
Some researchers such as Mincer (1991) have found that this correlation is positive. This may be
explained by omitted variable bias or an alternative theoretical model such as efficiency wages.

11

The last term in (8), ε ibt, is the transitory component which is modeled in (10) as
following a first order autoregressive process with a factor loading, λt , on innovations. 11 The
factor loading terms simply capture changes over time in the relative importance of the
components. These are standardized to equal 1 in the base year, 1983. Thereafter, increases in p t
relative to increases in λt reflect movements in the permanent component relative to the transitory
component. Finally, (11) models the innovations in the transitory component as following a
quartic in experience since age 26, to capture life-cycle effects.
For clarity, an example of an element of the implied variance-covariance matrix is shown
below. The variance of log earnings for the 1949/50 cohort in 1990 is presented in (12):
(12)

var(y49/50, 1990) = p2 1990 (σ2 α + 15 2 σ2 β+ 30σ2αβ + 15σ2 r )+ ρ2 var(εi,49/50,1990 ) +
λ2 1990 (γ0 + 15γ1 + 152 γ2 + 153 γ3 + 154 γ4 )

The multiples of 15 in the expression arise from the fact that the cohort born in 1949 is 41 years
old in 1990, and therefore has 15 years of experience since age 26. As in the first stage, the
transitory variance has a recursive structure that must be traced back to the cohorts’ initial entry
into the sample.12

11

In this formulation there is no term that corresponds to measurement error. This was omitted to maintain
comparability with Baker and Solon.
12
Following Baker and Solon, the initial transitory variance for each cohort is separately estimated since it
makes no sense to impose a common initial variance when the model is designed to differentiate life-cycle
effects.

12

IV. Results
The results for the first stage analysis are shown in Table 3. Here each row represents a
different sample used for estimating the autocovariance of earnings. The first row utilizes the full
sample and provides a set of baseline estimates. The estimate for σ2 α, the fixed effect, is 0.2,
which is similar to previous estimates found by Baker (1997) and Card (1994). If the predicted
values for the various parameters are used to decompose the cross-sectional variance of log
earnings residuals over the fifteen year period into its permanent and transitory components, the
implied permanent share of the cross-sectional variance is only 43 percent. This compares to 50
percent found by both Card (1994) and Hyslop (2001) using the PSID. The share of variance due
to transitory earnings is 44 percent, similar to the estimated permanent share but sharply higher
than the estimates of 30 percent in the aforementioned studies. In accordance with earlier results,
however, ρ is estimated to be close to 0.8. The estimate of σ2 ζ , representing measurement error,
is 0.06 which implies that the share of variance due to this component is 13 percent —a figure
similar to what is found with survey data.13 Incorporating these baseline estimates into the
exercise discussed in Section II, confirms the notion that the use of short-term averages may lead
to substantial underestimates of the effects of permanent earnings in regression models. For
example, the parameter estimates suggest that a five-year average of earnings would lead to an
attenuation factor of 0.56 —implying that coefficient estimates are biased down by more than 40
percent.
The other rows of Table 3 compare differences by subgroups of the population. The
estimates for whites are virtually identical to that of the overall population while blacks have a
higher share of transitory variance at nearly 50 percent. In addition, the estimates of ρ are also a
bit higher for blacks at 0.81 compared to 0.78 for whites, a difference that is statistically
significant. These parameters suggest that five-year averages of earnings for blacks may result in

13

See Bound and Krueger (1991).

13

coefficient estimates that are biased down by more than 50 percent. One implication of this
finding is that tests designed to uncover differences in parameter estimates by race may be biased
away from finding differences.
One concern is that the selection criteria rule, by screening out those with very long spells
of unemployment, effectively eliminates some of the racial differences in earnings dynamics that
might otherwise be captured. To see what might happen if the selection rule was eased, the same
model was also run allowing for some years of zero earnings. 14 The results of this exercise are
shown in the last two rows of Table 3. The overall variance in log earnings is about two and a
half times larger using this less restrictive selection rule for both blacks and whites. As would be
expected, the transitory share is now sharply higher, reaching nearly two thirds in the case of
blacks. In addition, ρ is now estimated to be 0.83 for whites and 0.86 for blacks. Still, the
difference in the transitory share of the overall earnings variance between blacks and whites is not
appreciably different using this selection rule, suggesting that the requirement of positive
earnings in all years may not be distorting the comparison.
The fourth and fifth rows of Table 3 compare differences by educational attainment.
Here the sample is split between those who have completed college and those who haven’t. The
overall variance of earnings is sharply lower among college educated men. However, those with
college actually appear to have greater earnings instability, as the transitory share of the total
variance is higher for college graduates. Gittleman and Joyce, in contrast, found that those at the
lowest educational level have a higher share of transitory variance.15 One potential explanation is
that the analysis might conflate age effects with education level. In other words, older workers
may have more earnings stability than younger workers due to their position in the lifecycle

14

Specifically, individuals with positive earnings in approximately two-thirds of the years that they match
the age criteria are included. Since the analysis uses log earnings, zero earnings are recoded as $1000 or
approximately 6.9 on the log scale. The results are not very sensitive to the imputation value chosen.
15
It should be noted that in their second set of results (Table 2 on p.192), the coefficient of variation
actually rises with education after 12 years of schooling, a result that is consistent with what is presented
here.

14

despite having less education. The model in the second stage analysis will be able to separate
these effects.
One possible problem with this analysis is that it uses social security earnings data that is
censored at the social security taxable maximum. This might be especially important given the
fact that what is being estimated is the variance of earnings which may be more sensitive to
changes in the tails of the distribution. One comforting fact, however, is that the rate of
topcoding, has not changed very much over the period under examination, ranging from a low of
11.6 percent in 1983 to a high of 17.6 percent in 1997. 16 To try to gauge the sensitivity of the
results to topcoding, another estimation was attempted that imputed censored observations with
random draws from the upper tail of an estimated distribution. 17 The results for the full sample
are shown in the last row of Table 3. The only meaningful difference is that ρ is now estimated
to be close to 0.85. The implied share of the permanent component is exactly the same as before
while the share of earnings variance is now slightly higher than before.
The parameter estimates from the second part of the study are shown in Table 4. The
first panel of the table shows the estimates of the various parameters that comprise the permanent
component. Each pair of columns refers to a different sample used for analysis. Recall that the
model allows for heterogeneity across individuals in the intercept and the idiosyncratic growth
rate, a random walk component and year-specific factor loadings. For the full sample, the
estimate for the fixed effect, 0.17, is only slightly lower than what was found in the earlier results.
It also slightly larger than the 0.13 in the baseline estimates reported by Baker and Solon for
Canada. Unlike the findings from previous studies (Baker 1997, Haider 1998 and Baker and

16

It should be noted that the rising share of topcoded observation is due to the increasing age of the sample
over time. The rate of topcoding for those aged 35-45 in each year actually falls from 22.9 percent in 1983
to 16.5 percent in 1997.
17
The procedure was to assume that the true distribution of log earnings was normally distributed. The
mean of the truncated earnings distribution in each year along with the rate of topcoding was then used to
infer the parameters of the complete distribution (see Greene, p.951). The complete distribution was then
truncated from below at the censoring point and then used to randomly draw observations for the purpose
of imputing censored observations.

15

Solon, 1999), there does not appear to be any significant heterogeneity in the growth rate
component. Also the estimated covariance between the intercept and growth rate terms is
positive. Conforming to previous research, however, there is a positive and significant random
walk component. Still the economic significance of the parameter is not clear. For example, for
fifty year olds in 1990, the estimated contributed of the random walk component to the cohorts’
earnings variance is just 4.9%. The year specific loading factors on the permanent component
appear to rise over time but not in a smooth manner. They surge in the early 1990s but begin to
stabilize thereafter.
The transitory component is modeled as first order autogressive process with age-varying
parameters and different initial variances for each cohort. The estimate for ρ is 0.67, which is
considerably smaller than what was estimated in the bare-boned first stage analysis but still
suggests a significant degree of persistence in transitory shocks. The analogous estimate for ρ in
Canada as found by Baker and Solon was just 0.54. The implied effects of this degree of
persistence on short-term averages of earnings will be discussed below. There does not appear to
be any pattern in the initial variances of each cohort. Given that the initial age at which each
cohort is first observed (see Table 1) is monotonically declining, one might have expected a Ushaped pattern to be apparent in the initial variances given the findings of Baker and Solon.
One somewhat surprising result is that the year-specific weights on the transitory
component, as reflected by the λt ’s, decline through the 1980s and then reverse course and
sharply increase during the 1990s. While a higher transitory variance might be expected during
the recession years of the early 1990s, it is clear that there has been a secular increase in earnings
instability that has persisted through at least 1997.
One clear result is that the age parameters on the transitory variance do, indeed, imply a
U-shaped pattern as shown in Figure 1. This pattern supports the notion that regressions using
short-term averages of earnings may highly be sensitive to the age-composition of the sample.

16

Theoretical models that emphasize learning or matching can easily explain the falling transitory
variance in earnings as individuals enter their thirties and forties but it is not so clear what
accounts for the substantial increase in earnings instability as workers enter their fifties. Clearly
this result offers interesting fodder for future research.
The remaining columns in Table 4 estimate the same model by level of education. While
it would be ideal to have used the cohort-based approach to measure differences by race, initial
results indicated that the small sample of blacks led to unstable results. 18 The comparison
between education groups appears to be more meaningful since the sample sizes are reasonably
large for both groups. The fixed effect appears to be significantly higher for the no college group
compared to those with a college education. The random walk term, in contrast, is much higher
for the college sample. The loading factor on the permanent component has remained above 1 for
the no college group since 1988 but has been below 1 for the college group. The transitory
component appears to be more persistent for college graduates as the estimate for ρ is slightly
higher for this sample. The initial variances for the cohorts are higher for the college group in
two-thirds of the cases. The yearly loading factors on the transitory variance for the two groups
also show distinct patterns. For college graduates the loading factor has remained above 1 for
nearly the entire period with a more pronounced trend up in the 1990s. In contrast for the no
college group, the loading factor had declined on average, through the 1980s, but has rebounded
in the 1990s.
Taken together, these results appear to bolster the earlier finding that the permanent
component accounts for a larger share of the earnings variance of non-college educated men than
it does for college educated men. Figure 2 plots the share of earnings variance due to the
permanent component for those aged 40 in each year by education group. Figure 2 makes it clear
that the share of the earnings variance due to the permanent component was far higher for high-

18

Specifically some of the estimated initial variances were negative and the loading factors were extremely
volatile. Of some interest is that ρ was estimated to be about 0.95 indicating substantial persistence.

17

school educated men from 1985 until 1992. Since that time, however, both education groups
appear to have roughly similar shares of the permanent component. Put another way, rising
earnings instability affected college educated workers far more than high school educated
workers in the 1980s, but since the early 1990s it has become an equally important component of
the overall earnings variance of both education groups.
The key motivation in estimating this model, however, was to answer the question of how
reliable a measure of permanent earnings is a short-term average of earnings. In order to assess
this empirically, the following exercise was performed. As before let xit , the earnings of
individual i in period t, be decomposed into a permanent component a it and transitory component,
εit.19
xit = ait + εit

(13)

Essentially, (13) simply summarizes the more complicated expression for the permanent
component shown in (8), with a it . Now define permanent earnings, xpi as the average of the
permanent component of earnings, over the fifteen years spanning 1983 through 1997.
(14)

xpi =

1 1997
∑ a it
15 t =1983

With this setup we can then easily use the second stage baseline results to derive the
attenuation factors that would arise from using any multiyear average of earnings during the
1983-1997 time span as a proxy for xpi in a regression. In general, if an n year average of
earnings beginning in year s, x n, s , is used as a proxy for xpi , the attenuation factor λn,s is the
following:
(15)

19

λn,s =

cov( x n, s , x p )

For simplicity, the notation drops the indexing of cohorts.

18

var( x n, s )

To calculate the numerator and denominator of this expression would simply involve
summing various estimated variances and covariances involving both the permanent and
transitory components.20 This yields a huge number of estimated attenuation factors, since there
are unique results for each potential time span over which an average is taken and since there are
distinct results for each cohort. As an example, the attenuation factors for the cohorts born in
1943/44 and 1953/54 are shown in Table 5. Clearly, looking across the rows, as averages are
taken over progressively more years the attenuation bias declines as expected. This pattern is
robust across all cohorts. The results here support the findings in Mazumder (2001), however,
that even a five-year average still results in an estimate that is biased down by about 30 percent.21
What is quite important, however, is the age at which the average is taken. For example, in some
cases, the attenuation coefficient from using a single year of earnings, is actually higher than it is
when averages are taken over as many as five years. Given these results, it is clear that
extraordinary care must be taken in interpreting results about parameters dealing with permanent
earnings when only short periods are available for measurement. Clearly some corrections should
be undertaken to appropriately adjust the sample composition or to reweight observations,
however, such techniques are beyond the scope of this paper.
It is also important to note that there maybe many instances where researchers should not
be concerned about the earnings stream over one’s entire lifetime. For example, the dependent
variable of interest may be a child’s outcome that is related only to parent’s income at the time of

20

For example, if a five-year average of earnings covering the years 1983-1987,

x 5,83 , was used as a proxy

for xpi the resulting attenuation factor, λ5,83 is as follows:

λ5,83 =

21

1 87 1 97
∑ ∑ cov( a is , a it )
5 s=8315 t =83

87
87 87
87 87
1 87
( ∑ var( ais ) + ∑ var( ε is ) + 2 ∑ ∑ cov( a is , a it ) + 2 ∑ ∑ cov( ε is , ε it )
25 s= 83
s =83
s =83 t =s +1
s =83 t =s +1

The average of column 5 in Table 5 is 0.68.

19

child rearing. 22 In that case transitory fluctuations that occur at the time that parents are actively
raising children may actually matter. If such fluctuations are highly persistent, then a short-term
average may actually be preferable to a long-term average. The attenuation coefficients presented
here, obviously should not be applied in those instances.

22

For example certain health outcomes at young ages may be especially sensitive to current income,
especially among groups that are borrowing constrained.

20

V. Conclusion
As researchers increasingly exploit longitudinal data to study the effects of income on
various outcomes, it is essential that the pitfalls of using short-term proxies as a substitute for
their permanent counterparts, are well understood. This study adds to our knowledge by using a
new longitudinal data source that contains a large panel of years and a sizable sample to estimate
a detailed earnings dynamics model. The results of this analysis bolster the findings of other
studies that have found that the variance of the transitory component of earnings accounts for a
large share of the overall observed variance in earnings. In addition, the variance in transitory
earnings appears to follow a pronounced U-shaped pattern over the lifecycle as was found by
Baker and Solon (1999) and has risen considerably over time.
The estimates of the model suggest that a short-term average of earnings, when used as a
substitute for permanent earnings in a regression model, can lead to serious bias. In particular,
even a five year average of earnings can lead to a parameter estimate that is biased down by 30
percent. Of particular importance is the age over which earnings are averaged. In fact, earnings
taken from just one or two years at the right stage of the lifecycle may yield less biased estimates
than those stemming from a five or six-year average. Future research should pay careful attention
to the age composition of the sample and try to develop methods to overcome this bias.
Attempts to uncover differences in earnings dynamics among subgroups of the
population lead to some interesting results. The share of earnings variance due to transitory
factors is higher among blacks and the persistence of transitory shocks appears to be greater for
this group as well. This suggests that comparisons of the effect of income on outcomes by race
may lead to failure to detect differences when in fact, such differences may well exist. A
somewhat surprising result is that the transitory variance appears to be a more important factor in
explaining the overall earnings variance of college educated men than those without college.
However, in recent years, both groups appear to be equally impacted by growing earnings
instability.

21

References

Abowd, John M and David Card (1989), “On the Covariance Structure of Earnings and Hours
Changes” Econometrica, 57(2) 411-445
Altonji, Joseph G. and Lewis M. Segal, “Small Sample Bias in GMM Estimation of Covariance
Structures,” Journal of Business and Economic Statistics, 14() 353-366.
Baker, Michael (1997), “Growth-Rate Heterogeneity and the Covariance Structure of Life Cycle
Earnings”, Journal of Labor Economics, 15(2) 338-375
Baker, Michael and Gary Solon (1999), “Earnings Dynamics and Inequality Among Canadian
Men, 1976-1992: Evidence from Longitudinal Tax Records” NBER Working Paper 7370, NBER,
Cambridge Mass.
Blau, David (1999), “The Effect of Income on Child Development”, Review of Economics and
Statistics, 81(2) 261-276.
Bound, John and Alan B. Krueger (1991), “The Extent of Measurement Error in Longitudinal
Earnings Data: Do Two Wrongs Make a Right?”, Journal of Labor Economics, 9(1) 1-24.
Cameron, Stephen V. and James J. Heckman (2001) “The Dynamics of Educational Attainment
for Black, Hispanic and White Males” Journal of Political Economy 109(3):455-499.
Card, David (1994), "Intertemporal Labor Supply: An Assessment", in Christopher A. Sims (ed.)
Advances in Econometrics, Sixth World Congress, Vol. 2, Cambridge University Press.
Cambridge.
Clark, Todd (1996), “Small-Sample Properties of Estimators of Nonlinear Models of Covariance
Structure,” Journal of Business and Economic Statistics, 14() 367-373.
Corak, Miles and Andrew Heisz. (1999). "The Intergenerational Earnings and Income Mobility of
Canadian men: Evidence from Longitudinal Income Tax Data." Journal of Human Resources
34(3):504-533.
Duncan, Greg J. and Jeanne Brooks-Gunn (1997), eds. “Consequences of Growing up Poor”.
Russell Sage Foundation, New York
Gittleman, Maury and Mary Joyce (1996), “Earnings Mobility and Long-Run Inequality: An
Analysis Using Matched CPS Data”, Industrial Relations, 35(2) 180-196.
Gottschalk, Peter and Robert A. Moffitt (1994), “The Growth of Earnings Instability in the U.S.
Labor Market,” Brookings Papers on Economic Activity, 217-272
Grawe, Nathan D. (2000), “Lifecycle Bias in the Estimation of Intergenerational Income
Persistence”. Manuscript, University of Chicago.

22

Haider, Steven J. (1998), “Earnings Instability and Earnings Inequality of Males in the United
States 1967-1991,” Chapter 2 in Econometric Studies of Long-Run Earnings Inequality, PhD.
Dissertation, University of Michigan.
Hyslop, Dean (2001), "Rising U.S. Earnings Inequality and Family Labor Supply: The
Covariance Structure of Intrafamily Earnings," American Economic Review, 91:755-777.
Jenkins, Stephen (1987), “Snapshots Versus Movies: ‘Lifecycle Biases’ and the Estimation of
Intergenerational Earnings Inheritance”, European Economic Review 31:1149-1158
Lillard, Lee A. and Robert J. Willis (1978), "Dynamic Aspects of Earning Mobility,"
Econometrica 46:985-1012
MaCurdy, Thomas E. (1982), “The Use of Time Series Processes to Model the Error Structure of
Earnings in a Longitudinal Data Analysis.” Journal of Econometrics, 18:83-114.
Mayer, Susan (1997), “What Money Can’t Buy: Family Income and Children’s Life Chances”.
Harvard University Press, Cambridge Mass.
Mazumder, Bhashkar (2001), “Earnings Mobility in the U.S.” A New Look at Intergenerational
Inequality.” Federal Reserve Bank of Chicago Working Paper 2001-18.

Mincer, Jacob (1991), “Human Capital, Technology, and the Wage Structure: What do
Time Series Show?,” NBER Working Paper 3581.
Moffitt, Robert A and Peter Gottschalk, “Trends in the Autocovariance Structure of Earnings in
the U.S. 1969-1987,” Working Paper No. 335, Department of Economics, Johns Hopkins
University.
Mulligan, Casey B. (1997), Parental Priorities and Economic Inequality. University of Chicago
Press, Chicago.
Solon, Gary (1992), "Intergenerational Income Mobility in the United States," American
Economic Review, 82:393-408
Solon, Gary (1999), "Intergenerational Mobility in the Labor Market," Handbook of Labor
Economics, Elsevier
Zimmerman, David J. (1992), "Regression Toward Mediocrity in Economic Stature," American
Economic Review, 82:409-429

23

Table 1: Sample Size by Cohort

Birth Year

Sample
Size

1931/32
1933/34
1935/36
1937/38
1939/40
1941/42
1943/44
1945/46
1947/48
1949/50
1951/52
1953/54
1955/56
1957/58
1959/60
1961/62
1963/64
1965/66

728
735
795
802
806
1028
1047
1196
1436
1490
1537
1580
1647
1626
1732
1869
1923
1860

Total

23837

Years Observed

Initial
Age

1983-1989
1983-1991
1983-1993
1983-1995
1983-1997
1983-1997
1983-1997
1983-1997
1983-1997
1983-1997
1983-1997
1983-1997
1983-1997
1983-1997
1985-1997
1987-1997
1989-1997
1991-1997

Note : Age refers to age of older members in 2-year birth cohorts

52
50
48
46
44
42
40
38
36
34
32
30
28
26
26
26
26
26

Final
Age
58
58
58
58
58
56
54
52
50
48
46
44
42
40
38
36
34
32

Table 2: Sample Statistics by Year

Year
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997

N
16453
16453
18185
18185
20054
20054
21977
21249
23109
22374
22374
21579
21579
20777
20777

Mean
Std. Dev.
Log Earnings Log Earnings
10.273
0.767
10.348
0.699
10.344
0.695
10.386
0.691
10.367
0.702
10.402
0.660
10.371
0.678
10.370
0.678
10.275
0.715
10.244
0.713
10.324
0.753
10.367
0.713
10.373
0.727
10.376
0.733
10.394
0.757

Min
Age

Max
Age
25
26
25
26
25
26
25
26
25
26
27
28
29
30
31

52
53
54
55
56
57
58
57
58
57
58
57
58
57
58

Note: Earnings are measured in 1998 dollars deflated by using the CPI-U-X1 series.

Mean
Age
36.1
37.1
36.9
37.9
37.7
38.7
38.4
38.8
38.6
39
40
40.4
41.4
41.8
42.8

Table 3: Results from simple earnings dynamics specification
Implied shares of cross-sectional variance
due to…

σ2α

ρ

2

σ ut**

σ2ζ

permanent
transitory measurement
component
component
error
0.43
0.44
0.13

F-stat
163.29

N*
13393

0.06
(0.003)

156.46

12121

0.43

0.44

0.13

0.13

0.09
(0.011)

167.62

962

0.37

0.49

0.14

0.72
(0.018)

0.09

0.04
(0.005)

165.14

4312

0.41

0.49

0.10

0.20
(0.007)

0.75
(0.012)

0.11

0.06
(0.003)

200.52

9081

0.42

0.45

0.13

Whites
less restricted

0.34
(0.012)

0.83
(0.006)

0.25

0.16
(0.004)

238.23

17492

0.29

0.57

0.14

Blacks
less restricted

0.34
(0.064)

0.86
(0.018)

0.34

0.21
(0.016)

299.22

1568

0.22

0.64

0.14

0.43

0.41

0.16

(fixed effect)

(trans. Var.)

(meas. Error)

Whole sample

0.20
(0.006)

0.78
(0.010)

0.09

0.06
(0.003)

Whites

0.19
(0.005)

0.78
(0.010)

0.09

Blacks

0.24
(0.037)

0.81
(0.035)

College

0.14
(0.007)

No College

Full Sample
0.23
0.84
0.08
0.09
160.05
13393
Imputed
(0.007)
(0.009)
(0.003)
*Here, N refers to the number of observations used to calculate the variance-covariance matrix.
**This is the average of the transitory variance over the fifteen years
Notes: All specifications use a total of 120 moments, those used for row 1 are shown in Appendix Table A1.
Less restricted sample allows some years of zero earnings. Standard errors are shown in parenthesis

Table 4: Results from cohort-based earnings dynamics model

Full sample
estimate
s.e

σα
σ2β
σαβ
σ2r
2

0.170
1.01E-07
2.62E-04
6.52E-04

No College
estimate
s.e

permanent component
(0.005)
0.118
(0.007)
0.172
(0.006)
(1.56E-07)
-2.88E-06 (6.40E-07)
-4.89E-06 (6.75E-07)
(2.63E-05)
5.90E-04 (8.09E-05)
3.32E-04 (4.36E-05)
(6.36E-05)
1.49E-03 (2.12E-04)
8.17E-04 (1.07E-04)
yearly loading factors on permanent component
(0.017)
0.940
(0.031)
0.982
(0.022)
(0.019)
0.902
(0.036)
0.988
(0.023)
(0.019)
0.903
(0.036)
1.036
(0.024)
(0.020)
0.970
(0.037)
1.042
(0.025)
(0.020)
0.901
(0.036)
0.994
(0.024)
(0.020)
0.928
(0.036)
1.039
(0.025)
(0.020)
0.996
(0.037)
1.082
(0.025)
(0.021)
1.046
(0.038)
1.135
(0.026)
(0.021)
0.984
(0.037)
1.145
(0.026)
(0.021)
0.998
(0.037)
1.095
(0.025)
(0.020)
1.050
(0.037)
1.048
(0.024)
(0.020)
0.983
(0.035)
1.038
(0.024)
(0.019)
0.949
(0.034)
1.072
(0.024)
(0.019)
0.978
(0.034)
1.108
(0.023)

p84
p85
p86
p87
p88
p89
p90
p91
p92
p93
p94
p95
p96
p97

0.992
0.995
1.044
1.068
1.017
1.063
1.117
1.175
1.174
1.148
1.112
1.092
1.112
1.151

ρ

0.670

(0.006)

0.296
0.574
0.209
0.257
0.271
0.275
0.320
0.256
0.262
0.241
0.437
0.325
0.393
0.481
0.204
0.289
0.322
0.293

(0.022)
(0.022)
(0.023)
(0.021)
(0.021)
(0.025)
(0.024)
(0.022)
(0.022)
(0.022)
(0.023)
(0.023)
(0.025)
(0.024)
(0.025)
(0.023)
(0.025)
(0.025)

σ231/32
σ233/34
σ235/36
σ237/38
σ239/40
σ241/42
σ243/44
σ245/46
σ247/48
σ249/50
σ251/52
σ253/54
σ255/56
σ257/58
σ259/60
σ261/62
σ263/64
σ265/66

College
estimate
s.e

transitory component
0.694
(0.009)
cohort specific initial variances
0.411
(0.031)
0.571
(0.036)
-0.051
(0.031)
0.337
(0.035)
0.191
(0.034)
0.172
(0.032)
0.091
(0.032)
0.260
(0.029)
0.405
(0.033)
0.171
(0.029)
0.326
(0.031)
0.401
(0.033)
0.348
(0.034)
0.635
(0.034)
0.409
(0.036)
0.419
(0.033)
0.505
(0.032)
0.342
(0.035)

0.675

(0.008)

0.218
0.533
0.242
0.209
0.265
0.299
0.395
0.257
0.213
0.268
0.489
0.294
0.399
0.435
0.186
0.266
0.318
0.315

(0.027)
(0.029)
(0.029)
(0.029)
(0.026)
(0.026)
(0.028)
(0.025)
(0.026)
(0.030)
(0.029)
(0.026)
(0.027)
(0.029)
(0.029)
(0.028)
(0.027)
(0.028)

Table 4: Results from cohort-based earnings dynamics model (cont.)

λ84
λ85
λ86
λ87
λ88
λ89
λ90
λ91
λ92
λ93
λ94
λ95
λ96
λ97
γ0
γ1
γ3
γ4
γ5

Full sample
College
No College
estimate
s.e
estimate
s.e
estimate
s.e
yearly loading factors on transitory component
1.000
--1.000
--1.000
--0.995
(0.051)
1.377
(0.105)
0.897
(0.062)
0.953
(0.047)
(0.099)
0.936
(0.053)
0.875
(0.048)
1.079
(0.098)
0.840
(0.056)
0.918
(0.044)
1.023
(0.091)
0.887
(0.053)
0.801
(0.048)
0.996
(0.092)
0.748
(0.056)
0.875
(0.047)
1.041
(0.090)
0.832
(0.057)
0.940
(0.044)
1.041
(0.092)
0.907
(0.051)
1.103
(0.043)
1.218
(0.093)
1.076
(0.052)
1.149
(0.042)
1.193
(0.089)
1.148
(0.050)
1.106
(0.044)
1.063
(0.094)
1.099
(0.052)
1.252
(0.042)
1.327
(0.088)
1.225
(0.051)
1.237
(0.048)
1.358
(0.091)
1.191
(0.054)
1.244
(0.044)
1.219
(0.094)
1.256
(0.060)
parameters on quartic on age
0.172
(0.009)
0.101
(0.011)
0.181
(0.012)
-6.33E-03 (4.10E-04)
-3.64E-03 (4.48E-04)
-6.22E-03 (4.92E-04)
-1.54E-05 (2.32E-06)
-5.81E-08 (2.90E-07)
1.35E-06 (5.18E-07)
1.02E-06 (1.95E-07)
3.95E-07 (1.78E-07)
8.41E-07 (1.81E-07)
2.54E-07 (1.65E-08)
1.70E-07 (1.94E-08)
2.45E-07 (1.98E-08)

Table 5: Implied Attenuation Factors for 1943/44, 1953/54 Cohorts
starting starting
year
age
1983
40
1984
41
1985
42
1986
43
1987
44
1988
45
1989
46
1990
47
1991
48
1992
49
1993
50
1994
51
1995
52
1996
53
1997
54

1
0.40
0.49
0.54
0.58
0.62
0.63
0.66
0.64
0.60
0.54
0.50
0.48
0.42
0.39
0.36

2
0.47
0.55
0.60
0.64
0.67
0.69
0.69
0.66
0.62
0.57
0.53
0.50
0.41
0.38

3
0.53
0.60
0.65
0.68
0.71
0.71
0.71
0.67
0.63
0.59
0.55
0.51
0.47

4
0.59
0.65
0.69
0.72
0.73
0.73
0.71
0.68
0.64
0.60
0.56
0.52

1943/44 Cohort, Average earnings over…years
5
6
7
8
9
10
0.63
0.68
0.71
0.74
0.76
0.77
0.69
0.72
0.75
0.77
0.78
0.79
0.72
0.75
0.76
0.78
0.78
0.79
0.74
0.76
0.77
0.77
0.78
0.78
0.75
0.75
0.76
0.76
0.76
0.76
0.74
0.74
0.74
0.74
0.74
0.74
0.71
0.72
0.72
0.72
0.71
0.68
0.68
0.68
0.68
0.64
0.65
0.65
0.60
0.61
0.57

1953/54 Cohort, Average earnings over…years
1983
30
0.38
0.44
0.49
0.53
0.57
0.61
0.64
0.67
0.70
0.72
1984
31
0.42
0.47
0.52
0.56
0.60
0.64
0.67
0.69
0.71
0.73
1985
32
0.44
0.50
0.55
0.59
0.63
0.66
0.69
0.71
0.72
0.74
1986
33
0.47
0.53
0.58
0.62
0.65
0.68
0.70
0.72
0.73
0.74
1987
34
0.52
0.57
0.61
0.65
0.67
0.69
0.71
0.72
0.73
0.74
1988
35
0.53
0.59
0.63
0.66
0.68
0.69
0.71
0.72
0.73
0.73
1989
36
0.58
0.62
0.65
0.66
0.68
0.69
0.70
0.71
0.72
1990
37
0.58
0.62
0.63
0.65
0.66
0.67
0.69
0.69
1991
38
0.57
0.59
0.61
0.63
0.64
0.66
0.67
1992
39
0.53
0.56
0.59
0.61
0.63
0.64
1993
40
0.50
0.55
0.58
0.60
0.62
1994
41
0.51
0.54
0.57
0.59
1995
42
0.48
0.48
0.55
1996
43
0.47
0.48
1997
44
0.47
Note: Attenuation factors are calculated according to formula shown in equation 15

11
0.79
0.81
0.80
0.79
0.77

12
0.79
0.80
0.79
0.77

13
0.80
0.80
0.79

14
0.80
0.80

15
0.80

0.73
0.76
0.76
0.76
0.76

0.75
0.76
0.76
0.76

0.76
0.77
0.77

0.77
0.77

0.78

Table A1: The Variance-Covariance Matrix of Log Earnings Residuals for the Full sample

1983

1983
0.556

1984
0.705

1985
0.616

1986
0.563

1987
0.528

1988
0.505

1989
0.497

1990
0.475

1991
0.461

1992
0.424

1993
0.404

1994
0.396

1995
0.375

1996
0.365

1997
0.343

1984

0.361

0.472

0.750

0.638

0.588

0.559

0.551

0.522

0.505

0.460

0.447

0.441

0.420

0.408

0.384

1985

0.302

0.339

0.433

0.764

0.661

0.619

0.600

0.575

0.556

0.510

0.484

0.484

0.449

0.436

0.409

1986

0.279

0.292

0.334

0.442

0.770

0.669

0.651

0.614

0.578

0.528

0.509

0.507

0.474

0.455

0.423

1987

0.257

0.264

0.284

0.335

0.427

0.770

0.704

0.652

0.612

0.556

0.534

0.534

0.497

0.481

0.454

1988

0.229

0.234

0.248

0.271

0.306

0.370

0.791

0.703

0.647

0.587

0.561

0.558

0.525

0.502

0.471

1989

0.225

0.230

0.240

0.263

0.280

0.293

0.370

0.792

0.705

0.640

0.609

0.604

0.560

0.533

0.501

1990

0.223

0.225

0.238

0.257

0.268

0.269

0.303

0.396

0.789

0.678

0.645

0.634

0.586

0.555

0.517

1991

0.226

0.227

0.240

0.252

0.262

0.258

0.281

0.326

0.430

0.765

0.683

0.657

0.614

0.580

0.542

1992

0.221

0.220

0.234

0.245

0.254

0.249

0.272

0.298

0.351

0.488

0.771

0.692

0.633

0.582

0.543

1993

0.212

0.216

0.224

0.238

0.246

0.240

0.261

0.286

0.316

0.379

0.496

0.796

0.706

0.638

0.587

1994

0.199

0.204

0.215

0.227

0.235

0.229

0.247

0.269

0.291

0.326

0.378

0.455

0.815

0.719

0.661

1995

0.194

0.200

0.205

0.219

0.225

0.221

0.236

0.256

0.280

0.306

0.345

0.381

0.481

0.816

0.722

1996

0.195

0.200

0.205

0.216

0.225

0.218

0.232

0.250

0.272

0.290

0.321

0.347

0.405

0.511

0.820

1997

0.193

0.199

0.203

0.213

0.224

0.217

0.230

0.246

0.269

0.286

0.312

0.337

0.378

0.443

0.571

Note: Autocorrelations are presented above the diagonal

Figure 1: Lifecycle Pattern of Transitory Variance
0.30

0.25

0.20

0.15

0.10

0.05

0.00
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
Age

Figure 2: Permanent Component Share of Earnings Variance, 40 Year Olds
0.7

0.65

0.6

0.55

0.5

0.45

0.4

0.35

0.3
1984

1985

1986

1987

1988

1989

1990
high school

1991

1992
college

1993

1994

1995

1996

1997