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http://www.archive.org/details/risingwageinequaOOauto
^^l/Vfy
HB31
.M415
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
WAGE
INEQUALITY: THE ROLE OF
COMPOSITION AND PRICES
RISING
David Autor
Lawrence F. Katz
Melissa S. Kearney
Working Paper 05-22
August 18,2005
Room
E52-251
50 Memorial Drive
Cambridge,
MA 021 42
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://ssrn.com/abstract=803925
SEP
2 8 2005
LIBRARIES
Rising Wage Inequality:
The Role of Composition and Prices*
David H. Autor
MIT and NBER
Lawrence F. Katz
Harvard University and NBER
Melissa
The Brookings
S.
Kearney
and
Institution
NBER
August 2005
Revised from December 2004
Abstract
During the early 1980s, earnings inequality
in the
U.S. labor market rose relatively uniformly
throughout the wage distribution. But this uniformity gave
way
to a significant divergence
and lower tail (50/10) inequality
(1987 to 2003). This paper applies and
extends a quantile decomposition technique proposed by Machado and Mata (2005) to evaluate
the role of changing labor force composition (in terms of education and experience) and changing
starting in 1987, with upper-tail (90/50) inequality rising steadily
either flattening or
compressing
for the next 16 years
labor market prices to the expansion and subsequent divergence of upper- and lower-tail
We show that the extended Machado-Mata quantile
decomposition corrects shortcomings of the original Juhn-Murphy-Pierce (1993) full distribution
accounting method and nests the kernel reweighting approach proposed by DiNardo, Fortin and
inequality over the last three decades
Lemieux (1996). Our
analysis reveals that shifts in labor force composition have positively
impacted earnings inequality during the 1990s. But these compositional shifts have primarily
operated on the lower half of the earnings distribution by muting a contemporaneous,
countervailing lower-tail price compression.
The steady
rise
of upper
tail
inequality since the late
1970s appears almost entirely explained by ongoing between-group price changes (particularly
increasing
We
wage
differentials
by education) and residual price changes.
Chemozhukov. Paul Devereux, Francis Kramarz, Justin McCrary,
comments aiid to Michael Anderson and Tal Gross for excellent
Autor acknowledges generous support from the National Science Foundation (CAREER SES-
are particularly grateful to Josh Angrist, Victor
Thomas Lemieux and Derek Neal
research assistance.
0239538) and
for valuable
the Sloan Foundation.
Katz acknowledges financial support from the Spencer Foundation.
Introduction
During the early 1980s, earnings inequality
in the
U.S. labor market rose relatively uniformly
throughout the wage distribution. Between 1979 and 1987, the male 90/50 log hourly earnings
ratio rose
by
8.5 log points and the 50/10 earnings ratio rose by 13.0 log points (see Figure
This simultaneous expansion of upper and lower- tail inequality gave
way
1).
to a significant
divergence thereafter. During each of the two subsequent 8 year intervals, 1987 to 1995 and 1995
to 2003,
90/50 inequality rose by an additional 5.2 and 9.7 log points respectively, while 50/10
inequality contracted to levels roughly comparable to 1979.
In fact, fully
increase in male 90-10 earnings inequality between 1979 and 2003
the 90-50
wage
gap. Residual inequality
- that
is,
wage
is
90 percent of the net
accounted for by the
rise in
dispersion within demographic and skill
groups defined by sex, education, and experience (age) - followed a roughly similar pattern,
rising both
(Figure 2).'
above and below the median between 1979 and 1987, and then diverging thereafter
As discussed
in
Autor, Katz and Kearney (2005), this divergence in inequality trends
presents a puzzle for canonical explanations for rising
falling real
(often
minimum wages,
viewed as driven by
wage
inequality.^
declining unionization, and monotonicaliy rising
Skill
we
demand
for 'skill'
Biased Technical Change 'SBTC') do not generally predict
steadily increasing upper-tail inequality paired with fluctuating lower
In this paper,
Hypotheses such as
tail
inequality.
explore one potential explanation for the disparate patterns of upper and
These figures describe hourly wages for all male wage and salary workers from the merged monthly Outgoing
Group (ORG) files of the Current Population Survey (CPS) for years 1979 to 2003. Similar calculations
Rotation
performed using the March CPS reveal comparable results (also shown in Figure ). Appendix Table 1 demonstrates
qualitatively similar patterns for full-time workers in March and ORG samples. Details of all samples and calculations
are found in the Data Appendix.
1
The overall rise in the variance of male log hourly wages in the May/ORG CPS was 7.3 log points between 1979 and
1988 and 2.3 log points between 1988 and 2003, Estimated using a flexible Mincerian wage regression (see equation
(1 )). the residual component of this rise was 2.8 log points between 1979 and 1988 and 0.2 log points between 1988
^
and 2003. The very modest rise in inequality in the May/ORG CPS after 1988 is at odds with the March CPS data,
which show an overall rise of log wage inequality of 6.1 log points between 1979 and 1988 and 6.1 log points between
1988 and 2003. The contribution of the residual to this rise is also substantial in both periods: 3.1 log points between
1979 and 1988 and 3.2 log points beUveen 1988 and 2003. In section V, we analyze the discrepancies between the
May/ORG and March data. All analyses in the paper are performed using both samples.
''
The differences
in the
growth of the 90-50 and 50-10 wage differentials have previously been emphasized by Mishel,
Bernstein and Boushey (2002).
lower-tail inequality observed in the last
two decades: the changing age and educational
composition of the U.S. labor force. As shown
in
Figure
3, the
education and experience of the
U.S. labor force rose substantially over the last 25 years as the large 1970s college cohorts
reached mid-career during the 1990s. The full-time equivalent employment share of male workers
with a college degree rose from 18 to 32 percent of the U.S. male labor force between 1973 and
2003 and the employment share of workers with high school or lower education
41 percent. Gains in potential experience were similarly pronounced: the
mean
fell
from 62
to
potential
experience of males of high school or greater education rose by 2 to 5 years between 1973 and
2003, with the largest gains experienced by the most educated groups.'' Increases
potential experience
These large
among female workers were
behavior of upper and lower
tail
inequality.
As
to contribute to the divergent
highlighted in an insightful paper by
Lemieux (2005), the canonical Mincer (1974) earnings model implies
may
education and
similarly large.
composition have the potential
shifts in labor force
in
Thomas
that earnings trajectories
tend to fan out (become more dispersed) as workers gain labor market experience (see also
Heckman, Lochner and Todd 2003). And hourly wage dispersion
graduates than for less-educated workers. Consequently, changes
or experience of the labor force
may
give rise to changes
in
is
typically higher for college
in the distribution
of education
earnings dispersion. These
compositional effects are distinct from the standard price effects that are often invoked to explain
fluctuations in earnings inequality. Holding market prices constant, changes in labor force
composition can mechanically raise or lower residual earnings dispersion simply by changing the
employment share of worker groups
in
have more or
less dispersed earnings. Similar!},',
changes
workforce composition can also raise or lower overall earnings dispersion by increasing or
reducing heterogeneity
Juhn,
*
that
Murphy and
The average
in
observed
tlie
(education and experience), a point emphasized by
Pierce (1993). These observations suggest that measured earnings dispersion
potential experience
decline reflects
skills
of male high school dropouts actually fell by 2.6 yeai^ during 1973 to 2003. This
in the "dropout" group as adult educational attainment has
increased share of employed teenagers
risen (as our sample covers ages 16 to 64 years).
An
influx
of younger,
less
educated immigrants has also contributed.
may change due
to the
mechanical impact of composition without any underlying change
market prices.^
-
Building on this observation, Lemieux (2005) argues that the bulk of the growth
wage
- and
dispersion in the U.S. between 1973 and 2003
explained by mechanical effects of changes
in
Lemieux concludes
these compositional effects,
inequality in the U.S. labor market
—
is
of the growth
al]
after
workforce composition rather than
residual inequality within defined skill groups (what
1980s
in
we
call price effects).
in residual
1988 -
is
shifts in
After adjusting for
that the widely discussed rise in residual earnings
primarily attributable to institutional factors during the
in particular, the declining real
minimum wage - and
to the
mechanical effect of
composition during the 1990s.
In this paper,
we
consider the Lemieux composition hypothesis in an analysis of the divergent
trends in the upper and lower tails of the aggregate and residual
Our work
three decades.
First, in
differs
from Lemieux's analysis
keeping with our focus on trends
in
in
distribution.
Second,
we
in
wage
distributions over the last
two key substantive dimensions.
upper and lower
analyze the contribution of composition to changes
median of the
in
wage
tail
inequality,
we
separately
inequality above and
below the
assess the contribution of compositional shifts to changes
both overall and residual inequality since composition
may impact wage
dispersion through
either channel.
To perform
the analysis,
we
by Machado and Mata (2005).
'
*
apply and extend a quantile decomposition technique proposed
This decomposition uses quantile regressions to partition the
Labor force composition will also affect wage dispersion though general equilibrium effects of quantities on prices.
focus here on the partial equilibrium effects and discuss general equilibrium considerations later in the paper.
We
^
By
Murphy, and Pierce (1993) find that the contribution of labor force composition to overall male
weekly earnings inequality growth over 1964 to 1988 is negligible. They do not consider- and their
contrast. Juhn,
full-time
decomposition method does not readily admit -an effect of composition on residual inequality.
'
This contrasts to Lemieux's focus on the overall dispersion of wage residuals, measured by the variance or the 90/10
ratio
'
of log wage residuals.
We
also discuss results for these
The simple extension of the Machado-Mata method
independently developed by Melly (forthcoming),
growth over 1973 dirough 1989. Because
the
measures below.
to residual inequality
who
proposed and implemented here
applies this tool to analyzing sources of US
Melly analysis only extends
to
wage
is
inequality
1989 and does not distinguish between
observed distribution of earnings into 'price' components (wage coefficients) and 'quantity'
components (labor force composition) and
changes
wage
in overall
dispersion.
We
calculate, through simulation, the impact
implement
this
of each on
decomposition using representative
earnings data from the Current Population Survey (CPS). Samples include hourly earnings data
from the
May CPS
and Outgoing Rotation Groups (May /ORG)
for
weekly earnings data from the March CPS Annual Earnings Files
1973 to 2003 and hourly and
1976 to 2004 (earnings
for
years 1975 to 2003).
The Machado-Mata method
for calculating counterfactual densities
kernel reweighting approach proposed by DiNardo, Fortin and
and extended by Lemieux (2002, 2005).
attractive. First,
it
It
Murphy and
analyzing inequality introduced by Juhn,
kernel reweighting proposed by
Lemieux (1996; 'DFL'
has two features that
provides a precise link between the
'full
we
believe
'
JMP'
DFL. As we show below, both can be
(as
we do
inequality and residual inequality.
wage
counterfactual
it
particularly
hereafter) and the
interpreted as applications
to the analysis
distributions rather than (exclusively) conditional means. Second, the
can be readily extended
make
hereafter)
variance accounting' technique for
Pierce (1993;
of the canonical Oaxaca-Blinder decomposition, extended
closely related to the
is
of conditional
fiill
Machado-Mata approach
here) to provide a uniform, consistent treatment of both overall
By comparison,
alternative approaches for analyzing
distributions apply a hybridized set of methods
and conceptual models (OLS
regressions, parametric probability models, and kernel reweighting) to separately develop
counterfactuals for overall and residual inequality.
Our main
results are as follows.
We
find that
changes
in
labor force composition do not
contribute to an explanation for the diverging path of upper and lower
aggregate or residual)
First,
we show
trends
in
in the past
that the
upper and lower-tail inequality,
inequality (either
two decades. The composition hypothesis
impact of changes
(though similar to Lemieux 2005).
tail
its
in
labor force composition on
fails for
wage
two reasons.
dispersion occurs
substantive conclusions are almost entirely different from tliose here
almost entirely below the median of the earnings distribution
sample period This
in turn
1980s and 1990s
due
Second,
in the
is
we show
changing labor market prices not mechanical effects of composition.
to
is
,
slightly
by
tail
shifts in
of rising and then stagnating or falling lower
made more puzzling by adjustments
actually
the 1980s, increasing lower
augmented
On
net,
inequality
During
for composition.
composition. In the 1990s, by contrast, changing market prices
by compositional
inequality to increase).
tail
inequality appears explained by changing labor market prices,
generated considerable compression in lower
substantial part offset
the lower tail) during the
implies that the steady growth of upper-tail inequality during the
that the puzzle
1980s and 1990s
(i.e., in
we
shifts
tail
inequality, but these price effects
were
in
(which would otherwise have caused lower
tail
find that changes in the education and experience composition
of the labor force plays only a secondary
role in the evolution
of overall and residual inequality
since the early 1970s; the persistent rise of upper-tail inequality and the rise and then stagnation
of lower-tail inequality are both primarily accounted for by changing labor market prices.
These results lead us to
differ
from the interpretations offered by Lemieux (2005). Lemieux's
conclusion that the rising education and experience of the labor force can mechanically explain
the plateauing of residual inequality during the 1990s appears to aggregate over
countervailing forces. The
due
to
first is
compressing residual
rise in upper-tail inequality,
two
the contraction in lower-tail inequality in the 1990s,
'prices' partially offset
which
by changing composition. The second
which appears entirely explained by
price changes.
composition over-explains the former phenomenon and under-explains the
is
is
the
Because
latter,
it is
technically
accurate to say that composition can "fully explain" the aggregate trend in residual inequality
during the 1990s. But
when upper and
lower-tail inequality are considered separately
appropriate given their substantial divergence
explanation for either.
and lower
tail
We
- composition does
-
as
seems
not appear a satisfying
discuss possible alternative explanations for the divergence of upper
inequality in the conclusion (also see Autor, Katz and Kearney 2005).
In the next section,
we summarize
trends in U.S. overall and residual earnings inequality for
1973 to 2003. In section
counterfactua!
wage
II,
we develop
distributions
distributions. Sections
III
the
Machado and Mata methodology
and discuss our extension
A.
March and May/ORG CPS
Data sources and basic trends
I.
it
for analysis
and IV present our decomposition of trends
inequality into price and quantity components. Section
inequality trends between
to
V
in
for
forming
of residual wage
aggregate and residual
analyzes discrepancies
in residual
data sources. Section VI concludes.
in overall
and residual inequality
March and May/ORG Current Population Survey data
Our analysis draws on two data sources
CPS and
the
for
measuring trends
been widely used
in studies
year's annual earnings,
to
inequality: the
March
Data Appendix. The March
weeks worked, and hours worked per week.
salary workers.
CPS
data have
of wage inequality and provide reasonably comparable data on prior
2004, covering earnings from 1975
wage and
wage
combined CPS May and Outgoing Rotation Group. These sources are described
briefly here, with additional details provided in the
1976
in
Hourly earnings
to
We use the March CPS of
2003, to form a sample of real log hourly wages of
in the
March data
are calculated as the ratio of prior
year's annual earnings to prior year's annual hours.
We
complement
the
March
series using the
Outgoing Rotation Group samples
wage
data for
all
wage and
for
May CPS
for
1973 through 1978 and
1979 through 2003 (CPS
salary workers
May/ORG) to
in the
March CPS,
provide point-in-time measures of usual hourly or weekly earnings.
We
the
May/ORG
data
weight both March and
data by hours worked to provide a measure of the entire distribution of hours paid.'"
Both March and
period studied.
'
construct hourly
employed during the CPS sample survey reference
week. Unlike the retrospective annual earnings data
May/ORG
CPS
As
May/ORG CPS
surveys have features that limit their consistency over the
price and earnings levels have changed, each survey has applied successive
Prior to the 1976 survey, usual hours
worked per week
in
the earnings year are not available.
The March data are weighted by the product of weeks worked and hours per week in the prior \ ear. The May/ORG
data are weighted by hours worked during tlie survey reference week. Weighting by weeks is implicit in the May/ORG
sample since the probability that an individual is obser\'ed working during tlie sample reference week is proportional to
'"
weeks
in the labor force.
increases to the
maximum top-coded
issue for our analysis since
A potentially
more
earnings values. These changes probably present a minor
we focus on
significant issue
earnings quantiles between the lO"' and 90"' percentiles."
is
posed by the redesign of the
CPS
ORG
survey
1994.
in
This redesign changed the format of most survey questions, centralized the interviewing process
and introduced the use of Computer Assisted Personal Interviewing (CAPI). Perhaps most
important, the 1994 redesign revised the procedure used to collect earnings and hours information
with the goal of increasing the accuracy of earnings reports and reducing the undercount of
workers with part-time schedules (Polivka and Rothgreb 1993; Cohany, Polivka and Rothgreb
1994). Prior to 1994,
CPS May /ORG
earnings to the survey taker.
respondents directly reported their usual weekly and hourly
Commencing with
the 1994 redesign, respondents
were allowed
select a preferred pay frequency for earnings reporting (hourly, weekly, biweekly, monthly)
to report the corresponding earnings
of the revised procedure on the
(see Polivka 2000), but
seems plausible
its
that the
effect
and
amount. Using the respondent's self-reported usual hours,
the surveyor calculates an implied hourly
effect
to
wage and
level
verifies the figure with the respondent.'"
The
of reported hourly wages has received careful study
on the precision of earnings
reports has not
been explored.
enhanced procedure raised the precision of earnings reports
It
(as designed)
and so may have reduced measured earnings dispersion.
Adding
('flag')
to the uncertainty
surrounding the
imputed earnings observations
in the first
January 1994 to August 1995. Consequently,
observations, although
May/ORG
the
we exclude imputed
we
redesign, the
CPS
ORG
did not identify
21 months following the survey redesign of
are unable to exclude these
earnings observations from
all
imputed
other
March and
samples. Earnings imputations are potentially a non-trivial issue: the imputation rate
CPS ORG
One
CPS
rose substantially after the redesign, from 15.3 percent in 1993 to 23.3 percent in
topcoded value for secondary wage and salary earnings in the March CPS fell
to $37K in 2004). This does not appear a major issue since fewer than 1
percent of workers have top-coded secondary wage/salary earnings at the lower topcode value.
unfortunate exception
from $99K
'"
to
S25K
For respondents
in
who
is
that the
1996 (before rising
report that they are paid hourly, the self-reported
calculations, regardless of the preferred reporting interval.
wage
is
always used without
fijrther
in
the last quarter of 1995 (the
rise thereafter,
reaching 3
first
quarter in which allocation flags are available) and continued to
percent by 2001 (Hirsch and Schumacher 2004). Since the redesign
1
coincides with a sizable and sustained rise
in the identification
the earnings iinputation rate and a 21
in
of imputed observations,
particularly difficult to
it is
gauge
how
the survey affected the comparability of the earnings series before and after 1994.
A
final issue affecting the
consistency of the earnings reports
composition of pay reporting seen
in
the
May/ORG
samples.
is
month
hiatus
changes to
'''
a secular change in the
As documented by Hamermesh
(2002), the share of workers
who
forward, and this increase
found within education and experience groups (Lemieux 2005). This
is
report being paid by the hour increased substantially from 1973
May/ORG CPS
matters for inequality measurement because direct hourly earnings reports in the
appear to have greater precision than non-hourly wage reports
earnings to hours). Rising hourly pay reporting
residual variation in the
May/ORG
may
inequality series.
earnings measure (total annual earnings) for
all
tend to
(i.e.,
mask any underlying
The March survey uses an
hourly workers
March CPS
in
the
in
to overstate the
growth
in
essential trade-off between the
is
March-May/ORG samples
greater for hourly than for non-
wage
inequality in a period of an
further explore these issues in Section V.
March and May/ORG wage data
is
one of temporal
consistency versus point-in-time precision. The data collection procedures in the
more
major
'^
stable since the mid-1970s,
CPS
ORG
due
to the shift
Earnings imputations are not an issue confined to
1
1.8
percent
in
calendar year
1
tlie
percent
sizable and discontinuous than the increase in the
1
from
May
to
monthly
ORG
March
samples
data are
in 1979, the
redesign in 1994, and the changing frequency of hourly pay reporting. But. as
sample rose during the same period from
of 1995 (and 22.
identical
implies the rise in hourly pay reporting could lead the
residual (hourly)
We
increased share of hourly workers.
The
computed hourly wages
March sample. This
('true') rise in
respondents regardless of the pay period.
Nevertheless, Lemieux (2005) presents evidence using matched
suggesting that measurement error
those calculated as the ratio of
996).
May/ORG CPS. The
in
1993
to 13.5
earnings iinputation rate in the
percent
CPS May/ORG from
in
March
1996, This increase appears less
15.3 in 1993 to 23.3 percent in the last quarter
stressed
by Lemieux (2005), the May/ORG,
measure
at
each point
in
time.
We
is
likely to provide a
May/ORG
use both March and
more precise hourly earnings
series throughout
and compare
the sensitivity of our results to the choice of sample.
B.
Trends in overall inequality
Table
1
presents several
1973 to 2003 from the
summary measures of trends
CPS March and May/ORG
in
hourly earnings inequality for years
samples (plotted
Figure
in
Overall male
I).
hourly 90/10 earnings inequality rose by 30.2 log points between 1973 and 2003
May/ORG. Twenty-one
9.1 log points
this period.
in the
CPS
log points of this rise occurred between 1973 and 1988 and an additional
between 1988 and 2003. Earnings inequality did not grow uniformly throughout
Between 1973 and 1988,
the growth in upper and lower-tail inequality
approximately symmetric above and below the median; after 1988,
May/ORG
the upper-tail. In fact, the
inequality between
data
show a 4.7
it
was
.
of the overall expansion of the male 90/10 log earnings
Subsequent rows of Table
earnings samples from the
1
confinn
entirely concentrated in
log point compression in lower-tail
988 and 2003 Rising upper- tail inequality accounts
1
for over three-quarters
between 1973 and 2003.
ratio
that these patterns are also evident for
March CPS. As
is
was
the case with the
CPS May/ORG,
male hourly
lower-tail
inequality rises sharply from 1979 to 1988 then halts or reverses thereafter. Upper-tail inequality
grows steadily throughout, ultimately accounting
growth from 1975
tail
to
2003.
inequality appears far
Figure
1).
Whereas
indicate almost no
the
One discrepancy between
more pronounced
May/ORG
data
The
in
show
the
the data series
May/ORG
lower-tail
rise in
inequality
is
in
that the plateau
of lower-
after 1988, the
March
an important issue to which
May/ORG
versus
March
is
somewhat
data
we
sainples.
also evident for females (lower panel
female 50/10 earnings inequality
however, and roughly half of the overall growth
is
in the
is
than March samples (see also
compression
where we consider potential biases
The asymmetric growth of earnings
1).
over three-quarters of total male inequality
movement between 1988 and 2003. This
return in Section V,
Table
for
of
larger than for males,
female inequality occurs
in
the lower
tail
As
(relative to two-thirds for males).
compression of lower
Whereas female
March
March hourly data show
inequality for females after 1988 than
series indicates a continued rise
May/ORG
do the CPS
lower-tail inequality ceased rising after 1988 in the
much slower pace
C.
tail
the case for males, the
is
CPS May/ORG
less
data.
data, the
of lower-tail inequality during the 1990s, though
at a
than during 1975 to 1988.
Trends in residual inequality
To measure
trends in residual earnings inequality,
we
fit
the following earnings
model
separately by sample, year and gender:
In w,
(1
=a
In this equation,
-(-
vv,
5,
is
X,
-I-
+ (5, xxj + e^.
the log hourly or
weekly wage of individual
/,
is
5,
a vector of five
schooling completion categories corresponding to less than high school, high school graduate,
some
college, bachelor's degree,
and post-college schooling,
experience categories ranging from
The inclusion of a complete
set
to
38 years
in
their
hourly data,
pay on an hourly
we
of interaction terms
also include a
basis, as well as a set
schooling dummies. Changes
measured residual
affect
partial
adjustment for
in the
( 5,
'^
In a
wage
x
'''
x, )
is
an error term.
equation (1)
to the
is fit
variable equal to one for workers
of interactions between
this
pay control
dummy
in the
in
and the
May/ORG CPS may
equation (1) pennits
inequality increased sharply in the 1980s for
in
men and women
regardless of
equation (1) with a more conventional
interaction temis are replaced with a quartic in
potential experience interacted with four education groups (high school dropout, high school graduate,
components
The
report
and Figure 2 display the residual wage inequality series by
which the 65 education-by-potential-experience
college or greater).
who
subsequent variance decomposition.
subsequent section, we re-estimate the residual inequality model
specification in
e,
schooling and experience
frequency of hourly pay reporting
this factor in the
1
among
When
inequality. Inclusion of the hourly
The right-hand panel of Table
sex. Residual
dummy
a vector of thirteen potential
3-year increments, and
categories allows for a very flexible earnings equation.
May/ORG
is
.t,
results for trends in residual inequality
and
its
decomposition into
"price"
some
college,
and 'quantity'
are essentially identical.
10
the
wage measures
March CPS
in the
or sample used. Residual
shows
but
little
change
wage
in the
inequality began rising in the 1970s for males
1970s for males
Consistent with the trends for overall inequality, trends
parallel in the
upper and lower
rose sharply prior to
1
tails
988 and slowed or declined
series, there
is
in residual
thereafter.
in the
Upper
move
tail
in
inequality
inequality rose steadily
tail
a parallel rise in upper-tail inequality from the
CPS
In the
mid-1970s forward. This
upward trend
its
CPS.'^
inequality did not
March CPS samples.
over 1994 to 1999 and then resumes
rise plateaus or reverses
May/ORG
of the earnings distribution. Residual lower
from the mid-1970s forward for males and females
May/ORG
in the
in
1999 to 2003.
Tables 2 and 3 present the evolution of earnings inequality within narrow gender, education
and experience groups.
high school degrees
We tabulate inequality metrics
at potential
for those with exactly college
and exactly
experience levels of 5, 10, 15 and 25 years. Because these groups
are (a subset of) the gender-education-experience categories directly controlled (with
in
dummies)
our 'residualizing' specification above, inequality within these cells corresponds precisely to
We
the residual inequality construct used throughout our analysis. '^
period of 1975 to 2003
when both
data series are available.
We
point to enhance precision (hence comparisons are centered on
Tables 2 and 3 reveal that the trends
shown
in
example,
Table
in
1
in
limit the
comparison
pool three years of data
1
976,
1
each
988 and 2002).
aggregate lower and upper-tail res idual inequality
are robustly visible within detailed gender-experience-education cells.
CPS May/ORG and March
at
to the
series, upper-tail inequality rises
markedly
For
for both
genders and within most education and experience groups during both halves of the sample (the
one exception being female high school graduates).
The data also confirm noticeable compression
(or plateauing) of lower- tail inequality within
detailed gender, education and experience groups. This compression
'"^
Our
inability to
remove
allocated observations from the
likely accounts for the visible
Standard errors
upward jump
in these tables are
in residual
May/ORG
in
much more pronounced
January 1994 through August 1995
inequality in 1994 followed by a
downward jump
bootstrapped using 100 sample-weighted replications for each
Tables 2a and 2b present the levels (rather than the changes)
e.xperience cells and
sample
is
shows higher wage dispersion
for
in these inequality
in
statistic.
1996.
Appendi.x
measures for narrow gender-education-
more experienced and educated groups.
11
among
less-educated workers; in fact, the 50/10 earnings ratio
widened
in the latter half
among
of the sample, though less rapidly than
in the earlier
These detailed comparisons underscore several substantive points
because the
education
rise in upper-tail residual inequality is
cells,
it
for our analysis. First,
evident within detailed gender-experience-
this rise
is
not likely to be a survey design artifact since
data sources. Third, the fact that the compression of lower-tail inequality
among high
for our
decade.
cannot be ascribed exclusively (or even primarily) to changing labor force
composition. Second,
all
college males and females
is
it
is
confirmed by
concentrated
school graduates and high school dropouts (not shown) has an important implication
subsequent decomposition exercise: the roles attributed
depend sensitively on the weight given
to less educated
to prices
and quantities will
and experienced groups (which
experienced more compression) versus more educated and experienced groups (which
experienced more expansion). This observation
is
especially important because, as above, the
experience and education of the U.S. labor force rose substantially after 1980. Consequently,
demographic groups
increasingly
uncommon
greater expansion.
II.
that experienced the
as the
most residual compression
after
1980 become
sample progresses, and vice-versa for groups
We explore these points
in
that experienced
our decomposition.
Labor force composition and wage inequality: A quantile
decomposition
To
evaluate the contributions of changing labor market prices and quantities to the shifts
overall and residual inequality
documented
in
Tables
1
through
3,
decomposition technique proposed by Machado and Mata (2005,
we apply and extend
'MM'
hereafter).
The
in
a quantile
MM
technique uses quantile regressions to partition the observed distribution of earnings into "price"
components (wage
coefficients)
and "quantity' components (labor force composition) and
calculate, through simulation, the impact of each on changes in aggregate
A.
wage
dispersion.
Theory
Let Qg{w\x) for 6*6(0,1) denote the
0'''
quantile of the distribution of the log
wage
(ir)
12
We model these conditional quantiles as
given the vector x of covariates.
0,(w\x) =
(2)
where x
(QR)
is
x'/3(d),
a k-<\ vector of covariates
coefficients.
e
For given
(0, 1)
and
/?(i9) is
a conformable vector of quantile regression
/3{0) can be estimated by
,
minimizing
in /^
n
;7-';^/7,(w, -x;/?) with
(3)
i=i
'
where the
for
!/
[(d-\)u
for
M<0
expression
latter
>
idii
is
referred to as the 'check function' (see
Koenker and Bassett 1978,
Buchinsky 1994, Koenker and Hallock 2001, and Angrist, Chemozhukov and Femandez-Val
forthcoming).
As discussed by Machado and Mata,
quantile process
-
that
is,
Qgiw\x)
if equation (2) is
conectly specified, the conditional
as a function of 6'e(0,l)
the conditional distribution of wages given
x
.
- provides a
In this case, realizations of
full
m',
characterization of
given
x^
viewed as independent draws from the function x\P{6) where the random variable
uniformly distributed on the open interval (0,1)
in a
.
The conditional quantile model
is
will hold exactly
case where both location and scale depend linearly on the covariates (for example
classical location shift
model
cases, the conditional quantile
w = x' p + s
where ^
model may provide
is
a normal, iid error tenn). In
a reasonable
approximation
can be
in
the
more general
to the true
conditional quantile, and this approximation can generally be improved by specifying flexible
functions of x
quantile
model
Having
fit
when
estimating P{6)
to the
observed data
is
.
We show
below
that, in
our application, the
fit
of the
quite accurate.
the conditional quantile function, the estimated parameters can be used to simulate
the conditional distribution of
transformation: If
^
is
u'
a unifonn
given x via an application of the probabilify integral
random
variable on [0,1]
,
then F~'{U) has the density
F
.
13
Thus,
if 6^,6,, ...,0
are
drawn from a uniform
of the conditional quantiles of wages
at x,
(0,1) distribution, the
w,
,
= {^'A^,
(estimated) conditional distribution of wages given
)},''=i
corresponding j estimates
constitute a
.
random sample from
the
x,
This simulation procedure characterizes the conditional quantiles of the data for any given x
It
does not provide the marginal density of
both the conditional quantile function,
generate a
for each
m;^
=
/?( 6*)
w
,
.
This
is
because the marginal density depends upon
and the distribution of the covariates, g{x)
random sample from marginal density of w we can draw rows of data from
gi^
,
row
x,
x,/?'(^, )
'
,
draw a random
which
procedure repeatedly,
is
6^
from the uniform
(0,1) distribution.
We then
.'''
we
)
and,
form
draw from the wage density implied by the model. By applying
a
To
this
can draw an arbitrarily large random sample from the desired
distribution. This procedure
- successively drawing from g{x) and 6
to
form
w -
is
equivalent
to numerically integrating the estimated conditional quantile function ^^(m'I x) over the
distribution
of X and 6
to
form f(\v)= \\Qg{M>\x)g{x)dxd0
.^^
x,e
For the purposes of decomposition, the
conditional quantile
MM procedure has two attractive properties.
model conveniently divides
'quantity' components.'
This
is
the observed
By
contrast, the conditional quantile
this case, the
"For
'*
'"
OLS
As with
We
all
is
mean
model only characterizes
we
treat
g.i-
)
model characterizes both
througliout as
uniformly distributed on
tlie
OLS
the central
function, describing 'between-group" inequality)-
the central tendency of the data (in
median) and the dispersion of the outcome variable conditional on x,
simplicity,
Because 9
set.
the conditional
(i.e.,
distribution into 'price" and
similar to a standard Oaxaca-Blinder procedure using
regression coefficients, with the key difference that the
tendency of the data
wage
First, the
i.e.,
the
wage
known.
unit interval,
measures of 'residual' inequality,
/(d) -
this division
1
.
depends upon which .v'^are included
in tlie
conditioning
return to this point below.
14
'residuals.'
residual
This feature
wage
is
impact of composition on the shape of the
critical for estimating the
distribution.
Second, under the convenient (but economically unappealing)
that aggregate quantities
of skills
in the labor
market do not affect
partial
equilibrium assumption
skill prices,
we can
use the
conditional quantile model to simulate the impact of changing composition or prices on
distribution of wages."" In particular, by applying the labor force composition data g,
given time period
/
to the price matrix
P^{6) from any other time period r
,
we can
(,v)
from a
simulate the
counterfactual distribution of wages that would prevail if labor force composition were given as
time period
in
/
and labor market prices were given as
li,{9) matrix describes the conditional distribution
in
time period r Note that because the
.
of wages for given values of x
,
this
simulation captures the effects of composition on both between-group and residual inequality.
Although the Machado-Mata approach was not specifically developed
counterfactual measures of residual inequality,
the coefficient vector y9(50) as our
/?
= /?(50)
.
/?
y^i-,^
can be extended to
y5,„j in
conditional
is
Following
this logic,
we
is
.
In their analysis
it
as
it
In our application, the central
.
The difference between
not empirically important in our application.
define a measure of within-group inequality as the difference
between the estimated coefficient vector /][&) and the median coefficient vector
""
refer to
provides a measure of between-group inequality because
the conditional median, estimated by /]
means and medians
We define
a conventional Oaxaca-Blinder decomposition. In
estimates the central tendency of the data conditional on x
tendency measure
this application.
measure of between-group inequality, and we
serves a role akin to
the conventional application,
it
for estimating
of tlie contributions of price and quantities
to
/?*
nsing inequality during the 1980s, DiNardo, Fortin and
Leniieux (1996) perform supply and demand adjustments for obsen'ed wages by education by experience cells (in
addition to applying a kernel reweighting procedure). These supply-demand adjustments are shown by DFL to be
quantitatively important, explaining 21 to 33 percent of the growth in male 90/10 log hourly earnings inequality
between 1979 and 1988 (Tables 111 and V). This indicates that the independence assumption
supplies do not affect skill prices) is likely to be far from innocuous.
(i.e.,
that aggregate skill
15
r{9)^[m-p']ioreem).
(4)
Notice
by construction, p" (50) =
that,
.
Hence, the residual quantile coefficient matrix
w
purged of 'between-group' inequality, and measures the expected dispersion of
value of
-V
holding the conditional median
,
distribution of covariates, g(x)
,
we can
is
If,
for
example, p{0) =
the (correctly specified) conditional quantile
characterization of the distribution of
m'
as a function
covariates, g(x), the vector of between-group prices,
(residual) prices
(9
that
to the
is
then residual
,
P" We
write /(w,)
.
model provides a complete
of three components: the distribution of
/?'',
and the matrix of within-group
= fisX^XP^'k)-
Implementation and proof of concept
We
steps.
implement the augmented Machado and Mata quantile decomposition procedure
We
first
May/MORG
models
and March samples we estimate a wage model equivalent
OLS
model
fit
for the
median (quantile
'prices" for our simulation exercise. Here,
coefficients,
m
is
In the
P, ,a
the
where k
the
50.0).
P(d)
step,
we
These
a
is
in
kxm
we
.
fit
estimate
centile, with
P(d)
above,
one
provide the
matrix of quantile regression
the intercept in equation (1)) in
x
0.
calculate the residual price vector
vector of between-group prices, and P"
of a
QR coefficients,
number of elements (65 including
number of quantiles (501) estimated
second
kx\
is
to equation (1)
regressions. For each sample, year, and gender,
for quantiles [0.1, 0.3, ...,99.7, 99.9] at intervals of one-fifth
additional
in three
estimate quantile coefficient vectors for each time period and gender. Using the
using quantile rather than
and
P V
vi'
/?"
zero in this model.
To summarize,
B.
any given
applying the coefficient matrix
calculate the (estimated) dispersion of
exclusively attributable to residual inequality.
inequality
By
at zero.
at
is
P" using equation
,akx (m - 1)
(4).
This
>-ields
matrix of within-group prices.
16
In the final step,
the price matrices
Under
we draw simulated
P'^
data from the distribution /(g,(x),
/?,'',/?,")
by applying
to g,(x).^'
,13"
the maintained assumption that labor market prices and quantities can be treated as
independent, this procedure
may
be used to simulate any counterfactuai distribution of overall or
residual earnings inequality simply by pairing the quantity series from one time period with the
price series (overall and/or residual)
Before applying
this
g, (x)
we
technique to simulate counterfactuai distributions,
performance of the model
inequality.
from another.
in replicating
first
check the
observed ( actual ) distributions of overall and residual
To benchmark the model, we apply
QR
the
coefficients
/?,'',/?,"
to the quantity series,
from the contemporaneous time period to generate simulated wage distributions. The
simulated series are shown in Appendix Figure
conditional
wage
distributions, these series
between the actual
statistic
1
.
If the
QR
model were a perfect
would exactly overlap.
and the model-based simulations
is
fit
to the
In practice, the discrepancy
small enough to be almost
undetectable. Other distributional statistics for the simulated data, such as the 90/50, 50/1 0, and
variance of wages, are also extremely close to the corresponding values for the source data.
To benchmark
the performance of our simulation procedure for residual
compare simulated and
Figure
2.
The
actual 90/10 residual
series labeled
wage
wage
inequalit>',
dispersion by year and gender in
'Observed Median Reg Residual'
is
we
Appendix
formed from median regressions
of log hourly earnings on the covariates above. The series 'Simulated Median Reg Residual'
presents the corresponding statistics for the simulated series formed using
simulated residual series also
fit
the
finer
gl^
)
)
with replacement.
this
means
CPS
An
analysis by Angrist.
that our simulated data set
data (500 times larger, to be exact). Angrist, Autor and
and coarser bandwidths
verisimilitude in
gi.
finds that greater precision can be obtained simply by multiplying the endre
by the transposed P(d) coefficient matrix. In practice,
the original
and g,{^)
The
observed data quite accurately.
' Machado and Mata recommend drawing rows from
Chemozhukov (2004)
/?,"
for the quantile estimation
is
gi
many
Autor and
)
distribution
times larger than
Chemozhukov (2004) experiment with
and find that 500 quantile intervals provides excellent
samples, while finer bandwidths produces
little
marginal gain.
using
Since almost
for
all
prior residual decompositions analyze
comparison the 90/10 residual inequality
visible in
Appendix Figure
2,
OLS
OLS
regression residuals,
series for an identically specified
also plot
model. As
is
and Median Regression residuals have nearly identical
dispersion in our application, indicating that the distinction between
is
OLS
we
mean and median
regression
not substantively import for interpreting our residual decomposition results. These benchmarks
provide assurance that our approach
We next apply
this
we
able to capture relevant features of earnings distributions.
We
decomposition to the inequality data.
quantile regression version of the
Subsequently,
is
first
propose and implement a
well-known Juhn, Murphy and Pierce (1993) decomposition.
use the quantile model to implement a variant of the extended DiNardo, Fortin
and Lemieux (1996) kernel density reweighting approach. As we show below, these two
approaches are nested
in the quantile
model.
The contributions of between-group
III.
composition:
As
we implement
"JMP") decomposition.
In
a quantile analog of the well
Appendix
2,
we
write the observed distribution of wages at time
distribution of
worker
characteristics, g, (x)
,
t
fi,
in inequalit}'
components using
/
Murphy and
Pierce
decomposition.
As
before,
we
components: the
the between-group prices for those characteristics,
/?/'
(suppressing "hats" on the
and r
.
between any two periods,
t
and r can be decomposed
the following sequential decomposition. Let
AOg = Qg(f,{w)) — Og(f,{'^^'))
periods
Juhn,
vectors).
The observed change
into three
JMP
as a function of three
and the within-group prices for those characteristics,
estimated
known
provide a more thorough discussion of the
differences between our quantile approach and the canonical
/?*,
and
decomposition
a compact method of summarizing the contributions of prices and quantities to rising
earnings inequality,
(1993,
prices, residual prices,
A quantile JMP
equal the observed change in the d"
wage
quantile between
We define
18
Ao; =
(5)
a(/(.?.(^-),
as the contribution of
Ao: =
(6)
^Q: =
a ifigr i^i Pi
a ifig,
(-V),
as the marginal contribution
Notice that
This
is
this
A" ))-&,(/(§,(>••), A'- A"))
changing quantities (labor force composition)
as the marginal contribution
(7)
/?;,
^
to
AO^
.
We
define
p: ) - Qe ifisr i^\ p" ^pn
of changing between-group prices
p: p: ) .
a (/(§,
c^-).
an important advantage over the
total
.
finally define
-
to
AOy
.
observed change: AC'p + AC>* +
JMP procedure,
component' must be estimated as a remainder term
AO^ And, we
a: p: )
of changing within-group prices
decomposition sums to the
to
in
AOJ = Ag^
which the 'residual price and quantity
after the other
two components
are
calculated.^'
As
is
well known, the order of a sequential decomposition implicitly corresponds to a set of
weights reflecting which characteristics are held
components
(A()J, AC*^,
are changed, with the share of
at their start
or end period values as other
any observed change attributed to each component
AOJ) depending on which other components
decomposition above using two orderings. In the
first,
we
are varied
first
first.
A.
between-group prices and
Quantile
perform the
vary labor force characteristics,
then between-group prices and finally within-group prices. In the second,
prices, then
We
we vary within-group
finally labor force composition.
JMP i^esults
Table 4 presents results of the quantile
inequality data.
As shown
between 1973 and 1988
is
in
the upper
left
JMP
decomposition for the
CPS May/ORG
hourly
panel of the table, the rise of male earnings dispersion
almost entirely accounted for by prices rather than quantities.
Of 21.1
log points rise in male 90/10 inequality over this period, the decomposition attributes a small
offsetting roll (-1.0 log points) to quantities, versus 16.8 points to
""
The .IMP decomposition
-
that
is,
5.3
"add up" unless the conditional distribution of residuals is homoskedastic
depend on the x 's. As Tables 2 and 3 demonstrate, this assumption is amply
will not generally
residual dispersion does not
rejected by the data. See
between-group prices and
Appendix 2
for discussion.
19
When we
points to within-group prices.'^
reverse the order of the decomposition,
estimated contribution of labor force composition to inequality
is
in the rise
patterns prevail
when upper and lower
tail
B
for females also finds a
of earnings inequality. But
than for males and also more pronounced in the lower
tail
inequality are
find that the
within rounding error of zero,
with only a slightly larger role attributed to within-group prices." Panel
comparatively small role for composition
we
this role
is
larger
of the earnings distribution. Similar
decomposed
separately: composition
never explains more than a third of the growth of any 90/50 or 50/10 inequality metric during
1973 to 1988; the remainder
When we
perform
this
is
explained by prices."
decomposition for the growth of inequality between 1988 and 2003, an
important contrast with the earlier period emerges. Both prices and composition play an
economically significant role
in
explaining changes in lower-tail earnings inequality after 1988.
Male 50/10 inequality contracted by
the change in composition alone
4.8 log points during 1988 to 2003. Holding prices constant,
would have been expected
4.3 log points, reflecting, as noted
to increase
lower
tail
inequality by
by Lemieux (2005), the increasing education and experience of
the labor force. Offsetting this force,
between and within-group price changes reduced lower-tail
inequality by -1.2 and -7.9 log points respectively during the
same
interval.
On
net, the 4.8 log
points of observed lower-tail compression reflects the countervailing impacts of 'falling' prices
and an increase
in the
prevalence of characteristics associated with higher earnings dispersion.
But these discrepant forces are not responsible
^'
Small discrepancies between the tabulated changes
4 and 5 reflect simulation error, that
distribution.
make
These discrepancies
is,
instances
for trends in
in overall inequality in
where
are quite small (never
upper
Table
1
tail
inequality. In fact, the
and the changes shown
in
Tables
the quantile simulation does not perfectly capture the obser\'ed
more than
5 percent
of the observed change) and we do not
further adjustments for them.
^'
Note that when we decompose the change in inequality
subcomponents of tlie quantile decomposition do not sum
1973 to 2003 period (third panel of Tables 4). the
subcomponents of tlie decomposition for the subperiods 1973 to 1988 and 1988 to 2003. This is because the implicit decomposition weights differ between panels. In
the final panel, we apply 1973 quantities to 2003 prices and vice versa; in the prior two panels, the dates for the
quantities and prices do not differ by more than 15 years (i.e., 1973 vs. 1988 and 1988 vs. 2003).
"'
It is
common
in a sequential
decomposition
for the full
to the
for die factors that are varied first (e.g.. quantities or prices) to
credited with a larger contribution to the change in the outcome. That
is
not
tlie
case here;
in fact
be
the role of
composition appears more important when we vary
education and between-e.xperience group gaps
when we
first
vary allow these 'prices' to vary,
it third rather tlian first. The explanation seems to be that betweenwage variance became more pronounced during 1973 to 1988. Hence,
the subsequent quantity adjustments become more important.
in
20
contribution of changing labor force composition to rising upper
both males and females. The
rise
of upper-tail inequality after 1988
by rising between and within-group
prices, as
was the case
inequality
tail
is
is
negligible for
almost entirely explained
for the period
of 1973 - 1988. These
price increases are comparable in magnitude during 1973 through 1988 and 1988 through 2003
with the estimated
rise in
within-group prices for males
somewhat
is
larger in the latter period.
Table 5 presents the comparable decomposition for hourly wage inequality
data.
The conclusions
period, the
March
in
the
March CPS
are qualitatively similar to those from Table 4. In particular, in the earlier
data
show
a small role for composition (though larger for females than males)
and a predominant role for rising between and within-group prices
gro'Mh of upper and lower
inequality. Like the
tail
May/ORG
in
explaining the parallel
data, the
March
data reveal
countervailing effects of prices and quantities in the lower half of the distribution and almost no
role for quantities
(i.e.,
composition)
descriptive results in Table
distribution in the
1,
we
test,
we
upper half of the distribution. Consistent with our
find less price compression in the lower
March data than
As a robustness
in the
in the
May/ORG
tail
of the earnings
data."*^
also repeated the estimation exercise in Tables 4 and 5 using a
conventional Mincer model featuring a quartic in potential experience - replacing the 13
experience categories
in
qualitatively identical to our
Appendix Tables 3a and
that a focus only
on trends
in
wage
over 1988 to 2003 was 7.9 log points. Adjusting for changes
A
90/10 inequality (or
all
prices at their 1988 level,
we
in
variance
in the
lead to an incomplete view of the roles of prices and quantities in
periods. For example, the overall rise in male 90/10 hourly
period and holding
3b, are
main estimates.
These results demonstrate
may
dummy
our main model - interacted with four education categories. The
substantive findings of this alternative model, reported in
of log wages)
more
inequality in the
CPS May/ORG
composition during
calculate that 90/10 inequality
comparable analysis for the March full-time data (not shown) echoes these conclusions, though
is even less lower-tail compression than in either hourly sample.
some
this
time
would
in the full-time
data there
21
counterfactually have risen by 4.8 log points.
thirds
of the
rise in inequality during
One could conclude from
1988 to 2003
is
this exercise that
"explained by" compositional
This conclusion, however, ignores a substantial contemporaneous rise
prices.
Holding residual prices constant, we estimate
that rising
in
two-
shifts.
between-group
between-group prices would have
counterfactually raised 90/10 inequality by an additional 7.0 log points. Thus, between-group
What
prices could be said to "explain" 90 percent of the rise in 90/10 inequality.
claims
is
that within-group prices
compressed significantly over the same
reconciles these
interval
- reducing
90/10 inequality by 3.8 log points ("explaining" minus 48 percent of the phenomenon).
Although none of these statements
findings in Tables 4 and 5
is that:
is
factually incorrect, a
more precise statement of the
over 1988 to 1993, a
(1) upper-tail inequality rose steadily
rise
almost entirely explained by rising between and within-group prices; (2) lower-tail inequality
plateaued or compressed during the
changing composition (leading
prices (leading to
interval
due
to the countervailing effects
of
more expansion) and changing between and within-group
more compression).
IV.
Quantile decomposition:
In this section,
Methodologically,
we
An extended DFL approach
extend our analysis to the decomposition of residual inequality.
we demonstrate how
unify alternative models for
Substantively,
to
same time
the quantile decomposition technique
wage density decompositions
we demonstrate how our
core findings -
(e.g.,
i.e.,
JMP,
DFL
may
be used to
and extensions).
that prices, not quantities are the
predominant force explaining the growth of aggregate and residual inequality -can be reconciled
with the conclusion of Lemieux (2005) that changes
in
labor force composition essentially
explain the entire rise of residual inequality after 1988.
We
begin with a quantile implementation of the extended DiNardo, Fortin and Lemieux
(1996) procedure proposed by Lemieux (2002 and 2005). The original
observed wage densities to account for compositional (and other)
DFL
shifts.
procedure reweights
Lemieux (2002 2005)
extends this technique to the analysis of counterfactual residual wage densities. The extension
22
involves estimating flexible
wage models
similar to our equation
quantile regressions), assigning each observation
distribution
of x's to account for compositional
its
(
1
(using
)
OLS
rather than
regression residual, and reweighting the
between any two time periods.
shifts
To
the
extent that reweighting generates a counterfactual residual distribution that approximates the
observed change
in the residual distribution, the
changes to compositional
In
DFL
extended
procedure ascribes the observed
shifts."
our notation, the Lemieux approach (superscripted by L below) estimates the following
quantity:
AOj =
(8)
a ifigr
(X), /?'
= 0, js; )) -
a (fig,
=
(.V), /3'
0, /?; ))
Here, the counterfactual contribution of changing labor force composition to the change
quantile of the residual distribution
is
estimated by replacing the x distribution from period
with X distribution from period r while holding residual prices
setting
between-group prices
Lemieux/DFL
quantile Juhn-Murphy-Pierce decomposition
component ( AQ^
)
base (period
at their
t )
t
level
and
to zero.
Inspection of equation (8) reveals that the
full
in the 0'
.'^
of the three component quantile
More
JMP
calculation
specifically,
is
it is
a
subcomponent of the
identical to the first
decomposition above (and hence
straightforward for us to implement using the quantile tool) except that the calculation sets
/J* to
zero in both time periods, thus suppressing the role of between-group prices. The utility of this
extension
is
that
it
exclusively analyzes the contribution of labor force composition to changing
residual inequality, abstracting from the role played by
with labor force composition."
^'
Lemieux
A potential
between group prices and
limitation of this partial-decomposition
also proposes a variance decomposition that explicitly
models
"
It is
not a subset of the original
the residual
'
wage
JMP
distribution (see
The DFL approach does not
wage variance
is
that the
90/10. 90/50, etc.) and
we do
is
of
not suited for analyzing
not implement
it
here.
decomposition, however, which does not account for the heteroskedasticity of
Appendix
explicitly
Rather, the contribution of prices
(e.g.,
is
the conditional heteroskedasticity
regression residuals and applies this to the U.S. residual distribution. This decomposition
inequality measures other than the
their interaction
2).
model
the role
of prices
calculated as a residual
- that
in shifting the overall
is
the
component
that
or residual
wage
distribution.
remains after the quantity
23
allocation of total
arbitrary since
it
wage
depends upon the
and within-group inequality
A.
is,
of x
set
's
included
however, invariant
in the
conditioning
set.
is
inherently
The sum of between
to the conditioning set.
Extended DFL decomposition: Results for overall inequality
For comparison with the prior
overall inequality using the
results,
May /ORG
we
data.
by applying the labor force composition
(
components
variation into 'between-group' and 'residual'
first
implement the Lemieux-DFL analysis
We evaluate
data, g,{x)
,
for
the importance of compositional shifts
from each sample year
to the price series
from four different years: the contemporaneous year — thus producing that year's
P'^ ,P]' )
observed level of inequality - and the price series for years 1973, 1988 and 2003. Aggregate
inequality statistics (90/10, 90/50, 50/10) for these counterfactual densities are plotted in Figure 4
(see also Table 6).
The differences
figure reflect the effect of
in the vertical height
at their
The over-time change
of each series
the x-axis) reflects the effect of changes in labor force composition, holding prices
results stand out in Figure 4. First, there
not attributable to compositional changes.
reflected in the shallow
is
a large rise in overall earnings inequality that
The magnitude of the compositional
upward slope of the counterfactual
substantial rise in inequality observed
when comparing
series
between 1973 and 2003. Holding composition
estimate that this earnings ratio
at the
is
that revveights
is
-
small relative to the
ratio rose
by 29 log points
1973, 1988 or 2003 levels respecti\'ely.
would counterfactually have
Second, compositional and price shifts play distinct roles
reweigliting
-
effects
the price changes over the three decades
of the sample. For example, the male 90/10 log hourly earnings
between
in the level
1973, 1988 or 2003 level.
Two
is
in the
between and within-group prices on earnings inequality, holding labor
force composition at the appointed year's level.
(moving along
of each series within a given year
risen
we
by 22 to 25 log points.
in the
upper and lower
tails
of the
implemented. Leibbrandt, Levinsohn and McCrar)' (2005) propose an extension to tlie DFL approach
wage distribution for changes in prices as well as quantities, though it also does not differentiate
tlie
'residual'
and 'between-group" prices.
24
wage
As
distribution.
visible in
is
tlie
middle two panels of Figure
inequality over the entire three decades
and within-group prices.
x's
),
When
is
evaluated
series
The comparable analysis
-
is
of upper
tail
almost exclusively a consequence of changing between
at
any point along the x-axis
the counterfactual rise in upper-tail inequality
between the three price
4, the rise
— measured by
(i.e.,
using 1973 to 2003
the vertical difference
(about) equally pronounced during both halves of the sample.
for lower-tail inequality,
shown
lower panels of Figure
in the
4, also
reveals an important role for prices in the plateauing of 50/10 inequality after 1988. Here, the role
of prices
is
the opposite of that above; price compression substantially reduced lower
inequality after 1988
the 1988 series
-
- seen by the lower height of the 2003 counterfactual
a fact that
is
tail
price series relative to
also robust to the choice of the quantity series for any year. Labor
force composition also played a role
- by
offsetting lower-tail price compression. Using any of
the three counterfactual price series (1973, 1988, 2003), the simulated 50/10 log earnings ratio
slopes gradually upward from the late
raised observed 50/10 inequality
B.
Extended
We now
DFL
above what would have occurred had prices alone compressed.
use the extended
The
MM quantile tool
results
confirm the Lemieux findings and,
The top panel of Figure
5
to
implement the Lemieux/DFL decomposition
of this decomposition for the
we
shows
May/ORG
sample
once
at
believe, substantially alter their interpretation.
that holding
composition constant
at
the 1973,
1
988 or 2003
90/10 residua! inequality rose sharply between 1973 and 1988 (compare the height of the
1973 versus 1988
by about 15
finding of
series).
to 30 percent
Between 1988 and 2003, however,
of
Lemieux (2005)
vertical differences
that
980s, indicating that changing labor-force representation
decomposition: Results for residual inequality
for residual inequality.
level,
1
among
its
original rise, holding composition constant. This confirms the
that residual inequality plateaued or contracted after 1988.
But the
these three counterfactual series at each point along the x-axis reveal
changing 'residual prices" are primarily responsible
residual inequality in the
residual 90/10 inequality contracted
first
for the rise
and then contraction
and second halves of the sample. These
in
shifts in residual inequality
25
occur with composition constant.
What
upward slopes of each counterfactual
role did
series
composition play? As
(moving along the
may
be seen by shallow
x-axis), compositional shifts also
contributed to rising residual inequality (holding residual prices constant), particularly after 1988.
But these compositional
How can
explain the
shifts are
modest
relative to the price effects.
these modest effects be reconciled with the claim that compositional changes
full rise in
residual inequality after 1988?
from 1988
actual net rise in estimated residual inequality
residual").
it
at 0.4
The observed
The answer may be seen by studying
rise in residual inequality
can be said
rise in residual inequality for this period.
price contractions
were economically
inequality
As shown
in
the lower
(series labeled
But what Figure 5 reveals
as or
continued to
rise for
in the
quite small;
more than
is
all)
to
upper and lower
two panels of Figure
opposite direction.
By
we
estimate
of the observed
that the offsetting effects
more important than these compositional
5,
tail
shifts.
residual inequality treated
is
entirely a price effect;
contrast, upper-tail residual inequality
both genders between 1988 and 2003 - and substantially so for males, as
did in the prior half of the sample. In fact, only
when
of
composition-constant lower- tail
unambiguously contracted between 1988 and 2003. This
composition effects work
is
"observed
modest contribution of compositional
to explain all (in fact,
These points apply with even greater force
separately.
2003
over 1988 to 2003
log points (Table 7). Accordingly, the relatively
shifts to rising residual inequality
to
the
it
labor force weights from 1973 are used in
place of labor force weights from 1988 or 2003 does this rise appear muted for males and
reversed for females.
What
explains the sensitivity to the choice of weights? Recall from Tables 2 and 3 that 90/10
inequality rose
among
better educated workers after 1988 but fell
during the same interval. Since the labor force
highly educated workers and considerable
in
among
less
educated workers
1973 was composed of considerably fewer
more high school graduates and dropouts than
in
1988
or 2003, the use of 1973 labor force characteristics puts substantial weight on the groups that
experienced falling inequality and puts proportionately less weight on the groups that experienced
26
rising inequality, suggesting a smaller rise in counterfactual residual inequality than the
comparison made using 1988 or 2003
characteristics.
prices and quantities are independent,
no one weighting scheme
conclusions about trends
in inequality to the
Under
same
the maintained assumption that
is
correct.
But the sensitivity of
choice of weights cautions researchers against
focusing exclusively on one set of labor force characteristics.
In
summary, we
patterns of overall
find that composition plays only a secondary role in explaining the time
and residual inequality
in the
CPS May /ORG;
the ongoing rise of upper-tail
inequality and the rise and then stagnation of lower-tail inequality are both primarily accounted
for
by changing labor market prices.
Comparison with the March CPS
C.
The right-hand panels of Tables 6 and
7 present counterfactual simulations for
March hourly
earnings inequality, and Figures 6 and 7 plot these counterfactuals. The pattern of inferences
March versus May/ORG
quite similar for
the rise of overall or residual inequality
negligible
-
as
would be expected from
that lower-tail inequality (both overall
than
May/ORG
on the observed
This finding
rise
is
at
is
But the estimated contribution of composition
considerably smaller
earlier tables.
The
in these
less
to
data - though not
principle reason for this discrepancy
and residual) contracted by considerably
weight on
data. Placing greater
holding composition constant
data.
is
educated workers
in the
less in the
is
March
March data (by
an early period level) has a comparatively lesser offsetting effect
of overall or residual inequality during
qualitatively consistent with
this period.
Lemieux (2005), who
also reports that the
March
data reveal a smaller role for composition and a correspondingly larger role for prices in the
growth of residual earnings. Interestingly,
May/ORG
and March results
for the role
believe the source of the difference
residuals while ours
is
Appendix Tables 2a and 2b,
Lemieux's analysis, the discrepancy between the
of composition
that
decomposes wage
in
is
far greater than
we
report here.
We
Lemieux's analysis decomposes the variance of wage
quantiles (90/10) and their subcomponents.
As shown
there are substantially greater discrepancies between the
in
March and
27
May/ORG
data for variance than quantile measures, and this difference becomes particularly
pronounced between 1988 and 2002. The particularly high variance of the wage residual
measures
in the
March
data appear likely to reflect the fact that hourly wages are calculated in
these data using prior year's earnings divided by
which exclude the
tails
of the distribution, are likely
construction of hourly wages in the
Is
the
hence
we
is
less sensitive to outliers
is
more
reliable than the other?
March and May/ORG
Bias in the
V.
A key
issue in
May/ORG
May/ORG
of workers
who
and March
versus March
CPS
wage
in
data: Levels or trends?
whether the differences
in the
March CPS
of workers with well- measured hourly wages increases
hourly
wage
measurement
earlier, the share
wage
reporting
may make
the
May/ORG CPS
inequality relative to the
mean
it
in
a
relative to the
the
ORG/May CPS,
May/ORG
May/ORG. Although
more accurate measure of
becomes a preferred measure
March CPS.
simple variance decomposition can help clarify these issues. Let
o index the
in
points out that a growth in the share of hourly workers will tend to lead to a
inequality at a point in time, this does not necessarily
of trends
A
is
CPS
(Hamermesh 2002; Lemieux 2005).
measured residual hourly wage inequality
in
I.
report being paid by the hour has increased substantially since 1973, both in
Lemieux (2005)
growth
Section
inequality.
have remained stable over time. As noted
aggregate and within education/experience groups
as the share
in
data both have advantages and disadvantages and provide
comparing wage inequality trends
error in the
in
that
sample prov ides a more accurate measure of the hourly wage distribution and
complementary sources of information on the evolution of U.S. wage
this
Lemieux argues
a preferred data source for analysis of U.S. wage inequality. As discussed
believe the
growth
generated by the
March CPS.
there reason to believe that one series
May/ORG CPS
weeks and earnings. The quantile measures,
m
j index sex-education-experience group,
hourly workers (those paid by the hour), and n index non-hourly workers.
index the March CPS,
/
index year, h index
We define
V"'
and V°
28
wages
as the observed variances of hourly
workers
year
in
in
/
;
CPS; and
group
j
in
year
t.
We
a^,^ as
workers
in
measurement
the variance of
March CPS. The measurement
May/ORG CPS
in
year
error in hourly
measurement
wages
error in hourly
by al^ and
a^^
.
We
respectively for
wages
for hourly
wages
variances for hourly and
error
are analogously given
group j
March and May/ORG CPS
also define Cji as the true variance in hourly
as the variance of
(j,^„,
in the
group j
for
workers
in
March
for non-hourly workers in
non-hourly workers
also let //^^qua
the
in
the share of hourly
1
t
Under the assumption of white noise measurement
variances of hourly wages for group J in year
t
in the
error in hourly wages, the observed
March and May/ORG CPS can be
written
as:
Based on the estimates from matched March-May/ORG samples presented
we assume that
March CPS:
hourly wages are more accurately measured
cr^,„
hourly workers
is
>
crl^
.
We
also
assume
that
measurement
essentially equivalent in the
is
also reasonable to
assume
that hourly
than non-hourly workers in the
in levels than
wages
May/ORG
CPS
are
error in the hourly
than in the
wages
a'^^^
=
a^^
for
.
non-
These
generates higher (and less accurate)
does the
May/ORG CPS:
more accurately measured
samples: a^^ >
Lemieux (2005),
May/ORG CPS
March and May/ORG CPS:
assumptions imply, as Lemieux notes, that the March
measures of residual hourly wage inequality
in the
in
<jI^
.
Although there
K"'
> V°
.
It
for hourly workers
is little
reason to
believe in differential measurement error for the hourly wages of non-hourly and hourly workers
in the
March CPS, Lemieux's estimates imply
We
residual
o","
next consider the accuracy of the different
wage
inequality from period
t
to period r
> a'
.
CPS samples
when the
for
measuring changes
in
share of workers paid by the hour
is
29
rising
-
hourly
-
as has been the case since the 1970s. Let Ax,
wage variance
for
group J from
Mo
-.v,
x,
r in the different
.
The changes
CPS
in
measured residua!
samples are given by
^^^^^^^M"-""^"-^'
(10)
so that
AV:-AV;=AH,[{cTl,-al) + ial-aly].
(11)
Under
is
the assumptions given above, this difference
rising in the share
of workers paid by the hour: AF"'
Thus, as emphasized by Lemieux (2005), a
rise in the
systematically lead to a rise in measured residual
the
in contrast to the
-AV° =AHj,{a^^ -o"^)>0
is
positive
>0.
if A//^,
share of hourly workers should
wage
inequality in the
conclusion drawn by Lemieux (2004),
series does not imply that the
actual residual
downward
wage
May/ORG CPS
March CPS
relative to
is
rising (since
upward biased measure of changes
induce
in the
May/ORG CPS, we
<
cj]^).
inequality
In contrast, the
in actual residual
wage
(
AF° <
Acr^", )
at its
base (1974)
level. '°
inequality if
cr^^^
in residual inequality,
a^
>
provides a
when
frequency of hourly pay reporting
at its start
.
cells for
in
wage
may
inequalit)' in
is
formed using the
each year to maintain the
of period level within the gender by education by
increase the precision of this simulation by using the
by experience by gender
the
holding the frequency
This counterfactual series
MM quantile simulation procedure, reweighting the data
in
March CPS provides an
plot in Figure 8 observed trends in residual
alongside counterfactual trends
of hourly wage reporting
We
cr^^
wage
May/ORG CPS
a rough direct assessment of the bias that the rise of hourly pay reporting
May/ORG CPS
extended
divergence between the
provides a more accurate measure of changes
biased measure of changes in actual residual
To provide
this
inequality. Rather, equation (11) implies that the
share of hourly workers
'°
May/ORG
May/ORG CPS.
But
the
between March and
mean frequency of hourly pay reporting within education
1973, 1974 and 1975.
30
experience cells used
our analysis.
in
No
made
other adjustments are
for compositional
changes
Hence, the contrast between the observed and counterfactual
in the counterfactual series.
series
is
exclusively due to hourly pay reporting.
To provide
more detailed look
a
at the
hourly reweighting bias, Figure 9 plots the gap (by
gender) between estimated 90/10 residual inequality and the hourly-reporting-corrected series
alongside a chain-weighted index of the evolution of hourly pay reporting
in
our sample."" Figure
9 indicates that the rise in hourly pay reporting has probably led to a non-negligible
bias in
measured trends
in residual inequality in the
May /ORG CPS.
cumulates over 1973 to approximately 1989, plateaus
between 1997 and 2002. For females, the bias
sharp rise
in 1991.^"
The
is
to 1994,
and then appears
of hourly pay reporting
this bias
to increase again
1979 but then begins a
relatively stable after
further rise in the hourly-pay bias in the
particularly puzzling since the frequency
For males,
downward
MORG samples after
in the
May /ORG
1994
is
plateaued
in
the early 1990s. This suggests that the difference between the precision of hourly and non-hourly
wage
reports
became more pronounced
Notably, the hourly-pay bias in the
after the
1994
CPS
CPS May/ORG
redesign.
can potentially be 'controlled' by making
adjustments for hourly pay composition comparable to the ones
experience. In
fact,
our simulation procedure for the
throughout. Specifically,
we
in the
and residual) and we reweight
this covariate
accurate adjustment
"
May/ORG
if the
In the base year, this index
add
cell,
'"
the
to
it
is
data makes this adjustment
conditioning set used for the quantile analysis (both overall
along with other x's in the simulation.
possible that our analysis of residual inequality
in
apply for education and
include an indicator variable for hourly pay reporting, interacted
with each education category,
inequality trends
May/ORG
we
may
It is
therefore
correct for the hourly-pay bias in residual
sample. However, our procedure
is
unlikely to provide an
relationship between hourly pay and earnings precision in the
CPS
equal to the observed frequency of hourly pay reporting. In each subsequent year,
we
sum of year-over-year change in hourly pay-reporting in each education-by-experience group
weights are the employment share of each cell over the prior two years.
the weighted
where
the
Notably, the bias for females
is
particularly
pronounced
the plateau in female 50/10 inequality after 1989
is
in the lower-tail
an artifact of changes
of the distribution. This suggests
in
that part
of
hourly earnings reports.
31
survey undergoes a discontinuous change - as
In
summary, although
residual hourly
wage
residual hourly
Lemieux
wage
fiirther
measurement
March CPS
inequality while the
error in hourly
for
May/ORG may
trends) in
provide a downward biased estimate/^
March-May/ORG samples
wages within hourly and non-hourly workers increased over
March and May/ORG samples with
males and of similar magnitude
that both are attempting to capture the
in
1994.
analysis suggests that there are reasons to
argues and presents evidence using the matched
assume white noise measurement error
in
in
provides a more accurate measure of the level of
March CPS, our
variance than the
past three decades in both the
changes
CPS
occurred
March CPS may provide an upward biased measure of changes (and
suspect the
that
the IVlay/ORG
may have
that
is
same
in the
the
the rise being larger in the
two samples
for females.
These estimates
uncorrelated across the two samples and assume
true
measure of hourly earnings. But there are
real
the labor market and structure of compensation that could generate actual divergences
earnings inequality measures based on a comprehensive measure of annual earnings from the
March samples versus a
the
May/ORG
1990s
more
is
straight-time hourly
wage
rate or usual
weekly earnings measure from
samples. For example, the growth of bonuses and other contingent pay
likely to be captured in the
in the
March data than the May/ORG earnings measure
(Lebow, Sheiner, Slifman, and Starr-McCluer 1999; Lemiuex, MacLeod, and Parent 2005).
Changes
in the
importance of transitory versus permanent components of earnings could also
reduce the true covariance between annual and point-in-time measures of earnings. Furthermore,
most of Lemieux's estimated growth
ORG
samples comes
more
that
We
"''
in the
1990s
greatly affected the
therefore
wage
to
measurement
error in the
March versus
period overlapping the major 1994 revision of the
the
CPS
data.
do not concur with Lemieux's (2005) suggestion
in the
to researchers to use the
March and May/ORG samples are smaller for samples limited to full-time
in Appendix Table 1. The persistent rise in upper-tail
analyses of full-time, weekly earnings as indicated
inequality
earnings.
in the
ORG
The divergences of inequality trends
workers and
in the relative
combined with
A substantial
the post- 1988 stagnation of lower-tail inequality
rise in residual
wage
inequality after 1988
samples when examining full-time weekly earnings.
is
is
also apparent for full-time
apparent in both the March and
weekly
May/ORG
May/ORG CPS
rather than the
recent decades.
To be
clear,
March CPS
both
CPS
to study the evolution
samples have strengths and limitations.
actual labor market changes and data processing changes
of missing wage infoiTnation, changes
the actual earnings and the
of U.S. wage inequality over
in the
in
many
there are
- ranging from top coding, imputations
questions - that
wage and hour
measurement error
And
wage measures
may
in the different
differentially
CPS
samples.
Researchers would be wise to combine information from both sources for measuring changes
wage
the U.S.
in
structure.
VI.
Conclusion
This paper set out to evaluate one potential explanation for the diverging trends of U.S.
inequality during the 1990s.
Our analysis
may have
the U.S. labor force
dispersion from 1990 forward.
tested whether the rising experience and education of
led to a mechanical
We
fail to
confirm
(i.e.,
not due to price changes) rise
in
earnings
this hypothesis. Shifts in labor force
composition have affected earnings inequality during the 1990s. But these compositional
have primarily operated on the lower
primarily served to
tail
of the earnings distribution and, moreover, have
mute a contemporaneous, countervailing
contrast, the steady rise of
upper
tail
shifts
lower-tail price compression.
By
inequality since the early 1980s appears almost entirely
explained by ongoing between-group and residual price changes.
The source of the asymmetric
inequality and
some evidence of flat
making adjustments
pattern
is
workers
earnings inequality with a steady rise in upper-tail
or declining lower-tail
wage
wage
inequality (particularly after
composition) since the mid-1980s remains poorly understood. This
suggestive of a "polarization" of the labor market with a particularly strong market for
the middle,
demand
for
in the top part
Mumane
rise in
of the
skill distribution, deterioration in
and reasonably steady market conditions
market conditions
for
workers
for those near the bottom. Autor,
in
Levy, and
(2003) postulate that computerization could have such non-monotonic impacts on the
for skill: sharply raising
demand
for the cognitive
and interpersonal
skills
used by
educated professionals and managers; reducing demand for clerical and routine analytical
'
skills
-33
that
comprised many middle-educated white collar jobs; and reducing demand for routine manual
skills
of many previously high-paid manufacturing production jobs. But computerization has
probably had
little
impact on the
skilled' (in-person) service jobs
framework suggests
demand
for the non-routine
skills
that computerization
-
may have
raised
demand
left
Goos and Manning (2003)
call
distribution comparatively unscathed.
"polarization of work," and argue that
distribution in the United
We
it
may have
Kingdom
in
many
etc.
'low-
This
as well as the increased international outsourcing (off-
workers, depressed demands for 'middle-skill' workers, and
wage
used
such as health aides, orderlies, cleaners, servers,
shoring) of routine cognitive and manual tasks -
skill
manual
for skill
among
the bottom of the
high-
wage
such a process the
contributed to a similar hollowing out of the
during 1975 to 2000
finally stress that the informativeness
of the counterfactual exercises undertaken
in this
study depends critically on the maintained partial-equilibrium assumption that prices and
quantities can be treated as independent. If this assumption
is
substantially violated, the
counterfactual inequality series developed will not correspond to any potential state of the world
since altering labor force characteristics will necessarily alter the prices associated with those
characteristics.
Lending weight
to this
concern, the careful analyses of earnings premiums by
experience, age and education group performed by Card and Lemieux (2001) and Borjas (2003)
strongly affirm that the relative
responsive to
own
wages paid
to education, experience
supplv as well as aggregate supply. Hence,
and age groups are quite
shifts in
composition and
prices will generally negatively covary, particularly over long time intervals
- such
shifts
as the three
decades above. This underscores that the impact of changing composition on prices could
potentially be a
first
order source of bias
remains an important item
in
these counterfactual exercises. Assessing this bias
for analysis.
34
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1
37
Appendix
A.
Basic processing of May/ORG
We
use the
May CPS
for 1973 to
1:
Data
CPS data
1978 and the
CPS Merged Outgoing
Rotation Groups for years
1979 to 2003. All samples include wage/salary workers ages 16 to 64 with to 39 years of
potential experience in current employment. Earnings weights are used in all calculations. Full-
CPS sampling
time earnings are weighted by
product of CPS
weights. Hourly earnings are weighted by the
sampling weights and hours worked
week. Full-time earnings are the
wages are the logarithm of
hourly
earnings
for
those
paid
by
the
hour
and
the
logarithm
of usual weekly earnings
reported
divided by hours worked last week (not usual weekly hours) for non-hourly workers. We use
hours last week instead of usual weekly hours because usual weekly hours is not consistently
logarithm of reported usual weekly earnings. In
available: starting with the
CPS
all
in the prior
years, hourly
redesign in 1994, workers
who
report that their
weekly hours
vary are not asked to report usual weekly hours, yielding a non-report rate of 7.0 to 8.5 percent of
workers
1994 to 2003. To check
in
sensitivity,
we have
tabulated and plotted overall and residual
inequality measures using imputed usual weekly hours in place of hours last
1973 -2003. This has
little
impact on our
week
in all
years
results.
Topcoded earnings observations are multiplied by 1.5. Full-time earnings of below $67/week in
982$ ($ 2/week in 2000$) and hourly earners of below $ .675/hour in 982 dollars
($2.80/hour in 2000$) are dropped, as are hourly wages exceeding l/35th the topcoded value of
weekly earnings. All earnings numbers are deflated by the chain-weighted (implicit) price
1
1
1
1
1
consumption expenditures. Allocated earnings observations are excluded in
where allocation flags are unavailable (January 1994 to August 1995). As
discussed by Hirsch and Shumacher (2004), only about 25 percent of allocated observations in
the MORG CPS are flagged as allocated between 1989 and 1993. Following Lemieux (2004), we
identify and drop non-flagged allocated observations by using the unedited earnings values
deflator for personal
all
years, except
provided
in the
source data.
Basic processing ofMarcIt
B.
We
use the
CPS
data
March Current Population Survey
for earnings years
1975 to 2003 for workers age 16
39 years of potential experience whose class of work in
their longest job was private or government wage/salary employment. Hourly earnings are
calculated as annual earnings divided by the product of weeks worked and usual hours in the prior
to
64 (during the earnings year) with
year. Full-time, full-year
to
workers are those
who work
35 hours per
Bureau's full-time worker flag) and worked 40+ weeks
in the
week
(using the Census
previous year. Full-time weekly
earnings are calculated as the logarithm of annual earnings over weeks worked for the full-time,
full-year sample. Allocated earnings observations are excluded using family earnings allocation
and individual earnings allocation flags. Weights are used in all calculations. Full-time earnings
are weighted by the product of the CPS sampling weight and weeks worked. Hourly earnings are
weighted by the product of the
CPS sampling
weight, weeks worked, and hours worked in the
prior year.
Prior to
March
variable,
1
989,
all
wage and
which was topcoded
at
salary
income
in the
March CPS was
values between $50,000 and $99,999
in
reported in a single
years 1975 to 1988. For
we multiply the topcoded earnings value by 1.5, following Katz and Murphy
Commencing in 1989, wage and salary incomes were collected in two separate earnings
these cases,
(1992).
variables, corresponding to primary and secondary labor earnings. After adjusting for topcoding.
we sum
these values to calculate total
wage and
salary earnings.
Topcodes
after
1988 are handled
as follows. For the primaiy earnings variable, topcoded values are reported at the topcode
maximum up
to 1996.
We
multiply these values by 1.5. Starting
mean of all
earnings values are assigned the
the topcoded value and, again, multiply by
maximum
is
set at
to 37,000 in 2004.
99,999 from
1
989
to
1
1
in
1996, topcoded primary
topcoded earners. In these cases,
.5.
we
simply reassign
For the secondary earnings value, the topcoded
995 and then
For lack of a better alternative,
falls to
we again
25,000
in
1
996
to
2003, and
rises
use the topcoded value multiplied by
1.5.
making adjustments for topcoding, full-time earnings of below $67/week in 1982$
12/week
in 2000$) and hourly earners of below $1 .675/hour in 1982 dollars (S2.80/hour in
($1
are
dropped,
as are hourly wages exceeding l/35th the topcoded value of weekly earnings.
2000$)
After
C.
To
Coding of education and potential experience
in
CPS samples
comparable educational categories across the redefinition of Census Bureau's education
CPS, we use the method proposed by Jaeger ( 997). In CPS
samples coded with the pre-1992 education question, we defined high school dropouts as those
with fewer than 12 years of completed schooling; high school graduates as those having 12 years
attain
variable introduced in 1992 in the
1
of completed schooling; some college attendees as those with any schooling beyond 12 years
(including an incomplete 1 S"" year) and fewer than 16 completed years; college graduates as those
with 16 or 17 years of completed schooling; post-college as those with more than 17 years of
completed schooling. In
CPS samples coded
with the revised education question,
we defme high
school dropouts as those with fewer than 12 years of completed schooling; high school graduates
as those with either 12 completed years of schooling and/or a high school
some college
as those attending
some college
diploma or G.E.D.;
or holding an Associate's Degree; college as those
with exactly a baccalaureate degree; and post-college as those with a post- baccalaureate degree.
To
calculate potential experience in data years coded with the revised education question,
we
from Park (1994) to assign years of completed education to each worker based upon
gender and highest degree held. Years of potential experience were calculated as age minus
assigned years of education minus 6. rounded down to the nearest integer value.
figures
use
race,
39
Appendix
JMP
Comparison of traditional and quantile
2:
decompositions
propose a model for wage inequality as a function of the distribution of covariates,
the vector of between-group prices
where 9 e
[0,1]
the resulting
wage
vi'_^
JMP
.
JMP
wage
implement
j3's
(
JMP's
=x„'y9, +/|(^,) where
fitting
F~\9) which
,
=/^~'(e„)and
e„
is
OLS
regressions to estimate /? and using
the inverse cumulative empirical residual
Vs wage, w, can be written
notation, individual
9,,
g(.r)
and the cumulative distribution of the residual, F{9)
model by
this
residuals to form
distribution. In
)
is
as:
V s wage residual from the regression.
JMP
use this methodology to decompose changes in the wage distribution over 1963 to 1989 into
components due to changes in prices ( A/? ), changes in quantities ( Ag(x) ), and changes in the
residual distribution
(
AF{9)). The principle virtue of the
Blinder-Oaxaca method
counterfactual
wage
various
wage
is
that
it
JMP
decomposition over the standard
can potentially be applied to simulate any feature of a
JMP's
distribution. Indeed,
principle focus
is
on earnings inequality among
quantiles: 90/10, 90/50 and 50/10.
JMP methodology has two shortcomings that are solved by the quantile model. The first
that the OLS wage regression at the heart of the JMP technique provides a model for the
The
conditional
quantiles.
that
mean of the wage
For example, there
distribution
and
=x,' /], + i^(50) This inconsistency
.
J',
its
results
do not extend naturally
no presumption that /^(50) =
is
,
and so
it
may
not present in the quantile model, which provides a
is
decomposition need not sum
distribution in period
t
for the
t
is
depends on both
.
that the
components of the
in
is
are
random
JMP
that
knowledge of the marginal
and covariance
(i.e.,
distribution
.
is
when
of x'/? and
w = x'/? + F(9)
=
x.'
/3+ F(9,))
their joint distribution). This covariance
decomposition unless F{9)
F{9) This
counterfactual
observed wage
variables, the distribution of their sum, g{w^
is
one special case where the marginal distribution of
distributions of x' /3 and
JMP
each of the three accounting components between
zVF((9)), will not generally recover the
The reason
their variances
not accounted for by the
is
change
is
observed change. Specifically, adjusting the wage
not generally sufficient to characterize the marginal distribution of
Because x'/? and F{9)
There
of the method
to the total
and r (A/?,Ag(x) and
distribution in period r
F{d)
this
not be substantively important, however.
A more significant shortcoming
periods
wage
need not be the case
uniform treatment of between and within-group price measurement. In practice,
inconsistency
to
is
allowed
vv is
to
depend
explicitly
is
on x
.'''
recoverable from the marginal
the distributions are independent.
Under
classical
OLS
assumptions - in particular, a normally distributed, homoskedastic error term —this
independence condition will hold. But as underscored by Lemieux (2005), this error structure
odds with the predictions of human capital theory. Moreover, the evidence
clearly demonstrates that trends in residual inequality differ
experience groups. Hence, the homoskedastic error structure
wage
is
at
Tables 2 and 3
markedly by education and
is
strongly rejected for the U.S.
distribution.'^
Lemieux (2002) provides
" JMP
in
recognize
tlnat
a thorough discussion of these points.
the 'adding up' property does not hold in their decomposition
and recommend calculating
the
contribution of the 'residual price and quantity component" as a remainder temi. after accounting for obser\ed prices
and quantities.
40
Unlike the original
JMP
decomposition, the quantile
the full conditional distribution of wages
independence nor homoskedasticity
is
is
JMP
decomposition does "add up" because
allowed to depend upon x through
/?'',/?"
.
Neither
assumed.
41
Figure
1.
Hourly
Overall Male 90/10 Hourly
1973
1976
1S79
'
1982
CPS
1985
1976
1979
s
1982
1985
Hourly
1988
Inequality
1991
1994
Overall Male 50/10 Hourly
in
May/ORG and March CPS
Wage
Inequality
1991
1994
CPS
1997
2000
2003
1973
1976
Inequality
1991
1994
1979
2000
2003
1973
1976
-
2003
Female 90/10 Hourly Wage
1982
Oveia'i
1997
1973
1985
1979
Female 90/50 Hourly Wage
1982
1985
Overall
1997
2000
2003
2000
2003
2000
2003
CPS May/ORG
1988
Inequality
1997
1994
1991
CPS May/ORG
CPSMarcti
s
Inequality
1994
1991
CPS March
=
Ivlay/ORG
Wage
Series,
Overall
CPS May/ORG
e
CPSMarcti
Inequality
Wage
»
Blardi
OwssS Mais 90S)
1973
1988
Wage
Female 50/10 Hourly Wage
Inequality
s
o
1973
1976
1979
'
1982
1985
CPSMarcti
19
1997
CPS May/ORG
2000
2003
1973
1976
1979
»
1982
1985
CPSMarcti
19
1991
—
1994
1997
CPS May/ORG
Figure
2.
Hourly Residual
Residual Male 90/10 Hourly
1973
1976
1979
»
1982
1985
CPS
1988
1976
1979
o
1982
Residual
1973
1976
1979
8
1985
1988
CPS March
1982
I^lale
1985
CPS March
19
in
May/ORG and
Wage
1997
2000
2003
1973
1975
1991
1997
2000
2003
1973
1976
1979
«
Series,
1973
1982
1985
1988
CPSMarrt
1982
CPS
1985
19
1997
CPS May/ORG
2000
2003
1973
1976
1979
«
1982
1985
2003
Inequality
1994
1991
1997
2000
2003
2000
2003
2000
2003
CPS May/ORG
Wage
Inequality
1994
1991
1997
CPS May/ORG
Marcti
CPS March
-
Wage
e
Residual Female 50/10 Hourly
Inequality
1994
CPS
Residual Female 90/'50 Hourly
CPS May/ORG
Wage
1979
e
Inequality
1994
1991
Marcii
Residual Female 90/10 Hourly
CPS May/ORG
9
50/10 Hourly
Inequality
Inequality
1994
1991
6
Marcti
Residual Male 90/50 Hourly
1973
Wage
Wage
19
Wage
1991
Inequality
1994
1997
CPS May/ORG
Figure 3. Education and Experience of U.S. Labor Force, 1973
fvlay/ORG)
A. Full-Time Equivalent
-
2003 (CPS
Employment Shares by Education
Males
Females
I,
1973
1
1
1
1
1978
1983
1988
1993
2003
1973
1978
1983
1993
1998
2003
College Grad
Dropouts
College Grad
High School
Post-College
High School
Post-College
Mean
Some
College
Potential Experience of
College
Employed Workers by Education
Females
Males
1973
1988
Dropouts
Some
B.
1—
1
1998
1978
1983
19
1993
—
Dropouts
-a
High School
-«
Some
College
—
1998
2003
1973
1978
1983
1993
19
College Grad
Dropouts
-'
Post-College
High School
-'
Some
College
1998
2003
College Grad
Post-Coliege
Figure 4. Actual and Counterfactual Overall Hourly
Wage
Inequality 1973-2003:
Actual and Counterfactual Overall Inequality (I^ORG)^ Male 90/10
CPS May/ORG
Actual and Counterfactual Overall Inequality (fylORG);
Female 90/10
en ^—
T^^
°,°.
N^
v-^
1973
1976
1979
1982
1985
—
1973
-e
2003 B's
1988
1994
1991
B's
1976
1979
1982
1935
1976
1979
1982
2003
1973
1976
1982
1979
1985
Actual 90/10
-e
2003 B's
Actual 90/10
(MORG);
Mas S^SI
1994
1991
1997
2000
Actual and CounterfacTjal OvsHii tnenuafity
2003
1973
1976
1979
1982
1985
1988 B's
-e
1973 B's
2003 B's
Actual 90/50
-^
2003 B's
1985
1973
B's
-«
2003
B's
1988
1991
——
»
1994
1988 ffs
1973 B's
o
1991
1S73B's
Actual and Counterfactual Overall Inequality
1973
2000
-
Actual and Counterfactual OveiaB Insqusfiiy
1973
1997
1988 B's
(MORG):
f^ale
1994
1997
2000
2003
(MORG): Female 90/50
1994
1997
2000
2003
Actual 90/50
Actual and Counterfxtual Overall Inequality (IWORG): Fennale 50/10
50/10
2000
1991
1997
2003
1973
1976
1979
1982
1985
1988 B's
1973 B's
Actual 50/10
2003 B's
1988
1991
~-v,—
1994
Actual 50/10
1997
2000
2003
Figure
5.
Actual and Counterfactual Residual Hourly
Actual and Counterfactual Residual Inequality
(MORG); Male 90/10
Wage
Inequality 1973-2003:
Actual and Counlerfactual Residual Inequality
_
—
1973
1976
1979
1982
1985
1988
1991
-•
1973 Residual B's
—
-e
2003 Residual
-9
teiuai
B's
aad Counteiaciual Residual
—
Inequality
1994
2000
1997
1988 Residual
2003
1973
B's
Observed Residual
(MORG):
Ivlale
CPS May/ORG
1976
1979
1982
1—
1985
1988
1991
1994
1997
2000
-•
1973 Residual B's
1988 Residual B's
-6
2003 Residual B's
Observed Residual
Actual and CouraeriBoua!
90/50
(MORG); Female 90/10
Rsadud iBsjiaHy (MORG): Female
2003
90/S)
-0—«—#—e—^;y^
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
1973
1976
1979
1982
1985
1988
1991
1994
1997
1988 Residual B's
1973 Residual B's
1988 Residual B's
2003 Residual
Observed Residual
2003 Residual B's
Obsen/ed Residual
B's
Actual and Counteilactual Residual Inequality (IvIORG): Male 50/10
1973
1976
1973 Residual B's
1979
1982
1985
-9
1973 Residual B's
-«
2003 Residual B's
1988
1991
1994
1997
1988 Residual
6
B's
Observed Residual
2000
Actual and Counterfactual Residual Inequality
2003
1973
1975
1979
1982
1985
1991
2000
2003
(MORG): Female 50/10
1994
1997
1973 Residual B's
1988 Residual B's
2003 Residual B's
Observed Residual
2000
2003
Figure
6.
Actual and Counterfactual Overall Hourly
Wage
1978
1981
1984
1987
1990
1978
1981
1996
B's
1988
2003
B's
Actual 90/10
tetu^ and Counterfactual Houriy Earnings
1975
1993
1975
1984
1987
1990
1999
2002
1975
1993
1996
Mate 90!W
1978
1981
1981
1999
2002
1984
1987
Actual 90/10
B's
1975
1978
1961
1984
1987
1988 B's
1975 Bs
2003
B's
Actual 90/50
2003
1990
1993
1996
B's
2002
B's
1990
-s
1993
1996
Actual 50/10
Female 90/10
1999
2002
Female S)/50
1999
2002
Actual 90/50
Actual and Counterfactual Hourly Earnings Inequality (March): Female 50/10
1975
1978
1981
1984
1987
1990
1993
1996
1975 Bs
1975 B's
2003
1999
1996
2003
B's
1987
1993
1988 B's
1975
1984
1990
1975 B's
AGiiai and Counterfxtual Hourly Earnings Inequality (March):
Actual and Counterfactual Hourly Earnings Inequality (March): Male 50/10
1975
1978
B's
Inequality (Maroi):
CPS March
Actual and Counterfactual Hourly Earnings Inequality (March)'
Actual and Counterfaclual Hourly Earnings Inequality (March): Male 90/10
1975
Inequality 1975-2003:
2003 B's
Actual 50/10
1999
2002
Figure
7.
Actual and Counterfactual Residual Hourly
Actual and Counterfaclual Hourly Residual Inequality (March); Male 90/10
Wage
Inequality 1975-2003:
CPS March
Actual and Counterfactual Hourly Residual Inequality (March):
_
Female 90/10
-9—«—»
1975
1978
1981
1984
1987
1993
1990
1996
2002
1999
1975 Residual B's
1988 Residual
2003 Residual B's
Observed Residual
1975
1978
B's
Actual and Counterfactual Hourly Residual Inequality (March); Male 90/50
1981
1984
1987
1993
1990
1995
1999
1975 Residual B's
ISBSRssidiaiB's
2003 Residual B's
OtEerved Residual
Actual and Counterfactual Hourly Residual Inequality (tifeii):
Fsnais
2002
9ffi3)
°/°'^&-^
'^
/^
V
Q-^
1975
—&—e—
—e
—«—9—o—e—o—s—e—o—o—*—*—
«
1978
1981
1984
•-"
1987
1993
1990
-B
1975 Residual B's
—
-o
2003 Residual
-Q
B's
—
1996
1988 Residual
1999
2002
1975
Observed Residual
Actual and Counterfactual Hourly Residual Inequality (March); Male 50/10
1975
1978
1981
1984
1987
1975 Residual
B's
2003 Residual
B's
1990
1993
»
—
1978
B's
1995
1988 Residual
1999
B's
Observed Residual
2002
Actual
1975
1981
1984
1987
1996
1999
1988 Residual B's
2003 Residual B's
Observed Residual
and Counterfactual Hourly Residual
1978
1993
1990
1975 Residual B's
1981
1984
1987
1975 Residual Bs
2003 Residual
Bs
Inequality (March);
1993
1990
'
!
1996
2002
Female 50/10
1999
1988 Residual B's
Observed Residual
2002
Figure 8. The Growth of Residual Inequality in the CPS I^ay/ORG data 1973-2003:
Accounting for the Rising Frequency ofHourly Pay
Residual Male 90/10 Inequality
in
CPS May/ORG: Observed
Residual Female 90/10 Inequality
and Hourly Pay Constant
in
CPS ftey/ORG
Observed and Hourly Pay Constant
B*=.
tOr—
s
1973
1976
>
1979
1982
1-985
Residual IWale 90/50 Inequality
1988
»
Observsl 90/1G
in
1991
1994
1997
2000
2003
1973
CPS May/ORG: Observed
1976
«
rimrtrPsyConaanl 1974
and Hourty Pay Constant
1979
1982
1985
1988
«
Otiserved 90/10
Residual Female 90/50 Inequality
in
1991
1994
1997
2000
2003
Hoiffiy?^(;anraffi'!S4
CPS May/ORG: Observed
and Hourty Pay Constant
Sin
1973
1976
e
1979
1985
1982
Residual Male 50/10 Inequality
1988
«
Observed 90/50
in
1991
1994
1997
2000
2003
1973
CPS May/ORG: Observed
1976
e
Hourly Pay Constant 1974
and Hourty Pay Constant
1979
1982
1985
1991
Residual Female 50/10 Inequality
1994
1997
2000
2003
Hourly Pay Constant 1974
Observed 90/50
in
CPS May/ORG:
Observed and Hourly Pay Constant
Sin-
1973
1976
'
1979
1982
Observed 50/10
1985
1988
»
1991
Hourly
1994
1997
Pay Constant 1974
2000
2003
1973
1976
»
1979
1982
Observed 50/10
1985
19
—
1991
1994
1997
Hourly Pay Constant 1974
2000
2003
Figure 9. Estimated Hourly Pay Bias for Residual 90/10 Inequality by
Gender
Hourly Pay Bias
in IVlale
in
CPS May/ORG, 1973
90/10 Residual Inequality
in
-
2003
CPS May/ORG:
Corrected-Observed
"a
r^
TO
Q.
"a
CO
£
o
crtM
CO
(U
CO
Oo
1
1973
1
1979
1976
Hourly Pay Bias
in
1982
1985
1^
1991
1994
1997
Understatement of 90/10 Residual Inequality
(left
Chain-Weighted Share
(right axis)
of
Female 90/10 Residual
Males Paid Hourly
Inequality
in
2000
2003
axis)
CPS May/ORG:
Connected-Observed
CO
ca
E
o
•
CO
Oo
to O)
O
1973
1976
1979
1982
Understatement
1985
1991
of 90/10 Residual Inequality
Chain-Weighted Share
of
1994
(left
Females Paid Hourly
1997
axis)
(right axis)
2000
2003
>-
^'
ro
o
>
rr
-S*
Q)
CD
3
c
E
f?
'
(D
Q)
_C
E
::3
o
u5
(D
>
O
T3
(U
_ro
E
El
21
VI
91.
S'l.
O!)EJ^BBM0^/06 Boi
V'l
Z'l
Z'l
ri
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E
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2'1.
0!)BJ
36emoi,/05
LL
Bo"|
9'L
SI
VI
i'l
o!]bj36b/«oi./06 Bo"!
tr
CO
OT
Q
o
rn
ce
>-
o
4-1
CO
en
03
cr
CO
3
(U
c
H-t
cu
CD
:^
CD
^
cr
en
m
^
3
T3
cr
^
cc
IT ce
o
5;
Em
o
(n
ID
a:
(U
CD
F
Oo
4-J
in
3
E
Sll
m
901
96'
98'
931.
9I.1.
901.
95'
O!)BJ0L/06Bo|
ORBJ 01./06 6o|
tn
•a
(D
e
(U
U)
JD
O
u_
O
c
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U)
1_
ro
Q.
CD
cn
S2
CD
m
>
a>
(T
Q
fi
rr
E
o
u
en
cz
fM
0)
L.
3
Ol
00
;>:•
ro
3
cr
X
T3
C
en
OJ
0)
03
ce ca
OJ 5?
OJ
Q.
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<
o
911
SOI.
oiiej
56'
01/06 6o|
98'
921
911
90'L
oijejol/OBBoi
96'
Table
1.
100 x Changes
in
Overall
and Residual Hourly Earnings Inequality: 1973
- 2003 (March CPS)
2003
-
(May/ORG CPS) and 1975
B. Residual Inequality
A. Overall Inequality
1973- 1988- 1973-
1979- 1989- 1979-
1973- 1988- 1973-
1988* 2003 2003*
1989
1999
1988* 2003 2003*
1999
1979- 1989- 19791989 1999 1999
Males
May/ORG CPS
90-10
90-50
50-10
21.0
10.1
10.9
9.1
13.8
-4.7
30.2
24.0
6.2
9.5
1.2
7.3
21.0
17.0
3.0
-0.4
4.1
6.4
3.8
-2.7
14.2
9.7
6.9
4.5
10.6
6.8
8.5
-2.1
6.4
2.9
3.7
3.8
5.6
0.9
-3.0
2.6
5.1
-2.5
12.6
9.4
2.6
March CPS
90-10
90-50
50-10
19.1
10.7
8.4
13.2
14.4
32.3
25.1
-1.2
7.1
17.3
10.6
6.7
5.3
6.6
-1.4
22.6
17.3
12.0
8.3
5.2
7.9
20.3
13.1
10.0
4.3
5.3
6.8
0.4
7.2
5.7
3.0
19.5
18.2
-1.9
16.3
3.7
3.2
Females
May/ORG CPS
90-10
90-50
50-10
25.1
10.5
14.7
9.9
10.1
-0.2
35.0
20.5
14.5
30.4
9.1
8.0
10.3
22.4
-1.2
39.6
18.3
21.2
16.5
7.8
2.3
10.1
3.8
-0.1
8.7
0.7
9.3
14.4
-1.8
12.6
15.5
6.1
5.4
5.2
3.3
3.4
17.4
8.6
9.6
0.7
21.6
11.3
10.3
14.1
5.9
8.9
-0.1
8.8
March CPS
90-10
90-50
50-10
9.1
14.6
9.6
14.0
5.0
23.1
37.7
18.7
19.0
24.3
8.4
8.3
4.9
16.0
3.5
32.7
13.2
19.5
*
March hourly series begin in 1975 rather than 1973.
Source data: May/ORG CPS 1973 - 2003 and March CPS 1976
2004.
Table 2. 100 x Changes in Male Hourly Earnings Inequality Within Narrow
Education and Experience Categories: 1976 to 1988 and 1988 to 2002
(May/ORG and March CPS)
Colleqe Grad uate
Potn'l
1976
Exp
ORG
-
1988
March
Ma les
1988
-
ORG
High School Giraduate Males
2002
March
14-16
24-26
34-36
14-16
24-26
34-36
14-16
24-26
34-36
1988
ORG
-
2002
March
17.4
14.3
5.5
10.7
7.6
8.4
-15.3
3.2
(4.5)
(2.9)
(4.6)
(2.1)
(2.4)
(2.0)
(2.7)
8.6
-0.8
14.2
21.2
15.6
28.2
-3.6
-5.5
(6.6)
(6.7)
(3.1)
(6.0)
(2.3)
(3.6)
(1.8)
(3.1)
5.1
-0.8
7.9
18.2
4.0
25.3
-0.2
-4.0
(7.9)
(7.3)
(4.6)
(6.4)
(3.9)
(3.9)
(2.0)
(3 A)
7.6
27.5
-7.1
16.5
14.7
22.6
-6.8
-0.1
(13.7)
(10.1)
(8.6)
(10.4)
(3.1)
(4.4)
(2.8)
(4.8)
90/50
5.0
2.0
6.6
10.7
4.9
4.8
-3.0
7.1
(1.9)
(2.4)
(1.8)
(2.4)
(1.6)
(1.8)
(1.8)
(2.0)
8.1
4.7
10.1
18.0
9.2
11.0
7.8
3.7
(3.7)
(3.5)
(2.4)
(3.3)
(1.4)
(1.8)
(1.4)
(2.0)
4.8
0.7
1.1
12.6
1.7
5.3
3.9
8.3
(6.8)
(6.1)
(3.9)
(5.9)
(2.2)
(2.7)
(1.4)
(2.2)
-1.2
7.6
-5.9
15.0
1.9
6.4
5.5
8.7
(9.0)
(6.6)
(5.5)
(5.9)
(2.1)
(3.4)
(2.2)
(3.9)
C.
4-6
1988
March
(2.6)
B.
4-6
ORG
-
90/10
A.
4-6
1976
50/10
12.3
12.3
-1.1
0.0
2.7
3.5
-12.3
-3.9
(2.3)
(4.0)
(2.5)
(4.1)
(1.7)
(2.0)
(1.3)
(2.4)
0.5
-5.4
4.0
3.2
7.3
17,2
-11.4
-9.2
(5.2)
(6.2)
(2.3)
(4.9)
(1.9)
(3.2)
(1.2)
(2.4)
0.3
-1.5
6.8
5.6
2.3
20.0
-4.1
-12.3
(5.2)
(5.9)
(3.2)
(4.7)
(3.2)
(3.1)
(2.0)
(2.8)
8.8
19.8
-1.2
1.5
12.7
16.2
-12.3
-8.9
(10.6)
(8.7)
(6.5)
(8.9)
(2.9)
(3.9)
(2.3)
(3.8)
Source data: May/ORG CPS 1975
2003 and March CPS 1976
2004.
on indicated year. Standarderrors in parentheses are bootstrapped using 100 replications. College
graduates are those with 16 or 17 years of completed schooling (surveys
prior to 1992) or a baccalaureate degree only (1992 forward). See the
Data Appendix for further details.
-
Statistics pool three years of data centered
-
Table 3. 100 x Changes in Female Hourly Earnings Inequality Within
Narrow Education and Experience Categories: 1976 to 1988 and 1988 to
2002 (May/ORG and March CPS)
High School Greiduate Females
College Gradijate Females
Potn'l
1976
Exp
ORG
-
1988
March
1988
-
ORG
2002
1976
March
ORG
14-16
24-26
34-36
16.2
10.6
0.6
14-16
24-26
34-36
14-16
24-26
34-36
-
2002
March
13.6
8.4
-14.2
0.4
(1-7)
(3.0)
(1.7)
(3.1)
(3.2)
(4.9)
(2.7)
(4.4)
7.8
-1.4
10.5
25.2
15.1
14.8
-11.7
-4.6
(3.4)
(1.6)
(3.1)
(5.8)
(7.1)
(2.8)
(5.1)
(1.9)
14.0
3.3
11.4
8.9
19.4
15.2
-6.1
-0.7
(5.2)
(8.9)
(2.4)
(6.9)
(2.8)
(4.2)
(1.9)
(3.2)
33.5
30.6
6.5
12.4
17.0
3.6
-6.4
9.1
(8.7)
(14.6)
(7.2)
(11.6)
(2.9)
(4.3)
(2.2)
(4.5)
90/50
4.7
9.2
4.5
2.5
5.3
2.5
-5.6
3.3
(2.4)
(3.1)
(1.9)
(2.7)
(1.4)
(2.4)
(1.6)
(2.7)
-0.7
-0.5
8.1
14.5
2.4
6.7
-4.9
-3.4
(3.8)
(5.3)
(2.4)
(3.0)
(2.1)
(2.3)
(1.3)
(2.3)
12.7
-2.0
8.0
10.2
7.7
8.1
0.1
-0.7
(4.0)
(4.4)
(2.3)
(3.3)
(2.6)
(2.9)
(1.6)
(2.5)
11.1
12.1
7.9
14.2
6.8
-2.7
0.5
2.1
(6.5)
(8.6)
(4.0)
(8.6)
(2.7)
(3.4)
(1.9)
(3.3)
C.
4-6
1988
ORG
1.3
B.
4-6
1988
March
90/10
A.
4-6
-
50/10
11.5
1.4
-3.9
-1.3
8.2
6.0
-8.7
-2.9
(2.1)
(4.0)
(2.0)
(3.5)
(1.1)
(2.3)
(1.2)
(2.2)
8.6
-0.9
2.4
10.7
12.7
8.1
-6.9
-1.3
(4.8)
(4,9)
(2.1)
(4.2)
(1.7)
(2.4)
(1.4)
(2.4)
1.3
5.3
3.4
-1.4
11.7
7.1
-6.2
0.0
(4.7)
(7.9)
(2.5)
(6.3)
(1.8)
(3.1)
(1.4)
(2.4)
22.4
18.5
-1.5
-1.8
10.2
6.4
-7.0
7.0
(6.9)
(12.0)
(6.6)
(8.9)
(2.3)
(3.0)
(1.8)
(2.8)
Source data: May/ORG CPS 1975
2003 and March CPS 1976
2004.
on indicated year. Standarderrors in parentheses are bootstrapped using 100 replications. College
graduates are those with 16 or 17 years of completed schooling (surveys
prior to 1992) or a baccalaureate degree only (1992 forward). See the
Data Appendix for further details.
-
Statistics pool three years of data centered
-
Table
4.
Quantile
JMP Decompositions
of Hourly Earnings Inequality into Price and Quantity
Components, May/ORG CPS 1973
(100 X log point
1973
Total
-
1988
1988
Quan-
Btwn
Within
tities
Prices
Prices
90-10
90-50
50-10
21.1
9.9
11.2
-1.0
16.8
0.4
-1.4
9.0
90-10
90-50
50-10
21.1
9.9
0.0
-3.0
14.4
11.2
3.0
4.5
7.9
9.9
Total
25.0
11.5
13.5
90-10
90-50
50-10
25.0
11.5
13.5
-
1973
2003
Btwn
Within
titles
Prices
Prices
Total
A. Males
Order: Quantities, Between B's, Witiiin B's
-3.8
5.3
7.9
4.8
7.0
29.0
0.6
12.7
0.5
8.1
4.1
22.6
-4.8
-1.2
-7.9
4.7
4.3
6.4
Order: Within B's, Between B's, Quantities
-1.3
6.7
7.9
4.3
4.9
29.0
3.0
12.7
0.5
5.3
5.9
22.6
-2.0
-7.2
3.7
-4.8
4.4
6.4
-
2003
Quan-
Btwn
Within
tities
Prices
Prices
22.7
17.0
2.6
3.0
0.6
5.7
0.0
6.8
-J.VJ
0.1
19.2
14.2
6.7
5.0
-5.3
10.7
12.5
11.9
4.1
6.7
10.3
6.6
5.9
1.5
3.6
2.6
3 n
8.3
Females
2.2
9.5
-2.4
5.3
3.6
3.7
Order: Quantities, Between B's, Witliin B's
13.3
10.3
5.0
5.1
0.2
35.2
6.0
9.6
1.8
3.1
4.8
21.1
-4.6
6.1
0.7
3.2
2.1
14.2
4.3
7.0
Order: Witliin B's, Between B's, Quantities
13.6
-3.0
10.3
10.1
3.2
35.2
13.6
10.7
1.2
3.2
7.1
9.6
2.3
3.6
3.7
21.1
3.9
8.0
10.9
9.2
3.2
3.8
6.5
0.7
7.9
-0.4
-6.8
14.2
9.7
2.7
1.7
Source data: May/ORG CPS 1973
procedure.
2003
Quan-
B.
90-10
90-50
50-10
-
changes)
-
2003. See text for details of quantile decomposition
Table
5.
Quantile
JMP Decompositions of Hourly Earnings
Components, March CPS 1975
(100 X
1975
Total
-
•
log point
1988
1988
Quan-
Btwn
Within
tities
Prices
Prices
Total
Inequality into Price and Quantity
2003
-
changes)
-
1975- 2003
2003
-
Quan-
Btwn
Within
titles
Prices
Prices
Total
Quan-
Btwn
Within
tities
Prices
Prices
A. Males
Order: Quantities, Between
B's, Witiiin B's
90-10
90-50
50-10
18.8
-0.6
8.2
11.1
13.4
2.1
5.6
5.7
32.1
2.8
14.3
15.1
9.5
-1.2
5.8
4.8
14.5
-1.4
6.3
24.0
1.2
11.5
11.2
9.3
0.6
2.4
6.3
-1.1
3.5
-0.7
9.6
-3.9
8.2
1.6
2.7
3.9
90-10
90-50
50-10
18.8
9.5
1.0
-1.1
6.4
4.0
9.3
2.1
2.4
Order: Within
11.4
13.4
6.6
14.5
4.7
-1.1
5.5
6.3
1.6
4.3
4.3
9.5
-1.6
2.1
9.0
19.7
3.9
2.0
7.8
4.5
2.3
3.0
-0.8
18.2
2.8
-1.5
6.5
4.6
7.1
4.3
2.0
7.5
23.9
10.2
13.7
90-10
90-50
50-10
23.9
10.2
13.7
Quantities
5.9
4.7
7.6
1.5
9.4
9.0
14.9
5.2
32.1
24.0
7.9
1.7
1.0
0.7
-2.8
8.2
6.3
0.4
1.4
Order: Quantities, Between B's, Witiiin B's
12.1
14.0
0.7
5.2
8.2
37.9
7.5
11.7
18.7
1.9
5.5
12.3
5.6
6.2
6.4
0.1
11.0
16.8
2.5
7.4
9.7
7.6
3.6
7.1
Order: Witiiin
14.5
14.0
Source data: March CPS 1976
procedure.
B's,
2.7
B.
90-10
90-50
50-10
Between
B's,
-
B's,
13.4
Females
Between
B's,
Quantities
4.6
4.9
9.5
4.5
-0.4
4.8
5.1
4.5
4.9
-0.2
-0.2
37.9
19.7
18.2
2004. See text for details of quantile decomposition
Table
6.
100 x Observed and Composition-Constant Changes
Overall Hourly Inequality Measures
A.
M ay/ORG CPS
B.
1973-
1988-
1973-
1975-
1988
2003
2003
1988
in
March CPS
198819752003
2003
A Male 90/10
Observed
1973 X's*
1988 X's
2003 X's
21.1
7.9
29.0
18.8
13.4
32.1
21.1
22.1
1.1
22.2
17.7
5.5
24.3
3.0
19.3
10.7
30.0
22.2
3.1
25.2
25.3
18.1
11.2
29.3
6.S
14.5
11.8
12.8
15.9
24.0
22.4
23.4
22.7
8.2
A Male 90/50
Observed
1973 X's*
1988 X's
2003 X's
9.9
12.9
12.7
9.5
7.4
12.2
9.5
12.2
22.6
22.5
21.8
19.6
9.5
10.6
10.7
A Male 50/10
Observed
1973 X's*
1988 X's
2003 X's
11.2
8.2
12.6
14.8
-4.8
5.4
93
-1.1
-8.5
-0.3
7.1
-5.3
1.8
-9.2
3.4
8.7
-2.1
5.5
-9.1
5.7
11.3
-4.6
6.5
23.9
21.1
18.4
14.0
5.7
17.1
13.3
37.9
27.8
27.9
30.4
A Female 90/10
Observed
1973 X's*
1988 X's
2003 X's
25.0
20.5
22.8
19.2
10.3
1.0
0.1
5.3
35.2
21.5
22.9
24.5
9.5
A Femahe 90/50
Observed
1973 X's*
1988 X's
2003 X's
11.5
9.5
21.1
10.3
6.9
17.1
12.9
7.4
20.3
8.6
9.9
18.5
9.1
7.9
17.0
6.7
11.1
17.8
10.2
11.7
19.7
17.2
9.5
5.5
A Femah2 50/10
Observed
13.5
0.7
14.2
13.7
-5.9
1973 X's*
10.3
4.5
9.4
-7.2
1988 X's
9.9
2.5
9.8
-2.5
2003 X's
10.1
10.4
7.5
Source data: May/ORG CPS 1973 - 2003 and March CPS
4.5
18.2
1.2
10.7
-0.4
9.4
12.5
2,2
1975
-
2004.
Table
7.
100 x Observed and Composition-Constant Changes
in
Residual Hourly Inequality l^easures
May/ORG CPS
A.
B.
1973-
1988-
1973-
1975-
1988
2003
2003
1988
March CPS
198819752003
2003
A Male 90/10
Observed
1973 X's*
1988 X's
2003 X's
10.2
0.4
10.6
13.2
7.6
11.5
-5.1
6.4
14.3
3.7
18.1
11.4
10.3
-3.6
7.8
6.3
20.1
-2.1
8.1
13.8
12.5
7.0
19.6
7.3
13.1
20.8
A Male 90/50
Observed
1973 X's*
1988 X's
2003 X's
3.6
2.9
6.6
5.8
5.8
1.5
7.3
6^
6.0
3.6
2.3
5.9
6.1
5.8
12.3
13.0
1.6
2.5
4.1
5.3
7.6
12.9
A Male 50/10
Observed
1973 X's*
1988 X's
2003 X's
6.6
-2.5
4.1
7.4
0.3
7.7
5.7
-6.6
-0.9
8.0
-2.3
5.7
7.7
7.2
-0.5
7.2
-0.5
6.7
6.7
21.4
2.0
15.5
3.9
17.3
5.8
20.1
11.2
7.8
-5.9
1.9
8.7
-4.6
4.1
A Female 90/10
Observed
1973 X's*
1988 X's
2003 X's
15.9
3.1
19.0
13.5
-1.5
12.0
13.8
-2.6
11.2
14.7
13.5
13.4
13.6
-0.6
13.0
14.3
A Female 90/50
Observed
1973 X's*
1988 X's
2003 X's
7.5
2.4
9.9
5.9
5.3
6.9
-0.5
6.3
6.6
1.6
8.2
6.5
-0.4
6.0
5.4
3.7
9.1
5.6
1.9
7.5
5.0
5.9
10.9
10.2
A Female 50/10
Observed
8.4
0.7
-1.0
1973 X's*
6.6
-2.2
1988 X's
7.3
-2.4
2003 X's
7.9
Source data: May/ORG CPS 1973
-
9.1
8.9
1.4
5.7
6.9
0.4
7.3
5.1
8.0
0.2
8.2
5.5
9.3
-0.1
2003 and March CPS 1976
9.1
-
2004.
Appendix Table
1.
100 x Changes
1973
A. Overall
I
in
-
Overall and Residual Full-Time
2003: May/ORG and March CPS
nequality
1973- 1988- 19731988 2003 2003
Weekly Earnings Inequality,
B.
1979- 1989- 19791989 1999 1999
Residual Inequal ity
1973- 1988- 1973-
1979- 1989- 1979-
1988
1989
2003
2003
1999
1999
Males
May/ORG CPS
90-10
90-50
50-10
34.0
16.4
17.6
9.6
11.6
-2.0
43.6
28.0
15.6
26.9
17.4
9.6
5.6
6.8
-1.2
32.5
24.2
24.9
13.3
13.4
8.3
11.7
28.5
11.8
10.2
5.6
38.7
17.4
5.2
38.3
21.5
16.8
16.7
4.6
21.3
8.2
March CPS
90-10
90-50
50-10
23.2
9.8
17.9
15.7
13.4
2.2
41.2
25.5
15.7
20.
11.2
9.6
10.3
10.5
31.3
21.7
17.5
10.4
28.0
12.8
6.3
7.0
8.8
15.8
6.1
5.0
19.0
11.1
0.0
9.6
10.5
1.6
12.2
6.7
1.3
8.0
Females
May/ORG CPS
90-10
90-50
50-10
22.3
8.6
13.7
10.4
13.7
3.3
36.0
19.0
17.0
24.6
7.4
17.2
12.6
7.8
4.8
37.2
15.2
16.1
8.4
3.2
18.6
5.4
24.5
15.0
15.4
9.6
5.1
3.6
8.8
22.0
6.5
3.0
9.5
10.2
-0.4
9.8
25.2
15.0
10.2
18.8
2.6
21.4
5.8
3.3
9.1
13.0
-0.6
12.3
March CPS
90-10
90-50
50-10
18.5
6.8
11.7
8.7
8.0
0.7
27.2
14.8
12.3
Source data: May/ORG CPS 1973
14.5
4.7
19.2
19.5
5.7
6.7
4.4
11.1
9.7
5.3
7.9
0.3
8.1
9.8
0.4
-
2003 and March CPS 1974
-
2004.
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Appendix Table 3a. Quantile JMP Decompositions of Hourly Earnings Inequality into Price and
May/ORG CPS 1973 - 2003: Model Using Quartic in Potential Experience
(100 X log point changes)
^
Quantity Connponents
1973
Total
-
1988
1988
Quan-
Btwn
Within
titles
Prices
Prices
Total
-
2003
1973
Quan-
Btwn
Within
titles
Prices
Prices
Total
-
2003
Quan-
Btwn
Within
titles
Prices
Prices
A. Males
Order: Quantities,
90-10
90-50
50-10
21.9
11.3
10.6
90-10
90-50
50-10
21.9
Between
B's, Within B's
7.0
-3.7
11.0
4.9
0.7
7.1
3.1
-2.8
4.1
-0.2
-6.8
30.0
22.3
7.7
23.3
17.4
3.6
2.3
0.8
5.9
1.0
Order. Within B's, Between B's, Quantities
-2.4
7.5
8.1
5.5
5.1
30.0
0.0
15.7
6.2
8.1
0.5
-0.5
9.6
1.3
6.1
5.0
13.6
11.3
0.8
-0.9
8.6
3.7
10.6
1.7
5.0
3.9
2.6
8.8
17.4
3.9
0.8
5.5
4.6
22.3
1.2
4.7
-0.5
-7.0
7.7
7.6
12.9
4.5
8.2
-4.4
Order: Quantities, Between B's, Witiiin B's
12.5
9.9
4.8
5.1
0.0
35.0
8.4
14.8
11.7
3.1
7.9
10.0
5.3
6,9
1.7
12.0
12.4
10.6
3.2
8.5
9.3
8.8
3.8
1.3
11.0
-2.8
B.
Females
90-10
90-50
50-10
25.1
12.3
12.8
1.8
-0.5
10.8
5.7
7.1
8.8
1.1
3.3
4.5
2.3
5.1
5.5
1.1
3.7
1.8
-4.5
90-10
90-50
50-10
25.1
12.3
3.5
8.5
13.1
9.9
9.0
3.4
-2.6
1.2
4.2
6.9
8.8
2.6
3.2
3.1
12.8
2.3
4.3
6.2
1.1
6.5
0.3
-5.7
Order: Witiiin
Source data: May/ORG CPS 1973
procedure.
3.1
-
B's,
Between
21.1
13.9
B's, Quantities
35.0
21.1
13.9
2003. See text for details of quantile decomposition
Appendix Table 3b. Quantile JMP Decompositions of Hourly Earnings Inequality into Price and
Quantity Components, March CPS 1975 - 2003: Model Using Quartic in Potential Experience
(100 X log point changes)
1975
Total
-
1988
1988
Quan-
Btwn
Within
tities
Prices
Prices
Total
-
2003
1975
Quan-
Btwn
Within
titles
Prices
Prices
A.
Total
-
2003
Quan-
Btwn
Within
tities
Prices
Prices
10.0
Males
Order: Quantities, Between B's, Within B's
90-10
90-50
50-10
17.5
8.3
90-10
90-50
50-10
-1.0
9.8
8.7
10.3
2.6
3.7
4.0
16.2
5.9
2.1
12.9
-0.5
3.5
9.9
27.8
21.2
1.6
1.9
11.8
7.6
9.2
0.3
-1.3
3.9
6.6
-2.6
3.1
0.2
-5.9
6.6
-0.2
4.4
2.5
17.5
-0.3
8.2
6.6
8.3
-0.8
4.8
1.4
11.4
8.2
11.7
9.2
0.5
3.4
5.2
3.3
-1.9
13.1
Order: Within B's, Between B's, Quantities
9.6
10.3
23 4.8 3.0
27.8
-0.2
4.4
12.9
4.4
8.7
21.2
-5.7
-2.6
5.2
2.7
0.4
6.6
B.
Females
Order: Quantities, Between
B's, Wittiin B's
90-10
90-50
50-10
18.6
9.5
2.3
7.7
8.6
13.5
1.9
5.7
5.9
0.3
3.8
5.4
8.4
-1.4
3.8
6.1
9.1
2.0
3.9
3.2
5.1
3.3
2.0
-0.2
90-10
90-50
50-10
18.6
1.0
6.6
11.0
9.5
-0.7
3.9
9.1
1.7
2.6
Order: Within
Source data: March CPS 1976
procedure.
-
B's,
9.8
Between
B's,
32.2
17.9
14.2
5.6
13.5
0.9
8.1
8.9
4.6
5.4
4.3
10.0
10.3
11.8
1.6
7.5
8.8
8.4
2.8
3.0
Quantities
5.7
4.9
3.0
6.3
13.5
8.4
0.5
4.0
3.9
4.7
5.1
5.2
0.9
-0.9
32.2
17.9
14.2
2004. See text for details of quantile decomposition
1
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Li
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r
33
MAR 2
4 2006
Date Due
MIT LIBRARIES
3 9080 02527 9669