The Gender Earnings Gap: Measurement and Analysis

Esfandiar Maasoumi
Emory University
Le Wang
University of New Hampshire, Harvard University, & IZA
Abstract
When summary measures of latent concepts such as the gender gap fail to be adequately represen-
tative, one must seek better denitions and measures. This paper presents a set of complementary
concepts and measurements of the gender gap that move beyond the traditional summary compar-
isons of the earnings distributions. In particular, we propose a new concept of the gender gap
based on the the distance between entire distributions with compelling properties: It is free of
outlier eects, is capable of representing populations with heterogeneous gaps at dierent parts of
the outcome distributions, and is invariant to increasing transformations. When the gender gap is
dierent or of even dierent sign at dierent quantiles, subjective comparisons become inevitable
in any summary, cardinal comparisons. In response, we introduce tests based on stochastic domi-
nance to allow for uniform rankings of the earnings distributions between men and women. Using
the Current Population Survey data, we rst construct a new series on the gender gap from 1976
to 2011 in the United States. We nd that traditional representative or moment-based mea-
sures underestimate a declining trend in the gender gap during this period. More important,
these traditional measures do not necessarily reect the cyclicality of the gender dierentials in
earnings distributions, and may even lead to false conclusions about how labor market conditions
are related to the gender gap at the aggregate level. Second, while we nd rst-order stochastic
dominance in most cases, even for the recent recession where men were hit harder, we also nd a
few instances where denite conclusions regarding the gender gap cannot be drawn at all or only
under more restrictive social evaluation functions. Finally, we conduct full distribution counter-
factual analysis which suggests that, in many cases, altering the earnings structure would be more
eective in improving womens welfare (reducing discrimination) than would changing human
capital characteristics.
The authors would like to thank seminar participants at Bentley University, Union College,
Emory University, and University of New Hampshire for their helpful comments.
1
1. Introduction
Studying the gender gap, generally referencing the earnings dierences between men and
women, is an important undertaking. It is at the core of social sciences to understand
inequality/inequity in a society, as well as the labor market outcomes, and helps shed light on
potential policy directions. Policy makers and economists are interested in several questions.
One is, How large is the gender gap? Another is, How do women generally fare compared
to men in the labor market? We emphasize the question of What is the gender gap,
quantitatively speaking? The answers to these questions are more complex than is implicitly
assumed in many of the current responses. They require a careful analysis of the earnings
dierentials between groups. When summary notions of the gap, such as average/mean
or median earnings dierentials fail to be representative of diverse magnitudes and signs at
dierent parts of the earnings distribution, the very notion of the gap is itself in need
of reection and innovation. This paper oers some proposals in this regard, and develops
the statistical means for implementing them. We oer alternative summary measures to
dene the gap, as well as rigorous means of dening and testing rankings between entire
distributions.
Conventional wisdom about the gender gap is that women do not fare as well as men
do in the labor market. Often cited to support this view is the examination of the earnings
dierentials between average or median men and women (e.g. Polachek, 2006; Blau and
Kahn, 2006). The sign of the dierence tells us which group fares better in the labor market,
and the magnitude is a measure of the severity of the situation. Although useful, the gender
dierences reported by these summary measures may not represent the gender earnings
gap in all parts of the whole distribution of earnings. This is especially so when the sign
and/or magnitude of the gap is dierent at dierent quantiles of the earnings distribution.
Researchers are increasingly aware of these issues, and dierences at other parts of the
earnings distributions (e.g quintiles and percentiles) are also reported in recent years. These
dierent summary statistics greatly improve our understanding of the extent and location
2
of the gender gap, but may still present a bewildering view of the distribution of the gap,
both at a given point in time, and its evolution over time. Better and more comprehensive
summary measures can help.
All summary measures are aggregation devices which assign subjective, explicit and im-
plicit weights to dierent groups and parts of distributions (high and low earners, for exam-
ple). This calls for an examination of potential uniformrankings that are robust to the
subjective weight distributions/welfare functions that underlie summary measures.
To make some of our points more concrete, consider the following numerical examples
for a society with only two men (MA and MB) and two women (FA and FB).
Example 1 The dierence in earnings between FA and MA (who have similar char-
acteristics other than gender) is $200, and that between FB and MB is $500 (also
with similar characteristics other than gender). A typical measure, the average dier-
ence, suggests that the gender gap is $350. However, the average person here is not
representative. And reporting either $200 or $500 would also ignore the other
half of the society and consequently would not summarize the situation well. Note that
in this example, at least the summary measure as well as the quantile dierences are
all negative, implying that men fare better than do women in the labor market.
Example 2 The dierence in earnings between FA and MA is $200, but that between
FB and MB is now $200. The average gender gap is $0! Again, this fails to be
representative, since it suggests there is no gender gap at all. Both the $200 and
$200 strongly misrepresent the rest of the society. Compared to Example 1, only
extremely subjective weights would support any ranking. Since these dierences are
of opposite signs, they suggest dierent rankings of the earnings distributions between
men and women. Any conclusions would be based on an arbitrary weighting scheme.
Example 3 Consider another example similar to the second one but with more in-
formation on actual earnings for each individual. MA earns $55, 000 and FA $54, 800.
3
MB earns $1200 and FB $1, 000. The dierence at both parts of the distribution is
$200, and in one direction. The average gap of 200 would give the same weight what-
ever the level of earnings. Given the additional information on each persons earnings,
greater aversion to inequality may give greater weight to the dierence in the lower
tail, concluding existence of a greater gender gap in favor of men. However, these
types of subjective preferences are usually not explicitly stated alongside summary
measures. The typical utility function in economics is a von Neumann-Morgenstern
type function, being increasing and concave. Can we empirically identify situations in
which the gender gap will be ranked uniformly by all observers subscribing to any
member of a family of utility functions?
The measurement problem would be even more acute when examining the time trend
of the gender gap. The timing of temporal deviations from the long-run trend could vary
across dierent measures, which could in turn lead to, for instance, a confused sense of the
impact of business cycles on the gender gap. We rst propose a distributional measure of
the gender gap based on the normalized Bhattacharay-Matusita-Hellinger entropy measure
proposed by Granger et al. (2004). One important feature, among others, of this measure
is its ability to summarize the distance between two entire distributions, instead of binary
dierences at dierent parts of the distributions. Another advantage of our measure is its
invariance to transformations, generally, and to log earnings transformation, particularly.
Second, we employ stochastic dominance (SD) tests to rank the earnings distributions. The
SD tests have been widely used to analyze poverty issues and nancial outcomes, but not to
analyze the gender earnings gap. The advantage of our SD approach is its explicit welfare
underpinning, utilization of the entire earnings distributions, and ability to yield uniform
rankings of distributions that are robust across a wide class of welfare functions, as well
as underlying (and unknown) earnings distributions. Inferring a high dominance relation
implies that comparisons based on multiple measures, while supported, are often unnecessary.
Moreover, the inability to infer a dominance relation is equally informative, indicating that
4
any ranking must be based on a particular weighting scheme or a specic welfare function.
In the latter instances, conclusions are revealed to be highly subjective and may not be
conducive to consensus policy-making.
Our methodology here is broadly applicable, including to counterfactual analysis of pol-
icy experiments, in which one compares the potential outcome distribution for individuals
impacted by a policy with their actual outcomes. Policymakers and economists are often
interested in certain policies to bridge the gender gap and improve the well-being of women.
These policies can be loosely classied into two groups: (1) policies aimed at changing wom-
ens pay structure and (2) policies aimed at changing their observable characteristics that
aect their earnings. These types of policies are related to two major reasons that many
believe explain the dierences in earnings between women and men: dierences in wage
structure and dierences in human capital characteristics. The former is often identied
with discrimination. It is useful to provide an assessment of the changes in the potential
earnings among women resulting from any implemented policy. To evaluate a policy, we
need to compare the original earnings distribution with the potential earnings distribution
resulting from a policy. We employ new developments for identifying counterfactual earn-
ings distributions based on estimated inverse probability weighting methods, see Fortin et al.
(2011).
To illustrate our proposals, we utilize the Current Population Survey (CPS) data 1976
- 2011 in the U.S. for our empirical analysis. We reach several conclusions. First, we nd
that traditional summary measures severely underestimate the declining trend of the gender
gap in the U.S. In particular, our entropy gender gap measure implies the gap narrowed at
an average annual rate of about 11% during the period 1976-2011, while the largest annual
rate recorded by conventional measures (based on the median) is only 5.2% during the same
period. It may be helpful to note that, entropy measures are functions of all the moments of a
distribution, much as moment generating functions. As such, they gauge the convergence
between the entire distributions for men and women accordingly. Our measure may thus
5
be seen as a broad measure. The broad measure of gender gap dropped precipitously
before 1990s, but the convergence has drastically slowed down since. Moreover, even though
all measures show a consistently declining trend of the gender gap, the timing of temporal
deviations from the long-run varies across dierent measures, which in turn can lead to a
false reading of the impact of business cycles on the gender gap. Our measure indicates
that our broad measure of the gender gap is relatively insensitive to changes in economic
conditions, except around 2001.
Second, comparing the actual earnings distributions, we generally observe rst-order
stochastic dominance to a degree of statistical condence throughout the sample period,
implying that men have generally performed better in the labor market. To our surprise,
we nd dominance even for the beginning of the recent recessionary period when men were
viewed as having been hit harder than women. This conclusion is robust to a wide class of
increasing social welfare functions. However, we do nd several cases where the relation is
only second-order, and one case where no statistically meaningful dominance exists. In these
cases, the inference that men fare better than do women is only supported by a narrower class
of social welfare functions that are both increasing and increasingly averse to inequality
(concave). Moreover, it is less likely to nd statistically signicant rst-order dominance
relations during the pre-1994 period. These results altogether suggest that womens labor
market situation has over time improved relative to mens. Nevertheless, strong evidence of
dominance relations in most cases indicates that the improvement is still far from satisfactory;
this result casts doubt on the broad eectiveness of the reforms intended to improve womens
relative labor market outcomes.
Finally, combining the methods proposed here and the recent development in identi-
cation of counterfactual analysis, we compare the actual female earnings distribution with
two female counterfactualdistributions: (a) women earning distribution under the earnings
structure of men (discrimination) and, (b) women earnings distribution should they have
mens characteristics. The former captures structural eects and the latter composition ef-
6
fects. We nd that structural eects are generally more important than composition eects.
However, the importance of structural eects has declined over time, while that of composi-
tion eects has increased. Our SD results indicate that policies aimed at changing womens
pay structure are generally eective in improving womens earnings prospects, while policies
aimed at changing womens human capital characteristics are not. However, for policies
aimed at changing pay structure, we fail to nd rst-order dominance, even second-order
dominance, to a statistical degree of condence, in a few cases. This implies that there are
winners and losers, and broad policy conclusions cannot be drawn without imposing
more subjective weights on subgroups through narrower well being functions. We want to
emphasize that the two thought experiments conducted here are by no means precisely iden-
tied with specic policies. However, they do represent the traits of the policies generally
considered for relative improvement in womens labor market outcomes. Working through
such exercises using our proposed tools illustrates the importance of these tools in a broader
analysis of the gender gap.
While in this paper we focus on measurement and analysis of the broad gender earnings
gap, we believe that our research could be further extended along several dimensions. First,
our approach could be readily adapted to measure and analyze other types of earnings
distances, such as advantaged vs. disadvantaged groups (e.g. white v.s. black the racial
gap). Second, in this paper we focus on the earnings as the only attribute of welfare.
However, researchers have long recognized that welfare involves not only earnings but other
attributes such as health, and, as a result, a growing literature has developed investigating
multi-dimensional welfare measures that take into account earnings and other factors jointly
(e.g. Wu et al., 2008). Our approach is constructed over the space of distributions and
can be seamlessly applied to univariate and multi-outcome contexts. Finally, aggregate time
series of our distributional measure of the gender gap, once obtained, can be used for further
empirical analysis. For example, Biddle and Hamermesh (2011) has noted that little is known
about how wage dierentials vary with the extent of labor market conditions. Our measure
7
can directly be used for this purpose (in the spirit of Ashenfelter (1970)) to examine the
aggregate relationship between the gender gap and the aggregate unemployment rate.
The rest of the paper is organized as follows. Section 2 presents the empirical meth-
ods employed; Section 3 describes the data; Section 4 discusses the results, and Section 5
concludes.
2. Empirical Methodology
2.1. Basic Notations
To begin, let ln(w
f
) and ln(w
m
) denote the log of earnings for females and males, respec-
tively. We observe a random sample of N = N
0
+ N
1
individuals. {ln(w
f
)}
N
1
i=1
is a vector
of N
1
observations of ln(w
f
) (denoted by D
i
= 1); similarly, {ln(w
m
i
)}
N
0
i=1
is a vector of N
0
observations of ln(w
m
) (denoted by D
i
= 0). Let F
1
(y) Pr[ln(w
f
) y] represent the
cumulative density function (CDF) of ln(w
f
) (i.e. the log of earnings for females) and f
1
(y)
the corresponding probability density function (PDF); F
0
(y) and f
0
(y) are similarly dened
for ln(w
m
) (i.e. the log of earnings for males). Individual earnings are determined by both
observable characteristics X
i
and unobservable characteristics
i
via unknown wage structure
functions,
ln(w
d
i
) = g
d
(X
d
i
,
d
i
) d = m, f
This specication implies that the gender gap is from three sources: (1) dierences in the
distributions of observable human capital characteristics X
d
i
(e.g. years of schooling); (2)
dierences in the distributions unobservable human capital characteristics
d
i
(e.g. innate
ability); (3) dierences in the wage structures, g
d
(). Note that these wage functions are not
restrictive and allow for complicated interactions among X
d
i
and
d
i
.
2.2. A Distributional Measure of the Gender Earnings Gap
Usually, the gender gap is dened as the dierence in certain parts (or functionals)
of the earnings distributions between males and females. For example, average gender
8
gap is the dierence in the means of the earnings distribution between men and wom-
en (E[ln(w
m
i
)] E[ln(w
f
i
)]) (where the mean is the rst moment of the earnings distribu-
tion). The gender gap at a p
th
quantile is ln(w
m
i
)
p
ln(w
f
i
)
p
, where the p
th
quantile of F
0
(the CDF for womens wage distribution) is given by the smallest value ln(w
f
i
)
p
such that
F
1
(ln(w
f
i
)
p
) = p; ln(w
m
i
)
p
is similarly dened for F
1
(the CDF for mens wage distribution).
Even though these measures are all functionals of the wages distributions, none of them is
able to summarize the information in the whole distribution. This problem is particularly
acute when the measures dier in terms of magnitudes and sizes across dierent measures
used. Hence, needed is a distributional measure of the gender gap, or a measure of the
distances in the earnings distributions between females and males.
Several commonly used information-based entropy measures such as Shannon-Kullback-
Leibler are available to measure the information at the distributional level. However, Shan-
nons entropy measure as well as almost all other entropy measures are not metric; these
measures violate the triangularity rule and hence cannot be used as a measure of distance.
To this end, we use a metric entropy measure S

proposed in Granger et al. (2004), which

is a normalization of the Bhattacharya-Matusita-Hellinger measure of distance. It is given
by
S

=
1
2

(f
1
2
1
f
1
2
0
)
2
dy (1)
This measure satises several desirable properties as a distance metric between entire
distributions: (1) it is well dened for both continuous and discrete variables;
1
(2) it is
normalized to zero if Y
1
and Y
0
are equal, and lies between 0 and 1, (3) it is a metric and
hence a true measure of distance, (4) it is invariant under continuous and strictly increasing
1
Although (1) presumes that the variables are continuous, one can easily adapt this measure to the case
of discrete variables, S

=
1
2

(p
1
2
1
p
1
2
0
)
2
where p
1
(p
0
) is the marginal probability of the random variable Y
1
(Y
0
). This generalization allows us to measure the dierences in a broader set of outcomes between groups
at the distributional level.
9
transformation h() on the underlying variables.
2
Recall that following the literature we
utilize the log of earnings as the variable of main interest. Since the log is a strictly increasing
function, our measure of the gender gap is the same, whether we use the raw wages or the log
of it. Moreover, entropies are dened over the space of distributions and are consequently
dimension-less as it applies to univariate and multivariate contexts. Economists have been
increasingly aware of the fact that evaluation of individual well-being is inevitably a multi-
attribute exercise (Lugo and Maasoumi, 2008). This feature may become very useful when
we consider the multidimensional gender gap measure to incorporate attributes other than
wages.
Following Granger et al. (2004) and Maasoumi and Racine (2002), we consider a robust
nonparametric kernel-based implementation of (1) (The computer code -srho- written by
the authors in Stata is also available upon request). In our illustrative example below,
we use Gaussian kernels and a more robust version of the normal reference rule-of-thumb
bandwidth (= 1.06 min(
d
,
IQR
d
1.349
)n
1/5
, where
d
, d = m, f is the sample standard deviation
of {ln(w
d
i
)}
N
d
i=1
; IRQ
d
is the interquartile range of the sample d.). Interested readers are
referred to Li and Racine (2007) for more sophisticated bandwidth selection procedures.
Integrals are numerically approximated by the integrals of the tted cubic splines of the data,
which give superior results for most smooth functions (StataCorp, 2009). The asymptotic
distribution of the feasible measure has been derived by Skaug and Tjostheim (1996) and
Granger et al. (2004). However, these asymptotic approximations are well known to perform
very poorly in almost every case examined. As a result, in the analysis below, we instead
employ bootstrap re-sampling procedure based on 299 replications to obtain critical values
of hypothesis testing of H
0
: S

= 0.
Our entropy measure of gender gap gives us information on the strong ranking of two wage
distributions. However, it does not directly tell us which distribution is (weakly) uniformly
2
Integrated squared norm (L2) also shares many of these properties, but it is not normalized and is not
invariant to transformations. And it is also thought to be more sensitive inliers and outliers (Hart, 1997).
10
better relative to large classes of welfare functions. and under what conditions. Below, we
explicitly introduce these concepts to rank/compare two distributions.
2.3. Stochastic Dominance
We employ recent tests for Stochastic Dominance (SD) to enable uniform welfare com-
parisons of the earnings distributions between females and males (ln(w
f
) and ln(w
m
)). The
SD approach identies for which class of social welfare functions rankings of the earnings
distributions are possible. In this paper, we consider two classes of social welfare functions
that are commonly used in economics and nance. Let U
1
denote the class of all increasing
von Neumann-Morgenstern type social welfare functions u such that welfare is increasing in
wages (i.e. u

0), and U
2
the class of social welfare functions in U
1
such that u

0 (i.e.
concave). Concavity implies an aversion to higher dispersion (or inequality, or risk) of wages
across individuals. We are interested in the following scenarios:
Case 1 (First Order Dominance):
Male Earnings (ln(w
m
)) First Order Stochastically Dominates Female Earnings (ln(w
m
))
(denoted ln(w
m
) FSD ln(w
m
)) if and only if
1. E[u(ln(w
m
))] E[u(ln(w
f
))] for all u U
1
with strict inequality for some u;
2. Or, F
0
(y) F
1
(y) for all y with strict inequality for some y.
Case 2 (Second Order Dominance):
Male Earnings (ln(w
m
)) Second Order Stochastically Dominates Female Earnings (ln(w
f
))
(denoted ln(w
m
) SSD ln(w
f
)) if and only if
1. E[u(ln(w
m
))] E[u(ln(w
f
))] for all u U
2
with strict inequality for some u;
2. Or,

F
0
(t)dt

F
1
(t)dt for all y with strict inequality for some y.
11
These two cases imply rankings of the earnings distributions under dierent conditions.
Specically, if the case 1 holds (ln(w
m
) FSD ln(w
f
)), then the earnings distribution among
men is better than that among women for all policymakers with increasing utility functions
in the class U
1
(with strict inequality holding for some welfare function(s) in the class),
since the expected social welfare from ln(w
m
) is larger or equal to that from ln(w
f
). Note
that ln(w
m
) FSD ln(w
f
) implies that the average male wages are greater than the average
female wages. However, a ranking of the average wages does not imply that one FSD the
other; rather, the entire distribution matters (Mas-Colell et al., 1995, p.196). Similarly,
if (ln(w
m
) SSD ln(w
f
)), then the earnings distribution of males is better than that of
females for all those with any increasing and concave welfare functions in the class U
2
(with strict inequality holding for some utility function(s) in the class). Note that FSD
implies SSD. One immediate advantage of this approach is that our conclusions do not
depend on any specic wage distributions and/or weights assigned to subgroups within then
population. This approach is thus able to yield uniform rankings of distributions that are
robust across a wide class of welfare functions, rendering comparisons based on specic
indices unnecessary, but possible and more broadly supported. Higher order SD rankings
are based on narrower classes of welfare functions. For instance, Third Order dominance is
associated with welfare functions with increasing aversion to inequality which place greater
weight on welfare improving transfers at the lower tails of the earnings distribution.
In this paper, we employ stochastic dominance tests based on a generalized Kolmogorov-
Smirnov test discussed in Linton et al. (2005) and Maasoumi and Heshmati (2000). The
Kolmogorov-Smirnov test statistics for FSD and SSD are based on the following functionals:
d =

N
0
N
1
N
0
+N
1
min sup[F
1
(y) F
0
(y)] (2)
s =

N
0
N
1
N
0
+N
1
min sup

[F
1
(t) F
0
(t)]dt (3)
12
The test statistics are based on the sample counterparts of d, and s by replacing CDFs with
empirical ones; the empirical CDFs are given by

F
1
(y) =
1
N
1

N
1
i=1
I(ln(w
f
i
) y), where
I() is an indicator function;

F
0
(y) is similarly dened. The underlying distributions of the
test statistics are generally unknown and depend on the data. Following the literature (e.g.
Maasoumi and Heshmati, 2000; Millimet and Wang, 2006), we use bootstrap techniques
for iid samples based on 299 replications to obtain the actual sampling distributions of the
test statistics. This approach estimates the probability the statistics falling in any desired
interval, as well as indicate where the sample value of the test statistic lies. For instance,
if the probability of d lying in the non-positive interval (i.e. Pr[d 0] is large, say .90 or
higher, and

d 0, we can infer FSD to a high degree of statistical condence. We can infer
SSD based on s and Pr[s 0] in a similar fashion. All technical details are presented in
Appendix 1.
2.4. Counterfactual Distributions
We are often interested in assessing two types of counterfactual situations: First, what
if we interchange the wage structure of women with the wage structure of men, holding the
distribution of womens human capital characteristics constant? Second, what if we change
the distribution of womens human capital characteristics to that of mens, holding the wage
structure unchanged? Will these counterfactual distributions be dierent from the original
one? Will these dierences necessarily cover any distance between the earnings distribution-
s? Our proposed approaches can be readily applied to answer these counterfactual questions
by measuring the distances between the female earnings distribution and the counterfactual
distribution, and by ranking them. An important step is to identify the counterfactual dis-
tributions of interest. Specically, we want to identify the following counterfactual outcome
distributions:
ln(w
c1
i
) = g
0
(X
i1
,
i1
) (Counterfactual Outcome #1) (4)
ln(w
c2
i
) = g
1
(X
i0
,
i0
) (Counterfactual Outcome #2) (5)
13
F
c1
(f
c1
) represents the corresponding CDF (PDF) of the counterfactual outcome ln(w
c1
i
).
F
c2
(f
c2
) represents the corresponding CDF (PDF) of the counterfactual outcome ln(w
c2
i
).
Notice that the dierences in the distributions of F
c1
and F
1
(ln(w
c1
i
) v.s. ln(w
f
i
)) come
from dierences in wage structures; the comparisons of these two distributions thus provide
insight into potential discrimination. On the other hand, the dierences in the distributions
of F
c1
and F
1
(ln(w
c2
i
) v.s. ln(w
f
i
)) come solely from dierences in the distribution of human
capital characteristics; the comparisons thus provide some insight into the gender gap due
to productivity dierences across gender.
As shown in Firpo (2007, Lemma 1), the counterfactual distributions are identied under
the following assumptions:
[A1.] Unconfoundedness/Ignorability: Let (D, X, ) have a joint distribution. For all
x, is independent of D conditional on X = x, where, as dened above, D = 1 for
females and D = 0 for males; X, are observable and unobservable human capital
characteristics, respectively.
[A2.] Common Support: For all x, 0 < p(x) = Pr[D = 1|X = x] < 1.
The counterfactual outcome CDF of ln(w
c1
i
) is identied and F
c1
= E[
c1
(D, X) I[(ln(w
i
)
y)], where
c1
(D, X) = (
p(x)
1p(x)
) (
1D
p
). The counterfactual outcome CDF of ln(w
c2
i
), F
c2
,
is similarly identied. In practice, the scorep(x) is estimated by probit or logit. Here we
employed probit. p is the unconditional probability over the corresponding characteristics
X. Both assumptions (A1) and (A2) are commonly used in the literature. Assumption
(A1) implies here that given the values of observable human capital characteristics X, the
distribution of unobservable human capital characteristics such as ability is independent of
gender. Assumption (A2) rules out the possibilities that a particular value x belongs to
either male or female and that the set of wage determinants, (X, ) dier across gender.
Interested readers are referred to e.g. Fortin et al. (2011) for detailed explanations of these
two assumptions. p(x) is the selection probability (score) for each indidual. It is estimated
by a Logit model of a set of commonly employed characteristics X; see below for descrip-
14
tions. Once we identify the counterfactual distributions of interest, we can then perform our
counterfactual analysis using the approaches discussed above.
3. Data
To perform our analysis, we use data from the 1976-2011 March Current Population
Survey (CPS) (available at http://cps.ipums.org, King et al., 2010). The March CPS is
a large nationally representative household data that contain detailed information on labor
market outcomes such as earnings and other characteristics needed for our counterfactual
analysis. It thus has been widely used in the literature to study the gender gap (e.g. Wald-
fogel and Mayer, 2000). We begin at 1976 since it was the rst year that information on
weeks worked and hours worked are available in the March CPS. We restrict our sample to
individuals aged between 18 and 64 who work only for wages and salary. To ensure that our
sample includes only those workers with stronger attachment to the labor market, we include
only those who worked for more than 20 weeks (inclusive) in the previous year. Moreover,
we exclude part-time workers who worked less than 35 hours per week in the previous year.
Following the literature (e.g. Blau and Kahn, 1997), we use the log of hourly wages,
measured by an individuals wage and salary income for the previous year divided by the
number of weeks worked and hours worked per week. The dierences in the distributions
of log hourly wages between men and women are our measures of the gender gap. The
dierences in a specic part of the distribution can be interpreted as percentage dierences.
Note, however, that our distributional measure of the gender gap and SD tests are invariant
to increasing monotonic transformation, while conventional measures of the gender gap are.
In our counterfactual analysis, we include age, age squared, education (four education
groups: Below high school, High School, 1-3 years of College, and College and Above),
current marital status (1 if non-married and zero otherwise), race (1 if non-white and zero
otherwise), and region (northeast, midwest, south, and west). We also include occupations
which are divided into three categories: high-skill (managerial and professional specialty
15
occupations); medium-skill (technical, sales, and administrative support occupations); and
low-skill(other occupations such as helpers, construction, and extractive occupations).
4. Results
4.1. Baseline Analysis
4.1.1. Trend of the Gender Gap 1976 - 2011
Table (1) reports a number of popular measures of the gender gap. Column (1) displays
our distributional measure of the gender gap S

. Recall that, S

is normalized, taking values

in [0, 1], and to facilitate the presentation, the results reported are the original values 100
throughout the paper. The critical values based on 299 replications are reported in Table
(??), columns (1)-(3). Columns (2) and (7) in Table (1) display the gender gap measured as
dierence of log earnings at the selected percentiles of the log earnings distribution between
men and women (mean, 10th, 25th, 50th, 75th and 90th) that are commonly used in the
literature.
We note that all measures imply that there exist substantial earnings dierentials be-
tween men and women, and over the years. In particular, S

is statistically signicantly
dierent from zero (it is larger than the critical values calculated at 99th percentiles of the
bootstrapped distribution of S

in all cases).
It is important to note a crucial dierence between our broad entropy measure and others
in terms of standardization. Our measure is invariant to the logarithmic transformation of
the earnings series since, as was stated earlier, it is invariant to all monotonic (linear or non
linear) transformations. There is no need to reinterpret according to data transformations.
This is not so for all the other metrics in this table, since they will change depending on
whether one uses the actual earnings series, or their logarithm, or some other transformation.
We note that our entropy measure, being a function of many moments of the earnings
distributions, is able to account for increasing earnings that are accompanied by greater
dispersion (inequality increasing). Indeed, our entropy measure is based on a generalized
16
version of Theils inequality measures.
The dierences of the log-earnings at the selected percentiles of the earnings distribution
between men and women are consistently positive, suggesting that men earn more than
women do. However, the implied size of the gender earnings dierentials in the economy
vary with the conventional measures. For example, in 1976, the average gender gap measure
at the 10th percentile indicates the gap is about 37 percentage points, while the measure
at the 90th percentile implies that it is more than 50 percentage points. The dierence is
as large as 13 percentage points. The dierences at other parts of the earnings distribution
indicate the gender gap is between 45 and 47 percentage points. Even though consistently
suggesting the existence of the gender gap, none of the conventional measures at a specic
part of the distribution seems to represent the gender gap in the rest of the distribution.
What is left to be determined, is how to aggregate the dierent levels of the gap at dierent
quantiles. That is, what welfare function weights to use. The mean gap uses equal weights
at all earnings levels; see our example/case 3 above.
There is a further diculty with assessment of the conventional measures when one
examines the long-run trend in the gender gap. Looking at the trend from 1976 to 2011,
we see a decrease in the dierence between the earnings distributions of men and women
over the past four decades, regardless of which measure is used. However, the decrease is
not monotonic over time, and the timing of temporal deviations from the long-run trend
dramatically varies across dierent measures used. To ease the presentation, we report the
patterns of changes in dierent measures in Table (??). The cells with I highlighted in
green are the years when the measure increased, while the cells with D highlighted in light
grey are the years when the measure decreased. As we can clearly see, the conventional
measures of the gender gap generally do not move in the same direction together, except
in few years (1980, 1984, 1988, 1990, 1997, and 2004). For example, the gender gap at
the median increased in 1977, while the gender gap at other selected parts of the earnings
distributions between men and women decreased. As a result, it is not clear why any of
17
the conventional measures are representative of the rest of the earnings distribution and
informative of the general trend of the gap gap in the society.
On the other hand, our entropy measure of the gender gap, S

, provides a more complete

picture of the trend. An advantage of our measure is that it does not place all weights on a
particular part of the distribution, and the weights vary over time. For example, S

indicates
the broad gender gap decreased in 1977, which is consistent with the decrease at all parts but
the 90th percentile; S

indicates the gender gap increased in 1999, which is consistent with

the increase in at the 10th and 75th percentiles. Our measure becomes particularly useful
when the commonly used measures disagree with each other, especially during economic
downturns. For example, in 2009 (the current great recession), the gender gap implied by
the mean increased, while that by the median decreased! This conicting result could lead
to dierent conclusions about the cyclicality of the gap. In this particular instance, the
broad measure suggests that the gender gap indeed increased statistically (possibly due to
worsened economic conditions), in agreement with the mean. One interesting nding is worth
noting is that the gender gap at the 10th percentile uctuates more around the trend over
time, compared to the other parts of the distribution; the gender gap at the 90th percentile,
although uctuating sometimes, exhibits consistently a declining trend.
The magnitudes of S

and other measures reported in Table (1) are not directly compa-
rable. To further ease the comparisons of the patterns of the time trend implied by dierent
measures, we normalize these measures. In particular, we rst set the value of all measures
in 1976 to 100 and generate normalized values based on the original growth rates. These
normalized values are shown in Figure (??). As we can see, while both the measures at the
10th and 25th percentiles traced out the path of S

in the rst few years, none of the patterns

implied by the conventional measures are consistent with the one by S

. Our measure of the

gender gap indicates a continuing trend of decline in the gender gap over time. Although
this result is broadly consistent with the literature (e.g. Blau and Kahn, 2006), the rate of
decline implied by our measure is much larger than that by the conventional measures. All
18
traditional measures appear to severely underestimate the decline in the gender gap over
time. In particular, our S

implies the gender gap narrowed at average annual rate of about

11% during the period 1976-2011, while the annual rate implied by the gender dierence at
the median is only 5.2% during the same period, the largest among all conventional mea-
sures. Intuitively, this makes sense. If the gap at every part of the earnings distributions
between men and women decreases, the decrease in the distance between two distributions
should be even larger.
Another interesting phenomenon is observed when we plot the time evolution of these
measures against the dates of past recessions as announced by the National Bureau of E-
conomic Research (shaded areas). Conventional measures of the gender gap respond to
business cycles dierently, and for each measure, the directions of the responses also vary
across time. By contrast, our measure indicates that the gender gap for society as a whole
is relatively insensitive to changes in economic conditions, except in 2001.
Our measure of the gender gap also uncovers another interesting nding that is masked by
conventional measures: the gender gap dropped precipitously before 1990s, but the conver-
gence drastically slowed down since 1990s. Table (2) quanties these patterns. Specically,
the rate of decline was 7.6% before 1994, while it was only 2.5% afterwards. This result
is a bit surprising. Welfare reforms were enacted by many states in the mid-1990s and by
Congress in 1994 (Waldfogel and Mayer, 2000). Moreover, there was a new wave of skill-
biased technological progress during the 1990s and a marked acceleration in technology in
the period 1995-1999 (Basu et al., 2001). One might have expected that both welfare reform
and the technological progress might reduce the gender gap. However, our results indicate
that this is not necessarily the case, and even if these events helped in some metrics, the
eects were oset by some other movements.
4.1.2. Stochastic Dominance Test Results
As discussed above, these measures of the gender gap do not lend themselves to ranking
of the earnings distributions between men and women. Therefore, we now to turn to SD
19
tests. SD results are reported in Table (3) and the corresponding comparisons of CDFs over
time plotted in Figures (??)-(??). Note that the column labeled Observed Ranking details if
the distributions can be ranked in either the rst or second degree sense; the columns labeled
Pr[d 0] and Pr[s 0] report the p-values based on the simple bootstrap technique. If
we observe FSD (SSD) and Pr[d 0] (Pr[s 0]) is large, say 0.90 or higher, we may infer
dominance to a desirable degree of condence.
We rst notice that the earnings distribution among men lie predominantly to the right
of the earnings distribution among women, indicating higher level of earnings for men. This
casual observation is consistent with the fact that the dierences in selected percentiles of
the earnings distributions between men and women are uniformly positive. Moreover, we
also notice that the earnings distributions between men and women are getting closer over
time, in line with the results implied by our measure of the gender gap.
Our SD test statics conrm these casual observations. As we can see from Table (3), we
do observe stochastic dominance throughout the whole period. In particular, the earnings
distribution among men is generally found to empirically dominate, in a rst-order sense,
the earnings distribution among women in most cases. This result is extremely powerful:
any individuals with a social welfare function in the class U
1
(as long as it is increasing in
earnings) would prefer the male distribution to the female distribution, concluding that men
perform better than women in the labor market. In 2002 and 2010, we nd only second-
order dominance relations. In other words, any individuals with a social welfare function in
the class U
2
(increasing and concave in earnings) would conclude that men perform better
than women in the labor market. However, since we do not nd FSD, individuals possessing
dierent welfare functions in the class U
1
would disagree about this conclusion. Our SD
analysis makes explicit that such a ranking is possible only by accounting for dispersion
in the welfare criteria.
That we consistently nd dominance even for the beginning of the recent recessionary
period (2007-2008) is surprising. As we know, industries such as construction and manufac-
20
turing where men are primary workforce are hit harder in the current recession, and as a
result, men share a larger burden of the recession than women do (Sahin et al., 2010). Com-
pared the previous recessions, we are therefore less likely to nd any dominance relations in
the current one.
3
However, our result indicates that although disproportionately aected,
men still perform relatively better compared to women in the labor market.
Another nding is noteworthy. Despite the fact that the rate of decline has slowed down
since mid-1990s, it is less likely to nd statistically signicant rst-order dominance relations
during this period. In particular, there are 6 such cases out of 18. In one case (1998), we do
not even nd any statistically signicant dominance at all (even though we observe FSD, the
p-value is only 0.72; the p-value for SSD is 0.73). The inability to rank order the earnings
distributions between men and women in this case is equally informative. This nding implies
that for 1998, any welfare conclusions concerning that women fare worse than men in the
labor market are not robust to changes in the particular welfare function being used, despite
the fact that the dierences in selected percentiles of the earnings distributions between men
and women are, in most cases, positive and in favor of men. This result is in stark contrast
with the common belief based on the conventional measures above, illustrating the benet to
considering the entire distribution within the welfare economics framework when studying
the gender gap.
In sum, while we consistently nd dominance relations in most cases, it is less likely to
conclude that men perform better than women in the labor market without explicitly taking
into account dispersion after 1994. These results altogether suggest that womens labor
market situation has improved relative to mens. Nevertheless, strong evidence of dominance
relations in most cases indicates that the improvement is still far from satisfactory; this result
casts doubt on the eectiveness of the welfare reforms, or any similar reforms, intended
3
There is evidence that when the economy is further into the recession, men were likely to
nd jobs faster than women (partly because they work in elds previously dominated by wom-
en. Source: http://www.pewsocialtrends.org/2011/07/06/two-years-of-economic-recovery-women-lose-jobs-
men-nd-them/. The dominance relations are thus more likely to be found later.
21
to improve womens labor market outcomes. This result is consistent with the previous
literature such as Blau and Kahn (2006).
4.2. Counterfactual Analysis
Our measure of the gender gap and SD results above strongly support that the gender
gap remains and is in favor of men. Such conclusion is generally robust to a wide class
of social welfare functions. The question then is: Can we improve womens labor market
situation? Given the possibility that any policy proposed may result in both winners and
losers, could we still make robust statements that women would benet from certain type
of policies? Having these questions in mind, we now turn to our counterfactual analysis.
We rst consider a thought experiment that would change womens pay structure. This
type of thought experiment is closely related to policies aimed at promoting equal wage-
setting process/structure across gender, for example, pay equity programs that are designed
to addressing wage dierences between men and women with the same skills and work
by equalizing their pay structures. Due to data limitations, we only have a handful of
human capital characteristics available in our data, as in the literature. However, we want
to emphasize that such exercise is illustrative, and believe that it could still give us useful
information regarding the eectiveness of these potential programs. Table (4) reports various
measures of the dierences between the female wage distribution and the counterfactual wage
distribution (#1) corresponding to our thought experiment (i.e. the distribution of womens
wages when their human capital characteristics are paid under mens wage structure). We
nd that the distance between two distributions is large and statistically signicant. Recall
that the dierence captures only the dierence in wage structures between men and women,
while holding womens human capital characteristics constant. This result appears to be
consistent with the common nding of the importance of wage structure in explaining the
wage dierence between men and women. The importance of structural dierence, however,
decreased over time. The implied annualized rate of decline is about 4 percent. In this case,
we again nd that the implied distance (or importance) varies across various conventional
22
measures, and these measures severely underestimate the rate of the decline.
Turning to the SD results (Table (5)), we nd that the female wage distribution and the
counterfactual wage distribution # 1 are generally rankable. In most cases, we nd rst-order
dominance relations. This result implies that, in these cases, changing earnings structure
would result in a change in the earnings distribution for women, and that the change is
uniformly in favor of all women for any individuals with social welfare functions increasing in
earnings. In these cases, all women are winners! Such results are qualitatively consistent with
the prior ndings that such policies as equity pay could be potentially successful in closing the
gender earnings gap (e.g. Hartmann and Aaronson, 1994; Gunderson and Riddell, 1992).
However, our results are much stronger. Recall that the existing literature that typically
relies on regression analysis based on means or averages ignores the rest of the distribution.
Thus, it is a rather surprising yet strong result that all women would benet from a policy
that change their wage structure to mens.
However, we also nd several cases where such result fails to hold. For example, in two
cases (2002 and 2010), we fail to nd FSD but do nd SSD; this result means that even though
there are losers and winners from this type of policy the losers are mostly concentrated
in the extreme upper tail (highest earners). As a result, any individuals with social welfare
function increasing in wage and averse to inequality would still conclude there exists a welfare
improvement for women from changing the wage structure; however, such conclusion may
not necessarily hold for those with other social welfare functions in U
1
. Furthermore, in 1986
and 1999, the dominance relations are not statistically signicant. In other words, we fail
to nd that the female wage distribution and the counterfactual wage distribution # 1 are
rankable, in sharp contrast to the conclusion based on the signs of conventional measures.
This result implies that, although changing earnings structure would result in a change in
the earnings distribution for women, the change is not uniformly in favor of all women.
In the presence of both winners and losers, conclusions based on previous regression
analysis may not be robust at all. We emphasize this result: For any individuals with social
23
welfare functions either in U
1
(increasing in wage) or U
2
(increasing in wage and averse to
inequality), the change resulted from this type of policy does not necessarily represent a
welfare improvement for women. Failure to nd any statistically meaningful SD implies that
the conclusion of welfare improvement cannot be obtained without further restriction on
welfare functions.
We now consider another thought experiment resembling policies aimed at changing wom-
ens human capital characteristics such as education. In this thought experiment, we shall
contrast the female wage distribution with the counterfactual wage distribution (#2) (i.e.
the distribution of womens wages when they possess mens human capital characteristics
but holding womens wage structure unchanged). Table (6) reports various measures of the
dierences between these two distributions. In sharp contrast to the structural dierence
above, we nd that the compositional dierence dierence between the female wage distri-
bution and the counterfactual wage distribution (#2) is, albeit still statistically signicant,
rather small. In most cases, the magnitude of the compositional dierence is only about one
tenth of that of the structural eect. However, the magnitude has been increasing over time.
The annualized rate of increase is also about 4 percent. Moreover, unlike in the case of
structural dierence above, we nd that conventional measures trace out the pattern of our
distributional measure well.
Turning to the SD results (Table (7)), we fail to nd statistically meaningful SD ranking
of the female wage distribution and the counterfactual wage distribution (#2) in more than
half of the period (14 years). This result implies that even if dispersion is incorporated into
the welfare criteria, changing the distribution of womens human capital characteristics to the
distribution of mens characteristics may not necessarily represent welfare improvement from
the societal point of view. This result is also consistent with the above nding of a rather
small dierence between these two distributions. Further, in some cases where we do nd
dominance relations, the female wage distribution actually dominates the counterfactual
distribution. It implies that women could be even worse o when they have the same
24
distribution of human capital characteristics as do men. Altogether, our results imply that
the distribution of womens human capital characteristics is not necessarily inferior to that
of mens, and thus that policies aimed at changing the human capital characteristics only,
instead of wage structure, may not lead to welfare improvement for women.
5. Conclusions
In this paper, we present a set of complementary tools that move beyond the simple
moment-based comparison of the earnings distributions. In particular, we propose a new
measure of the gender gap based on the the distance between two whole earnings distribu-
tions, instead of their specic parts. We also introduce tests based on stochastic dominance
to allow for robust welfare comparisons of the earnings distributions between men and wom-
en. Using the CPS data 1976-2011, we apply this framework to analyze the gender gap in
the U.S. We reach several main conclusions. First, we nd that traditional moment-based
measures severely underestimate the declining trend of the gender gap in the U.S. Second,
we nd that even though rst-order stochastic dominance exists in most cases, there are
a few cases where we nd only second-order dominance or even no dominance; this result
highlights the importance in taking into account welfare criteria to evaluate the gender gap
situation. Finally, we further compare the female wage distribution to two counterfactual
distributions (the earnings that women would earn under the earnings structure of men and
the earnings that women would earn should they have mens characteristics). We nd that
structural eects are generally more important than composition eects. However, the im-
portance of structural eects has declined over time, while that of composition eects has
increased. Our SD results indicate that policies aimed at changing womens pay structure are
more likely to improve womens earnings prospects than policies aimed at changing womens
human capital characteristics. Even though this conclusion is largely true, we do nd several
cases where in the presence of winners and losers, we cannot draw denite conclusions
regarding the eectiveness of such policies unless we are willing to impose stronger and more
25
restrictive assumptions on social welfare functions. These results showcase the importance
of distributional aspects in measuring the gender gap, as well as taking into welfare criteria
in dening and testing rankings between two distributions.
26
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29
Table 1: Measures of The Gender Gaps
S

100 Mean 10th 25th 50th 75th 90th

Year (1) (2) (3) (4) (5) (6) (7)
1976 10.978 0.466 0.362 0.45 0.474 0.472 0.505
1977 10.252 0.444 0.318 0.414 0.488 0.470 0.480
1978 10.155 0.446 0.325 0.416 0.455 0.483 0.474
1979 9.891 0.436 0.288 0.386 0.473 0.495 0.484
1980 9.469 0.422 0.266 0.366 0.472 0.485 0.455
1981 8.957 0.403 0.241 0.354 0.442 0.474 0.459
1982 8.682 0.409 0.270 0.370 0.460 0.475 0.453
1983 7.576 0.387 0.229 0.298 0.433 0.431 0.464
1984 6.505 0.354 0.193 0.297 0.381 0.409 0.405
1985 6.190 0.355 0.209 0.29 0.392 0.414 0.419
1986 5.612 0.339 0.213 0.30 0.373 0.405 0.393
1987 5.009 0.333 0.231 0.297 0.355 0.389 0.382
1988 4.606 0.316 0.199 0.265 0.344 0.375 0.344
1989 4.425 0.315 0.223 0.292 0.359 0.354 0.350
1990 3.602 0.291 0.204 0.241 0.311 0.325 0.317
1991 3.134 0.269 0.163 0.244 0.288 0.306 0.316
1992 2.859 0.259 0.148 0.222 0.285 0.288 0.316
1993 2.662 0.241 0.136 0.21 0.235 0.295 0.289
1994 2.284 0.238 0.146 0.197 0.254 0.276 0.273
1995 2.329 0.248 0.173 0.206 0.260 0.288 0.272
1996 2.259 0.248 0.175 0.218 0.250 0.274 0.272
1997 2.173 0.238 0.160 0.191 0.248 0.262 0.266
1998 2.206 0.243 0.145 0.236 0.258 0.251 0.280
1999 2.320 0.242 0.149 0.230 0.232 0.268 0.274
2000 2.019 0.242 0.158 0.210 0.236 0.273 0.262
2001 2.384 0.266 0.214 0.223 0.266 0.301 0.313
2002 2.271 0.256 0.176 0.239 0.243 0.253 0.310
2003 2.139 0.245 0.182 0.191 0.239 0.262 0.291
2004 1.846 0.234 0.178 0.190 0.218 0.259 0.283
2005 1.908 0.234 0.168 0.182 0.216 0.255 0.288
2006 1.813 0.234 0.173 0.208 0.210 0.254 0.277
2007 1.588 0.224 0.163 0.195 0.244 0.254 0.268
2008 1.582 0.212 0.173 0.167 0.223 0.236 0.258
2009 1.640 0.215 0.154 0.172 0.193 0.222 0.273
2010 1.566 0.211 0.157 0.185 0.203 0.235 0.269
2011 1.436 0.202 0.172 0.185 0.182 0.259 0.248
1
Data Source: IPUMS CPS (http://cps.ipums.org/cps/). Column (1) reports the
overal gender gap (100) at corresponding functionals of the distributions of log wages
(measures the distance between the female and male wage distributions). Columns (2)-
(6) report conventional measures based on dierence in parts of the wage distributions
between males and females.
30
Table 2: Implied Rate of Decline by Measures of The Gender Gaps
S

100 Mean 10th 25th 50th 75th 90th

Year (1) (2) (3) (4) (5) (6) (7)
Pre-1994 -0.076 -0.036 -0.053 -0.041 -0.038 -0.026 -0.031
Post-1994 -0.025 -0.009 0.009 -0.003 -0.018 -0.004 -0.005
Whole Period -0.107 -0.045 -0.040 -0.048 -0.052 -0.033 -0.039
1
The calculations are based on Table (1).
31
Table 3: Stochastic Dominance Results (Female v.s. Male Wage Distributions)
Year Observed d
1,max
d
2,max
d Pr[d 0] s
1,max
s
2,max
s Pr[s 0]
Ranking
1976 FSD 54.68 -0.15 -0.15 1.00 2858.89 -0.15 -0.15 1.00
1977 FSD 57.97 -0.16 -0.16 1.00 2898.34 -0.16 -0.16 1.00
1978 FSD 57.07 -0.16 -0.16 1.00 2926.32 -0.16 -0.16 1.00
1979 FSD 57.77 -0.16 -0.16 1.00 2866.95 -0.16 -0.16 1.00
1980 FSD 61.66 -0.16 -0.16 1.00 2965.85 -0.17 -0.17 1.00
1981 FSD 59.44 -0.17 -0.17 0.99 2785.31 -0.17 -0.17 0.99
1982 FSD 54.43 -0.18 -0.18 1.00 2747.44 -0.18 -0.18 1.00
1983 FSD 49.74 -0.16 -0.16 1.00 2540.40 -0.17 -0.17 1.00
1984 FSD 46.47 -0.17 -0.17 0.99 2190.37 -0.21 -0.21 1.00
1985 FSD 46.10 -0.17 -0.17 1.00 2273.42 -0.17 -0.17 1.00
1986 FSD 43.40 -0.15 -0.15 0.99 2059.96 -0.17 -0.17 0.99
1987 FSD 41.47 -0.15 -0.15 1.00 2039.91 -0.16 -0.16 1.00
1988 FSD 40.25 -0.17 -0.17 1.00 2048.63 -0.17 -0.17 1.00
1989 FSD 37.94 -0.14 -0.14 1.00 1981.06 -0.16 -0.16 1.00
1990 FSD 35.94 -0.15 -0.15 1.00 3045.07 -0.17 -0.17 1.00
1991 FSD 33.32 -0.15 -0.15 1.00 2576.40 -0.19 -0.19 1.00
1992 FSD 31.99 -0.16 -0.16 1.00 1634.84 -0.16 -0.16 1.00
1993 FSD 30.24 -0.17 -0.17 0.97 1585.04 -0.19 -0.19 0.97
1994 FSD 27.94 -0.16 -0.16 1.00 1739.99 -0.17 -0.17 1.00
1995 FSD 28.74 -0.14 -0.14 1.00 1851.10 -0.16 -0.16 1.00
1996 FSD 25.73 -0.15 -0.15 1.00 1584.94 -0.15 -0.15 1.00
1997 FSD 26.14 -0.17 -0.17 0.93 1292.97 -0.17 -0.17 0.93
1998 FSD 26.18 -0.10 -0.10 0.72 1403.89 -0.16 -0.16 0.73
1999 FSD 26.50 -0.12 -0.12 0.57 1542.11 -0.17 -0.17 0.97
2000 FSD 25.93 -0.16 -0.16 1.00 1596.50 -0.16 -0.16 1.00
2001 FSD 34.60 -0.21 -0.21 1.00 2010.59 -0.21 -0.21 1.00
2002 SSD 33.76 0.29 0.29 0.03 1908.06 -0.20 -0.20 1.00
2003 FSD 31.19 -0.20 -0.20 0.88 1700.05 -0.20 -0.20 1.00
2004 FSD 30.20 -0.17 -0.17 1.00 1865.61 -0.21 -0.21 1.00
2005 FSD 30.10 -0.18 -0.18 1.00 1714.16 -0.20 -0.20 1.00
2006 FSD 29.25 -0.20 -0.20 1.00 1570.70 -0.21 -0.21 1.00
2007 FSD 27.94 -0.18 -0.18 1.00 1634.74 -0.20 -0.20 1.00
2008 FSD 27.49 -0.26 -0.26 0.99 1863.03 -0.26 -0.26 1.00
2009 FSD 27.64 -0.20 -0.20 0.88 1528.66 -0.20 -0.20 0.93
2010 SSD 27.29 0.30 0.30 0.02 1471.40 -0.19 -0.19 1.00
2011 FSD 25.04 -0.17 -0.17 0.95 1407.96 -0.19 -0.19 1.00
32
Table 4: Measures of Differences between Female and Female counterfactual #1 Distribu-
tions
S

100 Mean 10th 25th 50th 75th 90th

Year (1) (2) (3) (4) (5) (6) (7)
1976 8.998 0.417 0.317 0.383 0.431 0.438 0.460
1977 8.517 0.399 0.268 0.376 0.427 0.427 0.431
1978 8.565 0.403 0.276 0.349 0.412 0.448 0.452
1979 8.438 0.400 0.248 0.347 0.433 0.454 0.470
1980 8.400 0.402 0.262 0.340 0.432 0.468 0.436
1981 8.117 0.383 0.223 0.332 0.417 0.452 0.436
1982 7.885 0.389 0.270 0.341 0.428 0.438 0.428
1983 6.709 0.363 0.221 0.293 0.405 0.400 0.423
1984 6.151 0.346 0.199 0.293 0.375 0.397 0.392
1985 6.052 0.355 0.214 0.290 0.392 0.394 0.419
1986 5.457 0.334 0.218 0.300 0.373 0.405 0.393
1987 4.853 0.333 0.261 0.297 0.346 0.368 0.378
1988 4.636 0.323 0.228 0.274 0.344 0.375 0.340
1989 4.791 0.334 0.239 0.305 0.363 0.358 0.368
1990 4.181 0.319 0.257 0.288 0.336 0.340 0.339
1991 3.782 0.302 0.208 0.277 0.327 0.320 0.334
1992 3.622 0.299 0.198 0.282 0.310 0.315 0.316
1993 3.401 0.283 0.195 0.257 0.289 0.331 0.325
1994 3.036 0.280 0.223 0.257 0.300 0.312 0.307
1995 2.922 0.281 0.191 0.251 0.303 0.288 0.305
1996 3.050 0.294 0.210 0.272 0.297 0.304 0.316
1997 3.059 0.294 0.240 0.271 0.297 0.297 0.310
1998 3.101 0.296 0.210 0.288 0.292 0.307 0.344
1999 3.388 0.298 0.244 0.279 0.297 0.308 0.313
2000 3.165 0.308 0.248 0.287 0.307 0.332 0.318
2001 3.176 0.310 0.243 0.275 0.320 0.309 0.366
2002 3.215 0.309 0.240 0.288 0.288 0.313 0.364
2003 2.862 0.287 0.234 0.234 0.267 0.312 0.342
2004 2.641 0.283 0.227 0.250 0.273 0.312 0.312
2005 2.900 0.295 0.232 0.223 0.288 0.319 0.348
2006 2.811 0.296 0.223 0.262 0.288 0.323 0.359
2007 2.531 0.283 0.220 0.260 0.283 0.305 0.331
2008 2.640 0.279 0.242 0.243 0.279 0.300 0.324
2009 2.680 0.281 0.248 0.245 0.278 0.296 0.357
2010 2.589 0.278 0.223 0.262 0.280 0.307 0.325
2011 2.119 0.249 0.223 0.237 0.239 0.304 0.297
1
Data Source: IPUMS CPS (http://cps.ipums.org/cps/). Column (1) reports the
overal gender gap (100) at corresponding functionals of the distributions of log wages
(measures the distance between the female and female counterfactual #1 wage distribu-
tions). Columns (2)- (6) report conventional measures based on dierence in parts of
between the female and female counterfactual #1 wage distributions. Female counter-
factual #1 distribution is the counterfactual wage distribution among women when their
human characteristics are valued under mens wage structure.
33
Table 5: Stochastic Dominance Results (Female v.s. Female Counterfactual #1 Wage Dis-
tributions)
Year Observed d
1,max
d
2,max
d Pr[d 0] s
1,max
s
2,max
s Pr[s 0]
Ranking
1976 FSD 48.80 -0.14 -0.14 1.00 2562.04 -0.14 -0.14 1.00
1977 FSD 52.75 -0.16 -0.16 1.00 2605.25 -0.16 -0.16 1.00
1978 FSD 52.08 -0.15 -0.15 0.96 2646.30 -0.16 -0.16 0.96
1979 FSD 53.30 -0.11 -0.11 1.00 2629.37 -0.17 -0.17 1.00
1980 FSD 58.25 -0.16 -0.16 1.00 2817.56 -0.17 -0.17 1.00
1981 FSD 56.46 -0.17 -0.17 1.00 2644.61 -0.18 -0.18 1.00
1982 FSD 51.51 -0.16 -0.16 0.99 2612.90 -0.16 -0.16 1.00
1983 FSD 46.69 -0.15 -0.15 1.00 2380.20 -0.17 -0.17 1.00
1984 FSD 45.11 -0.16 -0.16 0.98 2145.20 -0.17 -0.17 0.98
1985 FSD 45.91 -0.16 -0.16 1.00 2268.15 -0.16 -0.16 1.00
1986 FSD 42.81 -0.21 -0.21 0.76 2045.17 -0.21 -0.21 0.77
1987 FSD 40.69 -0.14 -0.14 0.98 2040.58 -0.18 -0.18 0.99
1988 FSD 40.49 -0.17 -0.17 1.00 2091.63 -0.17 -0.17 1.00
1989 FSD 39.33 -0.16 -0.16 1.00 2096.96 -0.18 -0.18 1.00
1990 FSD 39.34 -0.16 -0.16 1.00 3336.83 -0.17 -0.17 1.00
1991 FSD 37.25 -0.17 -0.17 1.00 2887.26 -0.18 -0.18 1.00
1992 FSD 36.24 -0.16 -0.16 1.00 1889.86 -0.17 -0.17 1.00
1993 FSD 34.45 -0.16 -0.16 0.99 1858.63 -0.22 -0.22 0.99
1994 FSD 32.44 -0.15 -0.15 0.99 2051.06 -0.16 -0.16 0.99
1995 FSD 32.31 -0.16 -0.16 1.00 2094.29 -0.17 -0.17 1.00
1996 FSD 30.16 -0.11 -0.11 1.00 1877.99 -0.15 -0.15 1.00
1997 FSD 31.34 -0.15 -0.15 1.00 1589.95 -0.16 -0.16 1.00
1998 FSD 30.86 -0.17 -0.17 0.91 1703.95 -0.17 -0.17 0.92
1999 FSD 32.35 -0.15 -0.15 0.38 1902.00 -0.17 -0.17 0.87
2000 FSD 33.06 -0.17 -0.17 1.00 2034.39 -0.17 -0.17 1.00
2001 FSD 40.36 -0.18 -0.18 1.00 2347.71 -0.20 -0.20 1.00
2002 SSD 40.70 0.28 0.28 0.07 2301.80 -0.20 -0.20 1.00
2003 FSD 36.60 -0.21 -0.21 0.97 1996.78 -0.21 -0.21 1.00
2004 FSD 36.12 -0.24 -0.24 1.00 2261.05 -0.24 -0.24 1.00
2005 FSD 37.79 -0.18 -0.18 1.00 2158.72 -0.20 -0.20 1.00
2006 FSD 37.17 -0.19 -0.19 1.00 1988.91 -0.19 -0.19 1.00
2007 FSD 35.82 -0.17 -0.17 1.00 2069.90 -0.20 -0.20 1.00
2008 FSD 36.34 -0.19 -0.19 0.99 2464.95 -0.20 -0.20 0.99
2009 FSD 35.54 -0.20 -0.20 0.95 1995.00 -0.21 -0.21 1.00
2010 SSD 35.37 0.29 0.29 0.05 1939.45 -0.20 -0.20 1.00
2011 FSD 30.61 -0.19 -0.19 0.97 1735.31 -0.19 -0.19 1.00
34
Table 6: Measures of Differences between Female and Female counterfactual #2 Distribu-
tions
S

100 Mean 10th 25th 50th 75th 90th

Year (1) (2) (3) (4) (5) (6) (7)
1976 0.117 -0.026 -0.038 -0.032 -0.050 -0.023 0.000
1977 0.124 -0.030 -0.012 -0.041 -0.047 -0.010 0.000
1978 0.121 -0.032 -0.059 -0.048 -0.049 -0.017 0.000
1979 0.068 -0.022 -0.038 -0.036 -0.035 -0.018 0.000
1980 0.118 -0.041 -0.039 -0.049 -0.026 -0.025 -0.008
1981 0.155 -0.037 -0.079 -0.067 -0.028 -0.010 -0.003
1982 0.159 -0.041 -0.066 -0.051 -0.047 -0.029 -0.001
1983 0.158 -0.043 -0.065 -0.084 -0.036 -0.024 0.000
1984 0.157 -0.041 -0.057 -0.065 -0.069 -0.028 -0.025
1985 0.206 -0.057 -0.065 -0.078 -0.057 -0.043 0.000
1986 0.179 -0.052 -0.051 -0.051 -0.059 -0.004 -0.021
1987 0.204 -0.054 -0.053 -0.065 -0.069 -0.037 -0.004
1988 0.221 -0.061 -0.107 -0.095 -0.057 -0.031 -0.013
1989 0.246 -0.064 -0.102 -0.111 -0.065 -0.044 -0.028
1990 0.240 -0.069 -0.086 -0.107 -0.069 -0.046 -0.026
1991 0.334 -0.082 -0.100 -0.104 -0.116 -0.066 -0.036
1992 0.323 -0.078 -0.086 -0.109 -0.099 -0.075 -0.029
1993 0.297 -0.077 -0.077 -0.111 -0.104 -0.055 -0.031
1994 0.305 -0.084 -0.082 -0.111 -0.094 -0.068 -0.020
1995 0.242 -0.070 -0.098 -0.108 -0.079 -0.053 -0.029
1996 0.268 -0.075 -0.086 -0.088 -0.091 -0.047 -0.038
1997 0.284 -0.074 -0.073 -0.129 -0.078 -0.039 -0.046
1998 0.309 -0.084 -0.078 -0.079 -0.113 -0.086 -0.039
1999 0.369 -0.090 -0.094 -0.123 -0.125 -0.072 -0.059
2000 0.326 -0.086 -0.095 -0.078 -0.095 -0.059 -0.041
2001 0.232 -0.069 -0.061 -0.093 -0.056 -0.056 -0.039
2002 0.264 -0.078 -0.073 -0.090 -0.085 -0.072 -0.045
2003 0.204 -0.067 -0.080 -0.103 -0.097 -0.051 -0.037
2004 0.280 -0.081 -0.100 -0.097 -0.091 -0.050 -0.069
2005 0.357 -0.092 -0.119 -0.123 -0.109 -0.049 -0.049
2006 0.342 -0.091 -0.074 -0.105 -0.128 -0.082 -0.059
2007 0.340 -0.093 -0.105 -0.085 -0.084 -0.079 -0.069
2008 0.334 -0.087 -0.079 -0.095 -0.079 -0.074 -0.061
2009 0.336 -0.093 -0.077 -0.130 -0.105 -0.105 -0.074
2010 0.305 -0.088 -0.065 -0.104 -0.125 -0.086 -0.041
2011 0.487 -0.112 -0.065 -0.152 -0.154 -0.093 -0.088
1
Data Source: IPUMS CPS (http://cps.ipums.org/cps/). Column (1) reports the overal
gender gap (100) at corresponding functionals of the distributions of log wages (measures
the distance between the female and female counterfactual #2 wage distributions). Columns
(2)- (6) report conventional measures based on dierence in parts of between the female
and female counterfactual #2 wage distributions. Female counterfactual #2 distribution is
the counterfactual wage distribution among women when mens human characteristics are
instead valued under womens wage structure.
35
Table 7: Stochastic Dominance Results (Female v.s. Female Counterfactual #2 Wage Dis-
tributions)
Year Observed d
1,max
d
2,max
d Pr[d 0] s
1,max
s
2,max
s Pr[s 0]
Ranking
1976 None 0.29 5.59 0.29 0.01 2.32 174.48 2.32 0.23
1977 SSD 0.47 6.50 0.47 0.02 -0.17 207.86 -0.17 0.61
1978 SSD 0.51 6.58 0.51 0.02 -0.16 214.68 -0.16 0.79
1979 SSD 0.43 4.60 0.43 0.01 -0.17 147.37 -0.17 0.41
1980 SSD 0.16 6.47 0.16 0.19 -0.17 261.51 -0.17 0.98
1981 SSD 0.06 8.14 0.06 0.11 -0.17 256.43 -0.17 0.90
1982 SSD 0.18 7.69 0.18 0.15 -0.16 276.23 -0.16 0.97
1983 FSD 0.00 7.23 0.00 0.18 -0.17 270.50 -0.17 0.98
1984 FSD -0.11 7.42 -0.11 0.24 -0.19 265.35 -0.19 0.45
1985 FSD -0.08 8.55 -0.08 0.40 -0.17 356.83 -0.17 0.94
1986 FSD -0.17 8.26 -0.17 0.45 -0.17 315.12 -0.17 0.92
1987 FSD -0.15 8.67 -0.15 0.42 -0.17 338.91 -0.17 0.89
1988 FSD -0.16 9.23 -0.16 0.59 -0.16 390.16 -0.16 0.88
1989 FSD -0.11 9.59 -0.11 0.31 -0.17 400.09 -0.17 0.96
1990 FSD -0.17 9.68 -0.17 0.72 -0.17 712.75 -0.17 0.95
1991 FSD -0.14 12.27 -0.14 0.80 -0.17 774.47 -0.17 0.97
1992 FSD -0.11 11.75 -0.11 0.65 -0.17 494.34 -0.17 0.94
1993 FSD -0.17 11.12 -0.17 0.73 -0.20 510.55 -0.20 0.95
1994 FSD -0.16 10.91 -0.16 0.58 -0.17 602.71 -0.17 1.00
1995 FSD -0.16 9.86 -0.16 0.66 -0.18 515.70 -0.18 0.89
1996 FSD -0.10 10.21 -0.10 0.57 -0.16 463.37 -0.16 0.85
1997 FSD -0.15 10.02 -0.15 0.42 -0.17 405.20 -0.17 0.69
1998 FSD -0.17 11.11 -0.17 0.74 -0.20 476.77 -0.20 0.83
1999 FSD -0.11 12.03 -0.11 0.81 -0.16 568.01 -0.16 0.91
2000 FSD -0.16 11.54 -0.16 0.82 -0.18 569.25 -0.18 0.88
2001 FSD -0.21 12.41 -0.21 0.91 -0.24 519.59 -0.24 0.96
2002 FSD -0.19 12.55 -0.19 0.97 -0.20 574.93 -0.20 0.99
2003 FSD -0.21 11.00 -0.21 0.77 -0.25 460.15 -0.25 0.86
2004 FSD -0.20 13.07 -0.20 0.93 -0.21 636.64 -0.21 0.96
2005 FSD -0.17 14.22 -0.17 0.93 -0.19 668.74 -0.19 0.95
2006 FSD -0.20 14.24 -0.20 0.92 -0.20 613.36 -0.20 0.93
2007 FSD -0.19 14.09 -0.19 0.91 -0.20 669.56 -0.20 0.94
2008 FSD -0.21 13.70 -0.21 0.77 -0.31 770.09 -0.31 0.81
2009 FSD -0.17 14.04 -0.17 0.96 -0.20 638.77 -0.20 0.99
2010 FSD -0.19 13.22 -0.19 0.94 -0.19 600.92 -0.19 0.97
2011 FSD -0.20 15.98 -0.20 0.96 -0.20 777.12 -0.20 0.98
36
2
0
4
0
6
0
8
0
1
0
0
N
o
r
m
a
l
i
z
e
d

G
e
n
d
e
r

G
a
p
1980 1990 2000 2010
Year
1980
19811982
19901991
2001
20072009
Srho
Mean
10th
25th
50th
75th
90th
Figure 1: The Trend of Gender Wage Gap (Shaded Areas correspond to the recession periods announced by
NBER)
37
0
.
2
.
4
.
6
.
8
1
2 1 0 1 2 3
x
Female Male

F
(
x
)
(a) 1976
0
.
2
.
4
.
6
.
8
1
2 1 0 1 2 3
x
Female Male

F
(
x
)
(b) 1977
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Male

F
(
x
)
(c) 1978
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Male

F
(
x
)
(d) 1979
0
.
2
.
4
.
6
.
8
1
2 1 0 1 2 3
x
Female Male

F
(
x
)
(e) 1980
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Male

F
(
x
)
(f) 1981
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Male

F
(
x
)
(g) 1982
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Male

F
(
x
)
(h) 1983
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Male

F
(
x
)
(i) 1984
Figure 2: CDF Comparisons of Female and Male Wage Distributions (1976-1984)
38
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Male

F
(
x
)
(a) 1985
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Male

F
(
x
)
(b) 1986
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Male

F
(
x
)
(c) 1987
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Male

F
(
x
)
(d) 1988
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Male

F
(
x
)
(e) 1989
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Male

F
(
x
)
(f) 1990
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Male

F
(
x
)
(g) 1991
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Male

F
(
x
)
(h) 1992
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Male

F
(
x
)
(i) 1993
Figure 3: CDF Comparisons of Female and Male Wage Distributions (1985 - 1993)
39
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Male

F
(
x
)
(a) 1994
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Male

F
(
x
)
(b) 1995
0
.
2
.
4
.
6
.
8
1
0 2 4 6
x
Female Male

F
(
x
)
(c) 1996
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(d) 1997
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(e) 1998
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(f) 1999
0
.
2
.
4
.
6
.
8
1
2 0 2 4 6
x
Female Male

F
(
x
)
(g) 2000
0
.
2
.
4
.
6
.
8
1
2 0 2 4 6
x
Female Male

F
(
x
)
(h) 2001
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(i) 2002
Figure 4: CDF Comparisons of Female and Male Wage Distributions (1994 - 2002)
40
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(a) 2002
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(b) 2003
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(c) 2004
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(d) 2005
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(e) 2006
0
.
2
.
4
.
6
.
8
1
0 2 4 6
x
Female Male

F
(
x
)
(f) 2007
0
.
2
.
4
.
6
.
8
1
1 2 3 4 5
x
Female Male

F
(
x
)
(g) 2008
0
.
2
.
4
.
6
.
8
1
1 2 3 4 5
x
Female Male

F
(
x
)
(h) 2009
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Male

F
(
x
)
(i) 2010
Figure 5: CDF Comparisons of Female and Male Wage Distributions (2002 - 2010)
41
0
.
2
.
4
.
6
.
8
1
1 2 3 4 5
x
Female Male

F
(
x
)
(a) 2011
Figure 6: CDF Comparisons of Female and Male Wage Distributions (2011)
42
2
0
4
0
6
0
8
0
1
0
0
N
o
r
m
a
l
i
z
e
d

G
e
n
d
e
r

G
a
p
1980 1990 2000 2010
Year
Srho
Mean
10th
25th
50th
75th
90th
Figure 7: The Trend of the dierence between the female wage distribution and the counterfactual distribu-
tion #1
43
0
.
2
.
4
.
6
.
8
1
2 1 0 1 2 3
x
Female Counterfactual #1

F
(
x
)
(a) 1976
0
.
2
.
4
.
6
.
8
1
2 1 0 1 2 3
x
Female Counterfactual #1

F
(
x
)
(b) 1977
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Counterfactual #1

F
(
x
)
(c) 1978
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Counterfactual #1

F
(
x
)
(d) 1979
0
.
2
.
4
.
6
.
8
1
2 1 0 1 2 3
x
Female Counterfactual #1

F
(
x
)
(e) 1980
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Counterfactual #1

F
(
x
)
(f) 1981
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(g) 1982
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(h) 1983
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(i) 1984
Figure 8: CDF Comparisons of Female and Female Counterfactual #1 Wage Distributions (1976-1984)
44
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(a) 1985
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(b) 1986
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(c) 1987
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(d) 1988
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(e) 1989
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(f) 1990
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(g) 1991
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(h) 1992
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(i) 1993
Figure 9: CDF Comparisons of Female and Female Counterfactual #1 Wage Distributions (1985 - 1993)
45
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(a) 1994
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #1

F
(
x
)
(b) 1995
0
.
2
.
4
.
6
.
8
1
2 0 2 4 6
x
Female Counterfactual #1

F
(
x
)
(c) 1996
0
.
2
.
4
.
6
.
8
1
2 0 2 4 6
x
Female Counterfactual #1

F
(
x
)
(d) 1997
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(e) 1998
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(f) 1999
0
.
2
.
4
.
6
.
8
1
2 0 2 4 6
x
Female Counterfactual #1

F
(
x
)
(g) 2000
0
.
2
.
4
.
6
.
8
1
2 0 2 4 6
x
Female Counterfactual #1

F
(
x
)
(h) 2001
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(i) 2002
Figure 10: CDF Comparisons of Female and Female Counterfactual #1 Wage Distributions (1994 - 2002)
46
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(a) 2002
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(b) 2003
0
.
2
.
4
.
6
.
8
1
2 0 2 4 6
x
Female Counterfactual #1

F
(
x
)
(c) 2004
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(d) 2005
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(e) 2006
0
.
2
.
4
.
6
.
8
1
0 2 4 6
x
Female Counterfactual #1

F
(
x
)
(f) 2007
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(g) 2008
0
.
2
.
4
.
6
.
8
1
1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(h) 2009
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(i) 2010
Figure 11: CDF Comparisons of Female and Female Counterfactual #1 Wage Distributions (2002 - 2010)
47
0
.
2
.
4
.
6
.
8
1
1 2 3 4 5
x
Female Counterfactual #1

F
(
x
)
(a) 2011
Figure 12: CDF Comparisons of Female and Female Counterfactual #1 Wage Distributions (2011)
48
0
1
0
0
2
0
0
3
0
0
4
0
0
5
0
0
N
o
r
m
a
l
i
z
e
d

G
e
n
d
e
r

G
a
p
1980 1990 2000 2010
Year
Srho
Mean
10th
25th
50th
75th
90th
Figure 13: The Trend of the dierence between the female wage distribution and the counterfactual distri-
bution #2
49
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Counterfactual #2

F
(
x
)
(a) 1976
0
.
2
.
4
.
6
.
8
1
.5 0 .5 1 1.5 2
x
Female Counterfactual #2

F
(
x
)
(b) 1977
0
.
2
.
4
.
6
.
8
1
1 0 1 2
x
Female Counterfactual #2

F
(
x
)
(c) 1978
0
.
2
.
4
.
6
.
8
1
0 .5 1 1.5 2 2.5
x
Female Counterfactual #2

F
(
x
)
(d) 1979
0
.
2
.
4
.
6
.
8
1
2 1 0 1 2 3
x
Female Counterfactual #2

F
(
x
)
(e) 1980
0
.
2
.
4
.
6
.
8
1
1 0 1 2
x
Female Counterfactual #2

F
(
x
)
(f) 1981
0
.
2
.
4
.
6
.
8
.5 0 .5 1 1.5 2
x
Female Counterfactual #2

F
(
x
)
(g) 1982
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Counterfactual #2

F
(
x
)
(h) 1983
0
.
2
.
4
.
6
.
8
1
.5 1 1.5 2 2.5 3
x
Female Counterfactual #2

F
(
x
)
(i) 1984
Figure 14: CDF Comparisons of Female and Female Counterfactual #2 Wage Distributions (1976-1984)
50
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Counterfactual #2

F
(
x
)
(a) 1985
0
.
2
.
4
.
6
.
8
1
0 1 2 3
x
Female Counterfactual #2

F
(
x
)
(b) 1986
0
.
2
.
4
.
6
.
8
1
0 1 2 3
x
Female Counterfactual #2

F
(
x
)
(c) 1987
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(d) 1988
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3
x
Female Counterfactual #2

F
(
x
)
(e) 1989
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(f) 1990
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(g) 1991
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(h) 1992
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(i) 1993
Figure 15: CDF Comparisons of Female and Female Counterfactual #2 Wage Distributions (1985 - 1993)
51
0
.
2
.
4
.
6
.
8
1
1 0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(a) 1994
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(b) 1995
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(c) 1996
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(d) 1997
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(e) 1998
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(f) 1999
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(g) 2000
0
.
2
.
4
.
6
.
8
1
1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(h) 2001
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(i) 2002
Figure 16: CDF Comparisons of Female and Female Counterfactual #2 Wage Distributions (1994 - 2002)
52
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(a) 2002
0
.
2
.
4
.
6
.
8
1
1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(b) 2003
0
.
2
.
4
.
6
.
8
1
1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(c) 2004
0
.
2
.
4
.
6
.
8
1
0 1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(d) 2005
0
.
2
.
4
.
6
.
8
1
1 2 3 4 5
x
Female Counterfactual #2

F
(
x
)
(e) 2006
0
.
2
.
4
.
6
.
8
1
1 2 3 4 5
x
Female Counterfactual #2

F
(
x
)
(f) 2007
0
.
2
.
4
.
6
.
8
1
1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(g) 2008
0
.
2
.
4
.
6
.
8
1
1 2 3 4 5
x
Female Counterfactual #2

F
(
x
)
(h) 2009
0
.
2
.
4
.
6
.
8
1
1 2 3 4 5
x
Female Counterfactual #2

F
(
x
)
(i) 2010
Figure 17: CDF Comparisons of Female and Female Counterfactual #2 Wage Distributions (2002 - 2010)
53
0
.
2
.
4
.
6
.
8
1
1 2 3 4
x
Female Counterfactual #2

F
(
x
)
(a) 2011
Figure 18: CDF Comparisons of Female and Female Counterfactual #2 Wage Distributions (2011)
54
Table A1: The Patterns of Changes in Measures of The Gender Gap
S

100 Mean 10th 25th 50th 75th 90th

Year (1) (2) (3) (4) (5) (6) (7)
1977 D D D D I D D
1978 D I I I D I D
1979 D D D D I I I
1980 D D D D D D D
1981 D D D D D D I
1982 D I I I I I D
1983 D D D D D D I
1984 D D D D D D D
1985 D I I D I I I
1986 D D I I D D D
1987 D D I D D D D
1988 D D D D D D D
1989 D D I I I D I
1990 D D D D D D D
1991 D D D I D D D
1992 D D D D D D I
1993 D D D D D I D
1994 D D I D I D D
1995 I I I I I I D
1996 D I I I D D -
1997 D D D D D D D
1998 I I D I I D I
1999 I D I D D I D
2000 D D I D I I D
2001 I I I I I I I
2002 D D D I D D D
2003 D D I D D I D
2004 D D D D D D D
2005 I D D D D D I
2006 D I I I D D D
2007 D D D D I D D
2008 D D I D D D D
2009 I I D I D D I
2010 D D I I I I D
2011 D D I D D I D
1
Data Source: IPUMS CPS (http://cps.ipums.org/cps/). Column (1) reports
the overal gender gap (100) at corresponding functionals of the distributions of
log wages (measures the distance between the female and male wage distributions).
Columns (2)- (6) report conventional measures based on dierence in parts of the
wage distributions between males and females. The cells with I highlighted in
green are the years when the measure increased, while the cells with D highlighted
in light grey are the years when the measure decreased.
55
Table A2: Significance Testing of S

Year Female v.s. Male Female v.s. Counterfactual Female v.s. Counterfactual
#1 #2
90
th
95
th
99
th
90
th
95
th
99
th
90
th
95
th
99
th
(1) (2) (3) (4) (5) (6) (7) (8) (9)
1976 0.06 0.07 0.08 0.07 0.08 0.10 0.07 0.08 0.10
1977 0.04 0.05 0.05 0.06 0.06 0.07 0.05 0.06 0.06
1978 0.04 0.05 0.05 0.07 0.07 0.08 0.06 0.07 0.08
1979 0.05 0.05 0.06 0.06 0.06 0.07 0.05 0.05 0.07
1980 0.05 0.05 0.06 0.06 0.06 0.07 0.05 0.05 0.07
1981 0.04 0.04 0.04 0.05 0.05 0.06 0.04 0.04 0.05
1982 0.05 0.05 0.06 0.06 0.07 0.08 0.05 0.06 0.06
1983 0.04 0.05 0.05 0.05 0.06 0.07 0.05 0.05 0.06
1984 0.04 0.05 0.05 0.05 0.06 0.07 0.05 0.05 0.06
1985 0.04 0.05 0.05 0.05 0.05 0.06 0.04 0.05 0.06
1986 0.04 0.05 0.05 0.06 0.07 0.08 0.06 0.06 0.07
1987 0.04 0.05 0.06 0.06 0.06 0.07 0.05 0.05 0.06
1988 0.04 0.04 0.05 0.05 0.05 0.06 0.04 0.04 0.05
1989 0.04 0.05 0.05 0.05 0.06 0.07 0.05 0.05 0.06
1990 0.03 0.04 0.05 0.04 0.05 0.06 0.04 0.04 0.05
1991 0.03 0.04 0.04 0.04 0.04 0.05 0.04 0.04 0.05
1992 0.04 0.04 0.05 0.05 0.05 0.06 0.04 0.04 0.05
1993 0.04 0.04 0.05 0.04 0.05 0.06 0.04 0.04 0.05
1994 0.04 0.05 0.05 0.05 0.06 0.07 0.05 0.06 0.07
1995 0.04 0.05 0.05 0.05 0.05 0.05 0.04 0.05 0.05
1996 0.05 0.05 0.06 0.06 0.06 0.07 0.05 0.05 0.06
1997 0.06 0.06 0.07 0.06 0.06 0.07 0.05 0.06 0.07
1998 0.04 0.05 0.06 0.05 0.06 0.07 0.05 0.05 0.07
1999 0.04 0.05 0.06 0.05 0.05 0.06 0.05 0.05 0.06
2000 0.05 0.06 0.07 0.06 0.06 0.07 0.04 0.05 0.06
2001 0.04 0.04 0.04 0.04 0.05 0.05 0.03 0.04 0.04
2002 0.03 0.03 0.03 0.04 0.04 0.04 0.03 0.04 0.04
2003 0.03 0.04 0.04 0.04 0.04 0.05 0.03 0.04 0.04
2004 0.04 0.04 0.04 0.04 0.04 0.05 0.04 0.04 0.05
2005 0.04 0.04 0.04 0.04 0.05 0.05 0.04 0.04 0.05
2006 0.04 0.04 0.04 0.04 0.05 0.05 0.04 0.04 0.05
2007 0.04 0.04 0.04 0.04 0.05 0.05 0.04 0.04 0.05
2008 0.03 0.04 0.04 0.04 0.04 0.05 0.03 0.04 0.04
2009 0.04 0.04 0.05 0.05 0.05 0.06 0.04 0.04 0.05
2010 0.04 0.04 0.05 0.05 0.05 0.06 0.04 0.04 0.05
2011 0.04 0.04 0.04 0.04 0.05 0.05 0.03 0.04 0.04
1
Data Source: IPUMS CPS (http://cps.ipums.org/cps/). Columns (1)-(3) report the 90th, 95th, and
99th percentiles obtained under the null of no dierence between male and female wage distributions
(100). Columns (4)-(6) report the 90th, 95th, and 99th percentiles obtained under the null of no
dierence between female and the counterfactual wage #1 distributions ( (100)); Columns (7)-(9)
report the 90th, 95th, and 99th percentiles obtained under the null of no dierence between female and
counterfactual wage #2 distributions ( (100)).
56