Study Paper on Occupational Tasks and Changes in the Wage Structure

Description
A wage is remuneration paid by an employer to an employee. It may be calculated as a fixed task based amount, or at an hourly rate, or based on an easily measured quantity of work done.

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Forschungsinstitut
zur Zukunft der Arbeit
Institute for the Study
of Labor
Occupational Tasks and Changes in the Wage Structure
IZA DP No. 5542
February 2011
Sergio Firpo
Nicole M. Fortin
Thomas Lemieux

Occupational Tasks and
Changes in the Wage Structure

Sergio Firpo
São Paulo School of Economics, FGV
and IZA

Nicole M. Fortin
University of British Columbia
and IZA

Thomas Lemieux
University of British Columbia

Discussion Paper No. 5542
February 2011

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IZA Discussion Paper No. 5542
February 2011

ABSTRACT

Occupational Tasks and Changes in the Wage Structure
*

This paper argues that changes in the returns to occupational tasks have contributed to
changes in the wage distribution over the last three decades. Using Current Population
Survey (CPS) data, we first show that the 1990s polarization of wages is explained by
changes in wage setting between and within occupations, which are well captured by tasks
measures linked to technological change and offshorability. Using a decomposition based on
Firpo, Fortin, and Lemieux (2009), we find that technological change and deunionization
played a central role in the 1980s and 1990s, while offshorability became an important factor
from the 1990s onwards.

J EL Classification: J 3, J 5

Keywords: wage inequality, polarization, occupational tasks, offshoring, RIF-regressions

Corresponding author:

Sergio Firpo
Escola de Economia de São Paulo – FGV-SP
R. Itapeva, 474/1215
São Paulo, SP 01332-000
Brazil
E-mail: [email protected]

*
We are indebted to David Autor, David Card, David Dorn, Martin Goos, Caroline Hoxby, Luigi
Pistaferri, Anna Salomon, Alexandra Spitz-Oener, Frank Vella, and seminar participants at UC
Berkeley, Cornell, Georgetown, UCL, LSE, HEC-Montreal, Ottawa, Toronto, Calgary, Hawaii, Paris II,
PSE, Columbia, Stanford, Victoria, Collegio Carlo Alberto, UC Davis, the 2010 NBER Summer
Institute, the T.A.S.K.S. International Workshop in Nuremberg, the 2010 EALE/SOLE Conference, and
the ACAM Conference in Tokyo for useful comments on this and earlier versions of the manuscript.
Financial support from CNPq-Brazil for Firpo, from CIFAR and SSHRC for Fortin, and from SSHRC for
Lemieux was greatly appreciated. The usual disclaimer applies.
Most studies on changes in inequality and the wage structure have focused on explanations
based on changes in the returns to traditional measures of skills like education and experience
(e.g. Katz and Murphy, 1992) or institutions (e.g. DiNardo, Fortin, and Lemieux, 1996).
1
Until
recently, little attention had been paid to the potential role of occupations in changes in wage
inequality. This situation has changed over the last ?ve years for several reasons.
First, Autor, Levy, and Murnane (2003), Goos and Manning (2007), and Autor, Katz and
Kearney (2006) have proposed a new explanation for changes in wage inequality based on a
more “nuanced” view of skill-biased technological change. The idea is that the introduction of
computer and information technologies has not simply depressed the relative demand for less
skilled workers, as it was assumed in early studies such as Berman, Bound, and Griliches (1994).
Rather, computer and information technologies have depressed the return to “routine” tasks
that can now be executed by computer technologies. Autor, Katz and Kearney (2006) and Goos
and Manning (2007) argue that this nuanced view of technological change can help account
for the polarization of wages that has been observed since the late 1980s. Under this type of
technological change, it is plausible that moderately skilled workers who used to perform routine
tasks experienced a decline in relative wages during this period. Technological change could thus
explain why wages in the middle of the distribution fell more than wages at the bottom and top
end of the distribution.
2
This more nuanced view of technological change puts occupations at the forefront of the in-
equality debate since the task content of work (routine nature of the job, cognitive skills required,
etc.) is typically measured at the occupational level.
3
Occupations are, therefore, a key empir-
ical channel through which we can assess how technological change a?ects the wage structure.
An important empirical implication of this more nuanced view of technological change, that we
discuss below, is that changes in the wage structure within and between occupations should be
systematically related to the type of tasks performed in these occupations.
A second reason for looking at the contribution of occupations in changes in the wage structure
is o?shoring. Early explanations for the role of international trade in changes in inequality have
1
The role of industrial change due to de-industrialisation and foreign competition was also explored in some of the early
studies such as Murphy and Welch (1991), Bound and Johnson (1992), and Freeman (1995).
2
Acemoglu and Autor (2011) develop a formal model to show how this could happen in a model with three skill levels
(high, middle, and low).
3
Most studies have either used data from the Dictionary of Occupation Titles (DOT) or the more recent Occupational
Information Network (O*NET) to get information about the task content of jobs. Since jobs are de?ned on the basis of a
detailed occupational classi?cation, this naturally lead to an analysis at the occupational level. Alternatively, Goos, Manning,
and Salomon (2009) explore the role of o?shoring in the polarization of employment in Europe using counts of news reports
about o?shoring of European jobs from the European Restructuring Monitor.
1
focused on the role of trade in ?nal products that are de?ned at the industry level. It was later
argued (Feenstra and Hanson, 2003) that trade in intermediate inputs was a more promising
explanation for changes in wage inequality than trade in ?nal goods and services. More recently,
Grossman and Rossi-Hansberg (2008) have proposed a model where o?shoring ?gures as a source
of task supply among other competing sources. For instance, a U.S. multinational can hire
computer programmers (middle skilled) in India to update and debug a software product. This
lowers the relative demand for that particular occupation, computer programmers, in the United
States, which then depresses their wages. The work performed, say overnight, by the o?shored
programmers, can enhance the productivity of computer software engineers and developers and
contribute to wage increases at the other end of the skill spectrum. As in the case of technological
change, occupations are the key channel through which o?shoring can contribute to changes in
wage inequality. This suggests assessing the role of o?shoring in changes in the wage structure by
contrasting the evolution of wages and employment in occupations that are potentially o?shorable
(e.g. Blinder (2007) and Jensen and Kletzer (2010)) relative to those that are not o?shorable.
Although occupations now feature prominently as a possible channel for recent changes in
wage inequality, the role of occupations in these changes has not been systemically investigated
yet. Some studies do suggest an important role for an occupation-based explanations. Goos and
Manning (2007) show that the composition e?ect linked to changes in the distribution of occupa-
tions accounts for a substantial part of the increase in inequality in the United Kingdom. Autor,
Katz and Kearney (2008) provide evidence that, consistent with a nuanced view of technologi-
cal change, the share of employment in occupations in the middle of the wage distribution has
declined over time. Acemoglu and Autor (2011) explore this point in more detail and also show
evidence that changes in inter-occupation wage di?erentials are an important factor in the growth
in the variance of U.S. wages since 1980. While these ?ndings suggest a potentially important
role for occupations, it remains to be seen how much of the total change in the distribution of
wages can precisely be accounted for by occupation-based explanations.
The goal of this paper is to ?ll this gap by systematically investigating the contribution of
occupations to changes in the distribution of U.S. male wages.
4
We do so by ?rst presenting a
conceptual model of the labor market where productive skills are rewarded di?erently in di?erent
occupations, as in a standard Roy model. We argue that this simple model provides a general
way of capturing changes in the wage structure induced by factors like technological change and
4
We focus on men for which the phenomenon of polarization is thought to have the more dire e?ects (Autor, 2010).
2
o?shorability. Using Current Population Survey (CPS) data for the years 1988-90 and 2000-02,
we then show that the level and dispersion of wages across occupations have changed substantially
over the 1990s, and that these changes are linked to the task content of occupations. We measure
the task content of occupations using data from the O*NET, and create ?ve indexes of tasks that
arguably capture the potential e?ect of technological change and o?shorability on occupational
wages. We ?nd that task content measures explain well (at least half of the observed variation)
the changes in both the level and dispersion of wages across occupations. This evidence suggests
that changes in occupational wage setting are a promising way of accounting for the U-shaped
feature of changes in the wage distribution (Autor, Katz, and Kearney, 2006, 2008).
Second, we explicitly quantify the contribution of occupations, as summarized by the task
content of jobs, in overall changes in the distribution of wages over the last three decades.
We do so using a decomposition method based on the recentered in?uence function regression
approach of Firpo, Fortin, and Lemieux (2009, 2011). This approach enables us to evaluate the
contribution of changes in the returns to occupational tasks compared to other explanations such
as de-unionization and changes in the labor market wide returns to general skills (labor market
experience and education). We ?nd that technological change and de-unionization played a
relatively central role in the 1980s and 1990s, but had little e?ect in the 2000s. Increasing
returns to education played an important role in all three decades, while o?shorability became
an important factor in the 1990s and, especially, in the 2000s.
The paper is organized as follows. In Section I, we present a Roy model where the returns to
a variety of skills can be occupation-speci?c. This model provides a rationale for looking at the
contribution of changes in the occupational wage structure in overall changes in inequality, and
helps connect the task content of occupations with wage setting in these occupations. Section II
describes the wage data used, introduces the measures of task content computed from the O*NET
data, and explains how they are linked to the concepts of technological change and o?shorability.
Section III documents the changes in the level and dispersion of wages across occupations and
shows that they are connected to our measures of the task content of jobs. The second part of
the paper begins, in Section IV, with a short exposition of the decomposition methodology based
on recentered in?uence function regressions. The ensuing results are presented in Section V and
we conclude in Section VI.
3
I. Wage Setting in Occupations
A. Roy Model of Wage Setting
Most of the wage inequality literature follows a traditional Mincerian approach where wages
are solely determined on the basis of (observed and unobserved) skills. Equilibrium skill prices
depend on supply and demand factors that shape the evolution of the wage structure over time.
Underlying changes in demand linked to technological change and o?shoring can certainly have an
impact on the allocation of labor across industry and occupations, but ultimately wage changes
are only linked to changes in the pricing of skills. Acemoglu and Autor (2011) refer to this
model as the “canonical model” that has been used in many in?uential studies such as Katz and
Murphy (1992), for example.
There is increasing evidence, however, that the canonical model does not provide a satisfac-
tory explanation for several important changes in the wage structure observed over the last few
decades. This is discussed in detail in Acemoglu and Autor (2011) who mention, among other
things, two important shortcomings of the canonical model that are particularly important in
the context of this paper. First, the canonical model does not easily account for di?erential
changes in inequality in di?erent parts of the distribution, such as the “polarization” of the wage
distribution of the 1980s. Second, the model does not provide insight on the contribution of
occupations to changes in the wage structure because it does not draw any distinction between
“skills” and “tasks”. Acemoglu and Autor (2011) address these shortcomings by proposing a
Ricardian model of the labor market that incorporates a clear distinction between skills and
tasks. This model goes a long way towards explaining the recent changes in the wage structure
that are hard to account for using the canonical model.
Relative to Acemoglu and Autor (2011), we go one step further here by allowing wages to
vary across occupations conditional on the skills of workers, as in the standard Roy model. In
Acemoglu and Autor’s Ricardian model, workers with di?erent levels of skills are systematically
allocated to di?erent occupations on the basis of comparative advantage. But, critically, the law
of one price holds within each skill group in the sense that wages are equalized across occupations,
conditional on skill.
Unlike Acemoglu and Autor, we do not develop a full model of the labor market showing how
skills are allocated to occupations (i.e. tasks), and how wages across skills and tasks are set
in equilibrium. But our approach that allows wages to vary across occupations, conditional on
4
tasks, follows a long tradition in labor economics. In Welch (1969), the wage w
it
of worker i at
time t is set as follows:
(1) w
it
= ?
t
+
K

k=1
r
kt
S
ik
+ u
it
,
where the S
ik
’s (for k = 1, ..., K) are skill components embodied in worker i, and u
it
is an
idiosyncratic error term. The r
kt
’s are the returns (or “prices”) to each skill component k, while
?
t
is a base payment that a worker receives regardless of her skills.
As ?rst pointed out by Rosen (1983), Welch (1969)’s model where wages solely depend on the
bundle of skills supplied by each worker is unlikely to hold when workers are allocated to di?erent
tasks or occupations. Consider what happens when workers have the choice between several
occupations that have di?erent production functions (or skill requirements). Following Rosen
(1983) and Acemoglu and Autor (2011), assume that the production function in an occupation
simply depends on the sum of skills supplied by all workers in the occupation. Then, for each
skill k, the aggregate supply of skill in the occupation is the sum of S
ik
over all workers i in the
occupation. Rosen (1983) shows that returns to skill only get equalized across occupations if
there is su?cient heterogeneity in skill mix across workers to accommodate the large di?erences
in skill requirements across occupations.
To take a simple example, consider two occupations, mathematicians and movers, and two
skills, cognitive and physical strength. Clearly, cognitive skills are a particularly productive
skill for mathematicians, while physical strength is essential for movers. Say, for instance, that
the marginal product of cognitive and physical skills will only be equalized across these two
occupations if the cognitive/physical skill ratio is 10 for mathematicians, and 0.1 for movers.
Because workers move into an occupation with their own bundle of skills, marginal products
will only be equalized if the average ratio of cognitive to physical skills is 100 times larger for
mathematicians than for movers. Although people who choose to be mathematicians certainly
tend to have a high ratio of cognitive to physical skills, it is very unlikely that people are
heterogenous to the point where it is possible to accommodate the skill ratios required in each
occupation. Therefore, there will be an oversupply of physical skills among mathematicians that
will drive the return to physical skills to almost zero in that occupation. Likewise, there will be
an oversupply of cognitive skills among movers that will drive the return to this skill to close to
5
zero. As a result, the return to skill will not be equalized across these two occupations.
The key problem here is that each worker comes with a bundle of skills to be used in a single task
or occupation. If skills could be unbundled and e?ciently allocated across occupations, returns
to skill would all get equalized across occupations, as in Welch (1969). Heckman and Sheinkman
(1987) test and soundly reject the unbundling hypotheses by showing that wages systematically
di?er across sectors even after controlling for observed and unobserved skills. Gibbons et al.
(2005) reach a similar conclusion when looking at both industry or occupation wage di?erentials.
In other words, there is a wide range of empirical evidence in support of the Roy model of wage
determination and self selection where skills are rewarded di?erently in di?erent occupations,
which leads to a systematic sorting of workers into these di?erent occupations. Given the strong
theoretical and empirical reasons why wages and returns to skill may not get equalized across
occupations, in this paper we explore the consequences for the overall wage structure of di?erences
and changes in wage setting across occupations.
5
Generalizing equation (1) to the case where returns to skill vary across occupations k (for
k = 1, .., K) yields the following wage setting equation:
(2) w
ijt
= ?
jt
+
K

k=1
r
jkt
S
ik
+ u
ijt
,
where w
ijt
is now the wage of individual i in occupation j at time t, the r
jkt
’s are the returns
(or “prices”) to each skill component k in occupation j, and ?
jt
is a base payment that a worker
receives in occupation j regardless of her skills.
This wage-setting model is general enough to capture the impact of factors such as technological
change or o?shoring on wages. For instance, consider the return to manual dexterity. Prior to
the introduction of sophisticated robots or other computer technologies, manual dexterity was
a highly valued skill in some particular occupations (e.g. precision workers) but not in others
(e.g. sales clerk). When routine manual tasks start getting replaced by automated machines or
robots, this depresses the return to manual dexterity in occupations where these returns were
previously high, but not in others where manual dexterity was not a job requirement.
Similarly, returns to social or communication skills are presumably high in occupations where
5
A numbers of other reasons such as compensating wage di?erentials, adjustment costs, or occupation-speci?c human
capital could also be invoked for explaining why wages fail to equalize across occupations, conditional on skill. We focus on
Rosen (1983)’s model instead as it provides a rationale for why the return to skill, and not just the level of wages, di?ers
across occupations. This plays a central role when looking at the contribution of occupational wage setting in the overall
distribution of wages.
6
face-to-face meetings with customers are important (e.g. sale managers). In occupations where
face-to-face meetings are not essential (e.g. computer programmers), however, the returns to
these skills have likely declined as ?rms are now able to o?shore a lot of this work. The general
point here is that the impact of technological change and o?shoring can be captured in the above
model by changes in the skill pricing parameters r
jkt
.
B. Empirical test of the occupational wage setting model
Ideally, we would like to estimate the skill pricing parameters r
jkt
using repeated cross sections
from a large data set containing detailed information on wages, skills, and occupations. We could
then look at the contribution of changes in occupational wage setting to the overall changes in
the wage structure by computing counterfactual distributions based on alternative measures of
r
jkt
(and ?
jt
). Unfortunately, no such data set exists. As a result, we instead derive some indirect
predictions from our Roy-type wage setting model (2) to look at the contribution of occupational
wage setting in changes in the wage structure.
A ?rst general prediction of the model is that if r
jkt
changes di?erently in di?erent occupations,
this should have an impact on both the between- and within-occupation dimensions of wage
inequality. The simple intuition for this prediction is that if the return to a skill heavily used in
one occupation goes up, the wage gap between that occupation and others will increase (between-
occupation dimension), and so will the wage dispersion within the occupation (within-occupation
dimension). One ?rst test of whether changes in occupation-speci?c skill prices contribute to
changes in inequality consists, therefore, in seeing whether there are signi?cant di?erences in the
changes in both the level and dispersion of wages across occupations.
A second prediction is that changes in both the level and dispersion of wages in occupations
should be systematically related to the task content of occupations. For example, in the O*NET
data, discussed in the next section, economists get a high score on the task “analyzing data or
information”. Presumably, having good cognitive skills is quite important for performing these
types of tasks. In the Roy model, we expect the return to cognitive skills to be high among
economists, so that people with high values of these skills sort into that occupation. To the
extent that the introduction of better computers increases the marginal product of cognitive
skills among economists, we expect both the level and the dispersion of wages (gap between
economists with more and less cognitive skills) to increase for economists, or other occupations
getting a high score on “analyzing data or information”.
7
To summarize, although wages depend solely on skills and occupation-speci?c returns to skill
in equation (2), the task content of occupations should be a useful predictor for changes in both
the level and dispersion of wages across occupations. Another advantage of using the task content
of occupations is that it reduces the dimensionality of the estimation problem by summarizing
a large set of occupation dummies using a more limited number of tasks performed in these
occupations.
If the only distributional statistic of interest was the variance, we could compute the contribu-
tion of occupations to the overall variance by simply looking at the mean and variance of wages in
each occupation, and plugging those into the standard analysis-of-variance formula. Looking at
the variance fails to capture, however, the polarization of the wage distribution that has occurred
since the late 1980s. As a result, we need an alternative way of summarizing changes in the wage
distribution for each occupation that is ?exible enough to allow for di?erent changes in di?erent
parts of the distribution.
We do so by ?rst estimating linear regression models that relate the changes in wages at
di?erent quantiles q of the wage distribution for each occupation, ?w
q
j
, to the corresponding
wage quantile in the base period, w
q
j0
:
(3) ?w
q
j
= a
j
+ b
j
w
q
j0
+ ?
q
+ ?
q
j
,
where ?
q
is a percentile-speci?c error component, which represents a generic change in the return
to unobservable skills of the type considered by Juhn, Murphy, and Pierce (1993), and ?
q
j
is an
idiosyncratic error term. As we explain in more detail in the technical appendix, the occupation-
speci?c intercepts (a
j
) and slopes (b
j
) from these regressions are two summary statistics that
can be directly linked to changes in returns to skill requirements in each occupation, ?r
jk
.
6
In
addition, the intercept depends on changes in occupational wage di?erentials that are unrelated
to skills, ??
j
. We use these parameters (a
j
and b
j
) to characterize the changes in the wage
distribution for each occupation. The intercepts a
j
capture between-occupation changes in wage
dispersion, while the slopes b
j
capture within-occupation changes. As in the single index model
of Card and Lemieux (1996), b
j
> 0 indicates an increase in returns to skill, while b
j
< 0 indicates
the opposite.
In the second step of the analysis, we link the estimated intercepts and slopes (´a
j
and
´
b
j
) to
6
More precisely, we show that a
j
= ??
j
+

K
k=1
?r
jk
S
jk
and b
j
? 1/?
2
j0
[

K
k=1

r
jk0
?r
jk

· ?
2
kj
+1/2??
2
uj
], where ?
.j
are the related within-occupation standard deviations.
8
measures of the task content of each occupation. Since technological change and o?shoring are
the key explanatory variables used in the second step, the next section discusses in detail how
we construct ?ve summary measures of occupational tasks. For the time being, de?ne these
summary measures of tasks as TC
jh
, for h = 1, .., 5.
The second step regressions are
(4) ´a
j
= ?
0
+
5

h=1
?
jh
TC
jh
+ µ
j
,
and
(5)
´
b
j
= ?
0
+
5

h=1
?
jh
TC
jh
+ ?
j
.
There is no direct mapping from the task content measures TC
jh
to the return to skill param-
eters, r
jk
. We expect to see, however, a steeper decline in the relevant r
jkt
’s in occupations with
traditional task requirements that are more easily replaceable by technology or o?shore workers.
For example, for occupations scoring high in terms of the routine aspect of the work performed,
we should observed negative estimates of both a
j
and b
j
. Similarly, for occupations that involve
face-to-face meetings are less likely to be o?shored, we should observed positive estimates of a
j
or b
j
parameters.
II. Data
A. Wage Data
The empirical analysis is based on data for men from the Outgoing Rotation Group (ORG)
Supplements of the Current Population Survey.
7
The wage measure used is an hourly wage
measure computed by dividing earnings by hours of work for workers not paid by the hour. For
workers paid by the hour, we use a direct measure of the hourly wage rate. CPS weights are used
throughout the empirical analysis. At the beginning and end of the three decades we analyze,
we pool several years of data together to improve the precision of the estimates. For the ?rst
period being analyzed (1976-78 to 1988-90), we start with data from the May CPS for the years
1976 to 1978.
8
For the second, and main period of analysis, we use 1988-90 as the base year and
7
The data ?les were processed as in Lemieux (2006b) who provides detailed information on the relevant data issues.
8
The reason we use the May CPS instead of the MORG CPS for 1979 or 1980 is that union status was not asked in
MORG CPS until 1983. Since inequality was relatively stable during the 1970s (see DiNardo, Fortin, and Lemieux, 1996),
9
2000-02 as the end year to make sure we fully capture all the changes that occurred during the
1990s.
9
The base year for the ?nal period is 2003-2004, which does not overlap with the end
year of the 1988-90 to 2000-02 period. The reason for this discrepancy is that there was a major
change in the coding of occupations when the 2000 census classi?cation was introduced in 2003.
For the sake of consistency in the coding of occupations, we only look at post-2002 data when
performing the decomposition for recent years. This explains why the ?nal period we consider
goes from 2003-04 to 2009-10.
10
Consistent with Autor, Katz and Kearney (2006), Figure 1 shows that 1988-90 to 2000-02
changes in real wages ($1979) at each percentile of the wage distribution follow a U-shaped
curve. In the ?gure, we also contrast these wage changes with those that occurred before (1976-
78 to 1988-90) and after (2003-04 to 2009-10) the 1990s. The ?gure illustrates that wage changes
in the top half of the distribution were quite similar during all time periods, though the changes
have been more modest since 2003. Wages at the very top increased much more than wages in
the middle of the distribution, resulting in increased top-end inequality. By contrast, inequality
in the lower half of the distribution increased rapidly during the 1980s, but decreased sharply
after 1988-90 as wages at the bottom grew substantially more than those in the middle of the
distribution. The bottom part of the distribution has remained more or less unchanged since
2003. This is a bit surprising since recessions are typically believed to have a particularly negative
impact at the bottom end of the distribution. More generally, wage changes for 2003-04 to 2009-
2010 should be interpreted with caution since macroeconomic circumstances were very di?erent
during these two time periods. By contrast, the overall state of the labor market was more or
less comparable in the other years considered in the analysis.
11
B. Occupational Measures of Technological Change and O?shoring Potential
Like many recent papers (Goos and Manning (2007), Goos, Manning and Salomons (2010),
Crin´o (2010)) that study the task content of jobs, and in particular their o?shorability, we use
the precise choice of base year for studying changes in inequality during the 1980s should not have much impact on the
results.
9
By pooling three years of data at each end of the sample period, we obtain relatively large samples both in 1988-90
(268,497 observations) and 2000-02 (252,397 observations).
10
Note that there was also a major change in the coding of occupations classi?cation when the 1980 census classi?cation
was introduced in 1983. The timing is unfortunate as it coincides with the time period when inequality expanded the most
dramatically (1980 to 1984). Since changes in occupational classi?cation were not as dramatic as those that happened in
the early 2000s, we used a crosswalk to keep a reasonably consistent de?nition of occupations between 1976-78 and 1988-90.
11
The average unemployment rate for the 1976-78, 1988-90, 2000-02, and 2003-04 period is 6.2, 5.9, 4.8 and 5.8 percent,
respectively, compared to 9.5 percent for 2009-10.
10
the O*NET data to compute our measures of technological change and o?shoring potential.
12
Our aim is to produce indexes for all 3-digit occupations available in the CPS, a feat that
neither Jensen and Kletzer (2007) nor Blinder (2007) completed.
13
Our construction of an
index of potential o?shorability follows the pioneering work of Jensen and Kletzer (2010) [JK
hereinafter] while incorporating some of the criticisms of Blinder (2007). The main concern of
Blinder (2007) is the inability of objective indexes to take into account two important criteria
for non-o?shorability: a) that a job needs to be performed at a speci?c U.S. location, and b)
that the job requires face-to-face personal interactions with consumers. We thus pay particular
attention to the “face-to-face” and “on-site” categories in the construction of our indexes.
In the spirit of Autor, Levy, and Murnane (2003), who used the Dictionary of Occupational
Titles (DOT) to measure the routine vs. non-routine, and cognitive vs. non-cognitive aspects
of occupations, JK use the information available in the O*NET, the successor of the DOT,
to construct their measures. The O*NET content model organizes the job information into a
structured system of six major categories: worker characteristics, worker requirements, experience
requirements, occupational requirements, labor market characteristics, and occupation-speci?c
information.
Like JK, we focus on the “occupational requirements” of occupations and also add some “work
context” measures to enrich the “generalized work activities” measures. JK consider eleven
measures of “generalized work activities”, subdivided into ?ve categories: 1) on information
content: getting information, processing information, analyzing data or information, document-
ing/recording information; 2) on internet-enabled: interacting with computers; 3) on face-to-face
contact: assisting or caring for others, performing or working directly with the public, estab-
lishing or maintaining interpersonal relationships; 4) on the routine or creative nature of work:
making decisions and solving problems, thinking creatively; 5) on the “on-site” nature of work:
inspecting equipment, structures or material.
We consider ?ve similar categories, “information content” and “automation”, thought to
be positively related to o?shorability (and technology), and “face-to-face”, “on-site job”, and
“decision-making”, thought to be negatively related to o?shorability.
14
Our ?rst category “infor-
12
Available from National Center for O*NET Development. We use the O*NET 13.0 which has many updatedelements by
comparison with the O*NET 10.0 used in Goos, Manning and Salomons (2010). Alternatively, using the German IAB/BIBB
survey, Spitz-Oener (2006) and Dustmann, Ludsteck and Sch¨onberg (2009) use task measures collected at the worker level.
13
Blinder (2010) did not compute his index for Category IV occupations (533 occupations out of 817), that are deemed
impossible to o?shore. Although, Jensen and Kletzer (2010) report their index for 457 occupations, it is not available for
many blue-collar occupations (occupations SOC 439199 and up).
14
Appendix Table A2 lists the exact O*NET reference number of the generalized work activities and work context items
that make up the ?ve indexes and indicate the elements also used by JK and/or Blinder (2007).
11
mation content” regroups JK categories 1) and 2). It identi?es occupations with high information
content that are likely to be a?ected by ICT technologies; they are also likely to be o?shored if
there are no mitigating factor. Our second category “automation/routinization” is constructed
using some work context measures to re?ect the degree of potential automation of jobs and is
an update on the manual routine index of Autor et al. (2003). The work context elements are:
“degree of automation”, “importance of repeating same tasks”, “structured versus unstructured
work (reverse)”, “pace determined by speed of equipment”, and “spend time making repetitive
motions”. We think of these ?rst two categories as being more closely linked to technological
change, thus we called the group “Technology”. We agree with Blinder (2007) that there is some
degree of overlap with o?shorability. Indeed, the information content is a substantial component
of JK’s o?shorability index.
Our three remaining categories “face-to-face contact”, “on-site job” and “decision-making” are
meant to capture features of jobs that cannot be o?shored. Note, however, that the decision-
making features were also used by Autor et al. (2003) to capture the notion of non-routine
cognitive tasks. Our “face-to-face contact” measure adds one work activity “coaching and devel-
oping others” and one work context “face-to-face discussions” element to JK’s face-to-face index.
Our “on-site job” measure adds four other elements of the JK measure: “handling and mov-
ing objects”, “controlling machines and processes”, “operating vehicles, mechanized devices, or
equipment”, and “repairing and maintaining mechanical equipment” and “electronic equipment”
(weight of 0.5 to each of these last two elements). Our “decision-making” measure adds one work
activity “developing objectives and strategies” and two work context elements, “responsibility
for outcomes and results” and “frequency of decision making” to the JK measure. We use the
reverse of these measures of non-o?shorability to capture “O?shorability”.
For each occupation, the O*NET provides information on the “importance” and “level” of
required work activity and on the frequency of ?ve categorical levels of work context.
15
We follow
Blinder (2007) in arbitrarily assigning a Cobb-Douglas weight of two thirds to “importance” and
one third to “level” in using a weighed sum for work activities. For work contexts, we simply
multiply the frequency by the value of the level. Each composite TC
h
score for occupation j in
15
For example, the work context element “frequency of decision-making” has ?ve categories: 1) never, 2) once a year or
more but not every month, 3) once a month or more but not every week, 4) once a week or more but not every day, and 5)
every day.
12
category h is, thus, computed as
(6) TC
jh
=
A
h

k=1
I
2/3
jk
L
1/3
jk
+
C
h

l=1
F
jl
? V
jl
,
where A
h
is the number of work activity elements, and C
h
the number of work context elements
in the category TC
h
, h = 1, . . . , 5.
To summarize, we compute ?ve di?erent measures of task content using the O*NET: i) the
information content of jobs, ii) the degree of automation of the job and whether it represents
routine tasks, iii) the importance of face-to-face contact, iv) the need for on-site work, and v)
the importance of decision making on the job. We use these measures to assess both the impact
of technological change and o?shorability on changes in wages.
Table 1 shows a number of summary statistics for the ?ve normalized measures of task con-
tent.
16
The table reports the average value of the measures of task content for ?ve major
occupational groups. In Panel A, these broad occupations are constructed using the 1980-1990
Census occupation codes. Corresponding measures based on the 2002 census occupation codes
are reported in Panel B. Since most of the empirical analysis presented below focuses on the
1990s, we limit our discussion to the results reported in Panel A.
The results reported in Table 1 are generally consistent with the evidence reported in related
studies. Professional, managerial and technical occupations have the highest score in terms of
their use of information technology, and the lowest score for automation. As a result, these
high wage occupations are likely to bene?t the most from technological change. Interestingly,
this broad occupation group also gets the highest score in terms of face-to-face interactions and
decision making, suggesting that they should not be too adversely a?ected by o?shoring.
17
At the
other end of the spectrum, production workers and operators have a relatively low score in terms
of their use of information technology and a high score for automation. These jobs also involve
little face-to-face interactions or decision making. Therefore, both o?shoring and technological
change are expected to have an adverse impact on wages in these occupations.
The pattern of results for on-site work is more complex. Consistent with our expectations,
primary, construction and transport workers have the highest score for on-site work, while clerical
16
The range of these measures goes from zero to one since we normalize the task measures by dividing them by their
maximum value observed over all occupation. These normalized tasks measures provide a useful ranking of occupations
along each of these ?ve dimensions, but the absolute values of the task measures have no particular meaning.
17
Including decision-making in our o?shorability measure thus allows a sharper distinctionbetween managerial and clerical
jobs.
13
and sales workers have the lowest score. Interestingly, production workers and operators also get
a high score for working on-site, suggesting that they should not be too a?ected by o?shoring.
This illustrates the limits of the O*NET measures as a way of capturing the o?shorability of jobs.
While it is true that production workers tend to work on a speci?c site, the whole production
process could still be o?shored. This is quite di?erent from the case of construction workers for
whom the “site” has to be in the United States. As a result, the e?ect of on-site work on wages
should be interpreted with some caution.
III. Occupational Wage Pro?les: Results
In this section, we ?rst estimate the linear regression models for within-occupation quantiles
from equation (3), and then link the estimated slope and intercept parameters to our measures of
task content from the O*NET as in equations (4) and (5). We refer to these regression models as
“occupation wage pro?les”. We focus this ?rst part of the analysis on the 1990s as it represents
the time period when most of the polarization of wages documented by Autor, Katz and Kearney
(2006) occurred.
Note that, despite our large samples based on three years of pooled data, we are left with a small
number of observations in many occupations when we work at the three-digit occupation level. In
the analysis presented in this section, we thus focus on occupations classi?ed at the two-digit level
(40 occupations) to have a large enough number of observations in each occupation.
18
This is
particularly important given our empirical approach where we run regressions of change in wages
on the base-period wage. Sampling error in wages generates a spurious negative relationship
between base-level wages and wage changes that can be quite large when wage percentiles are
imprecisely estimated.
19
In principle, we could use a large number of wage percentiles, w
q
jt
, in
the empirical analysis. But since wage percentiles are strongly correlated for small di?erences
in q, we only extract the nine deciles of the within-occupation wage distribution, i.e. w
q
jt
for
q = 10, 20, ..., 90. Finally, all the regression estimates are weighted by the number of observations
(weighted using the earnings weight from the CPS) in each occupation.
Detailed estimates of several speci?cations for equation (3) are presented in Appendix Table
18
Though there is a total of 45 occupations at the two-digit level, we combine ?ve occupations with few observations
to similar but larger occupations. Speci?cally, occupation 43 (farm operators and managers) and 45 (forestry and ?shing
occupations) are combined with occupation 44 (farm workers and related occupations). Another small occupation (20, sales
related occupations) is combined with a larger one (19, sales workers, retail and personal services). Finally two occupations
in which very few men work (23, secretaries, stenographers, and typists, and 27, private household service occupations) are
combined with two other larger occupations (26, other administrative support, including clerical, and 32, personal services,
respectively).
19
The bias could be adjusted using a measurement-error corrected regression approach, as in Card and Lemieux (1996),
or an instrumental variables approach.
14
A3 and discussed in the Technical Appendix. The main ?nding is that occupation-speci?c slopes
and intercepts both have to be included in the regression models to adequately account for the
observed wage changes. This general model explains over 90 percent of the variation in the data,
and all of the curvature (or U-shape feature) that characterizes wage changes over that period.
We illustrate the ?t of the model by plotting occupation-speci?c regressions for the 30 largest
occupations curves in Figure 2.
20
While it is not possible to see what happens for each and every
occupation on this graph, there is still a noticeable pattern in the data. The slope for occupations
at the bottom end of the distribution tends to be negative. Slopes get ?atter in the middle of
the distribution, and generally turn positive at the top end of the distribution. In other words, it
is clear from the ?gure that the set of occupational wage pro?les generally follow the U-shaped
pattern observed in the raw data. In light of the discussion in Section 2, this suggests that skills
that used to be valuable in low-wage occupations are less valuable than they used to be, while
the opposite is happening in high-wage occupations.
We next explore this hypothesis more formally by estimating the regression models in equations
(4) and (5) that link the intercept and slopes of the occupation wage change pro?les to the task
content of occupations.
21
The results are reported in Table 2. In the ?rst four columns of Table
2, we include task measures separately in the regressions (one regression for each task measure).
To adjust for the possible confounding e?ect of overall changes in the return to skill, we also
report estimates that control for the base (median) wage level in the occupation.
As some tasks involving the processing of information may be enhanced by ICT technologies,
we would expect a positive relationship between our “information content” task measure and
the measures of occupational wage changes. On the other hand, to the extent that technological
change allows ?rms to replace workers performing these types of tasks with computer driven
technologies, we would expect both the intercept and slope of occupational wage changes with
high degree of “automation” to decline over time.
22
Although occupations in the middle of the
wage distribution may be most vulnerable to technological change, some also involve relatively
more “on-site” work (e.g. repairmen) and may, therefore, be less vulnerable to o?shoring. We
also expect workers in occupations with a high level of “face-to-face” contact, as well as those
20
To avoid overloading the graph, we exclude ten occupations that account for the smallest share of the workforce (less
than one percent of workers in each of these occupations).
21
To be consistent with equation (A-8), we have recentered the observed wage changes so that the intercept for each
occupation corresponds to the predicted change in wage at the median value of the base wage.
22
In Appendix Figure A1, we show the connection between task measures and average occupational wages for all three
digit occupations. While some of the measures (information content and no decision making) tend to be monotonically
related to occupation wages, others follow a more interesting shape. Consistent with Autor, Levy and Murnane (2003), the
“automation” task follows an inverse U-shaped curve.
15
with a high level of “decision-making”, to do relatively well in the presence of o?shoring.
The strongest and most robust result in Table 2 is that occupations with high level of automa-
tion experience a relative decline in both the intercept and the slope of their occupational wage
pro?les. The e?ect is statistically signi?cant in six of the eight speci?cations reported in Table
2. The other “technology” variable, information content, has generally a positive and signi?cant
e?ect on both the intercept and the slope, as expected, when included by itself in columns 1 to
4. The e?ect tends to be weaker, however, in models where other tasks are also controlled for.
The e?ect of the tasks related to the o?shorability of jobs are reported in the last three rows of
the table. Note that since “on-site”, “face-to-face”, and “decision making” are negatively related
to the o?shorability of jobs, we use the reverse of these tasks in the regression to interpret
the coe?cients as the impact of o?shorability (as opposed to non-o?shorability). As a result,
we expect the e?ect of these adjusted tasks to be negative at the bottom end of the wage
distribution. For instance, the returns to skill in jobs that do not require face-to-face contacts
will likely decrease since it is now possible to o?shore these types of jobs to another country.
As discussed earlier and argued by Crisculo and Garicano (2010), increasing the o?shoring of
complementary tasks may increase wages at the top end of the wage distribution.
The results reported in Table 2 generally conform to expectations. The e?ect of “no face to
face” and “no decision making” is generally negative. By contrast, the e?ect of “no on-site work”
is generally positive, which may indicate that on average we are capturing the positive e?ect of
o?shoring. Another possible explanation is that the O*NET is not well suited for distinguishing
whether a worker has to work on “any site” (i.e. an assembly line worker), vs. working on a site
in the United States (i.e. a construction worker).
More importantly, Table 2 shows that the task measures explain most of the variation in the
slopes, though less of the variation in the intercepts. This suggests that we can capture most of
the e?ect of occupations on the wage structure using only a handful of task measures, instead of a
large number of occupation dummies. The twin advantage of tasks over occupations is that they
are a more parsimonious way of summarizing the data, and are more economically interpretable
than occupation dummies.
23
We draw two main conclusions from Table 3. First, as predicted by the linear skill pricing
model of Section 2, the measures of task content of jobs tend to have a similar impact on the
intercept and on the slope of the occupational wage pro?les. Second, tasks account for a large
23
Determining which tasks to include remains an important challenge of the approach. Here we simply follow the main
tenants of the literature.
16
fraction of the variation in the slopes and intercepts over occupations, and the estimated e?ect
of tasks are generally consistent with our theoretical expectations. Taken together, this suggests
that occupational characteristics as measured by these ?ve task measures can play a substantial
role in explaining the U-shaped feature of the raw data illustrated in Figure 1. These results also
show why models that do no account for within-occupation changes are likely to miss a signi?cant
part of the contribution of the task content of jobs to changes in the wage distribution.
Although the analysis presented above helps illustrate the mechanisms through which occu-
pations play a role in changes in the wage structure, it does not precisely quantify the relative
contribution of occupational factors to these changes.
24
We next examine the explanatory power
of occupational tasks in the context of a formal decomposition of changes in the wage distribution.
IV. Decomposing Changes in Distributions Using RIF-Regressions
In this section, we show how to formally decompose changes in the distribution of wages into
the contribution of occupational and other factors using the recentered in?uence function (RIF)
regression approach introduced by Firpo, Fortin, and Lemieux (2009).
25
As is well known, a
standard regression can be used to perform a Oaxaca-Blinder decomposition for the mean of
a distribution. RIF-regressions allow us to perform the same kind of decomposition for any
distributional parameter, including percentiles.
In general, any distributional parameter can be written as a functional ?(F
Y
) of the cumulative
distribution of wages, F
Y
(Y ).
26
Examples include wage percentiles, the variance of log wage, the
Gini coe?cient, etc. The ?rst part of the decomposition consists of dividing the overall change
in a given distributional parameter into a composition e?ect linked to changes in the distribution
of the covariates, X, and a wage structure e?ect that re?ects how the conditional distribution
of wage F(Y |X) changes over time. In a standard Oaxaca-Blinder decomposition, the wage
structure e?ect only depends on changes in the conditional mean of wages, E(Y |X). More
generally, however, the wage structure e?ect depends on the whole conditional wage distribution.
It is helpful to discuss the decomposition problem using the potential outcomes framework.
We focus on di?erences in the wage distributions for two time periods, 1 and 0. For a worker i,
24
Two limitations of the approach are the linearity of the speci?cation and the focus on the occupation-speci?c distribution
of wages. Also the approach does generally control for other commonly considered factors, such as education, experience,
unionization, etc.
25
Firpo, Fortin, and Lemieux (2007, 2011) explain in more detail how to perform these decompositions, and show how
to compute the standard errors for each element of the distribution. Here, we simply present a short summary of the
methodology.
26
In this section, we denote the wage using Y instead of W to be consistent with Firpo, Fortin, and Lemieux (2007) and
the program evaluation literature.
17
let Y
1i
be the wage that would be paid in period 1, and Y
0i
the wage that would be paid in period
0. Therefore, for each i we can de?ne the observed wage, Y
i
, as Y
i
= Y
1i
· T
i
+Y
0i
· (1 ?T
i
), where
T
i
= 1 if individual i is observed in period 1, and T
i
= 0 if individual i is observed in period 0.
27
There is also a vector of covariates X ? X ? R
K
observed in both periods.
Consider ?
?
O
, the overall change over time in the distributional statistic ?. We have
?
?
O
= ?
_
F
Y
1
|T=1
_
??
_
F
Y
0
|T=0
_
=
?
_
F
Y
1
|T=1
_
? ?
_
F
Y
0
|T=1
_
. ¸¸ .
?
?
S
+
?
_
F
Y
0
|T=1
_
??
_
F
Y
0
|T=0
_
. ¸¸ .
?
?
X
,
where ?
?
S
is the wage structure e?ect, while ?
?
X
is the composition e?ect. Key to this decomposi-
tion is the counterfactual distributional statistics ?
_
F
Y
0
|T=1
_
. This represents the distributional
statistic that would have prevailed if workers observed in the end period (T = 1) had been paid
under the wage structure of period 0.
Estimating this type of counterfactual distribution is a well known problem. For instance,
DiNardo, Fortin and Lemieux (1996) suggest estimating this counterfactual by reweighting the
period 0 data to have the same distribution of covariates as in period 1. We follow the same ap-
proach here, since Firpo, Fortin and Lemieux (2007) show that reweighting provides a consistent
nonparametric estimate of the counterfactual distribution under the ignorability assumption.
However, the main goal of this paper is to separate the contribution of di?erent subsets of
covariates to ?
?
O
, ?
?
S
, and ?
?
X
. This is easily done in the case of the mean where each component
of the above decomposition can be written in terms of the regression coe?cients and the mean of
the covariates. For distributional statistics besides the mean, Firpo, Fortin, and Lemieux (2009)
suggest estimating a similar regression where the usual outcome variable, Y , is replaced by the
recentered in?uence function RIF(y; ?) of the statistic ?. The recentering consists of adding
back the distributional statistic ? to the in?uence function IF(y; ?): RIF(y; ?) = ? + IF(y; ?).
Note that in the case of the mean where the in?uence function is IF(y; µ) = y ? µ, we have
RIF(y; µ) = µ + (y ? µ) = y. Since the RIF(y; µ) is simply the outcome variable y, the RIF-
regression for the mean corresponds to a standard wage regression.
It is also possible to compute the in?uence function for many other distributional statistics.
Of particular interest is the case of quantiles. The ?-th quantile of the distribution F is de?ned
27
Since a given individual i is only observed in one of the two periods, we either observe Y
1i
or Y
0i
, but never both.
18
as the functional, Q(F, ?) = inf{y|F ? ?}, or as q
?
for short. Its in?uence function is:
IF(y; q
?
) =
? ?1I {y ? q
?
}
f
Y
(q
?
)
.
The recentered in?uence function of the ?
th
quantile is RIF(y; q
?
) = q
?
+ IF(y; q
?
).
Consider ?
?
t
, the estimated coe?cients from a regression of RIF(y
t
; ?) on X
?
?
t
= (E[X · X

| T = t])
?1
· E[RIF(y
t
; ?
t
) · X | T = t] , t = 0, 1.
Because of the law of iterated expectations, distributional statistics can be expressed in terms of
expectations of the conditional recentered in?uence functions,
?(F
t
) = E
X
[E[RIF(y
t
;?)|X = x]] = E[X|T = t] · ?
?
t
.
In particular, the ?
th
quantile RIF-regression aggregates to the unconditional quantile of interest
and allows us to capture both the between and the within e?ects of the explanatory variables.
By analogy with the Oaxaca-Blinder decomposition, we could write the wage structure and
composition e?ects as:
?
?
S
= E[X|T = 1]

(?
?
1
? ?
?
0
) and ?
?
X
= (E[X|T = 1] ? E[X|T = 0])

?
?
0
.
This particular decomposition is very easy to compute since it is similar to a standard Oaxaca-
Blinder decomposition. Firpo, Fortin and Lemieux (2007) point out, however, that there may
be a bias in the decomposition because the linear speci?cation used in the regression is only a
local approximation that does not generally hold for larger changes in the covariates. A related
point was made by Barsky et al. (2002) in the context of the Oaxaca decomposition for the
mean. Barsky et al. point out that when the true conditional expectation is not linear, the
decomposition based on a linear regression is biased. They suggest using a reweighting procedure
instead, though this is not fully applicable here since we also want to estimate the contribution
of each individual covariate.
Firpo, Fortin and Lemieux (2007, 2011) suggest a solution to this problem based on an hybrid
approach that involves both reweighting and RIF-regressions. The idea is that since a regression
is the best linear approximation for a given distribution of X, this approximation may change
19
when the distribution of X changes even if the wage structure remains the same. For example,
if the true relationship between Y and a single X is convex, the linear regression coe?cient will
increase when we shift the distribution of X up, even if the true (convex) wage structure remains
unchanged. This means that ?
?
1
and ?
?
0
may be di?erent just because they are estimated for
di?erent distributions of X even if the wage structure remains unchanged over time.
But reweighting will adjust for this problem. Letting ?(X) be the reweighing function,
?(X) =
Pr(T = 1|X)/Pr(T = 1)
Pr(T = 0|X)/Pr(T = 0)
.
that makes the distributions of X’s in period 0 similar to that of period 1, one can estimate the
counterfactual mean as X
01
=

i?0
´
?(X
i
) · X
i
?? X
1
, and the counterfactual coe?cients ´?
?
01
as
the coe?cients from a regression of
¯
RIF(Y
0
; ?) on the reweighted sample {X
0
;
´
?(X
0
)}.
28
Then
the di?erence ´?
?
1
? ´?
?
01
re?ects a true change in the wage structure.
The composition e?ect
´
?
?
X,R
can be divided into a pure composition e?ect
´
?
?
X,p
using the wage
structure of period 0 and a component measuring the speci?cation error,
´
?
?
X,e
:
´
?
?
X,R
=
_
X
01
?X
0
_
´?
?
0
+ X
01
[´?
?
01
? ´?
?
0
] .
=
´
?
?
X,p
+
´
?
?
X,e
(7)
Similarly, the wage structure e?ect can be written as
´
?
?
S,R
= X
1
(´?
?
1
? ´ ?
?
01
) +
_
X
1
?X
01
_
´ ?
?
01
=
´
?
?
S,p
+
´
?
?
S,e
(8)
and reduces to the ?rst term
´
?
?
S,p
given that the reweighting error
´
?
?
S,e
goes to zero as X
01
??
X
1
.
Again, this decomposition is very easy to compute as it corresponds to two standard Oaxaca-
Blinder decompositions performed on the estimated recentered in?uence functions. The ?rst
compares time period 0 and the reweighted time period 0 that mimics time period 1 and allows
us to obtain the pure composition e?ects. The second compares the time period 1 and the
28
The reweighting function is computed as the ratio of the predicted probabilities obtained from a logit speci?cation that
includes a rich set of interaction between the explanatory variables.
20
reweighted time period 0, and allows use to obtain the pure wage structure e?ects.
V. Decomposition Results: Occupational Characteristics vs. Other Factors
The covariates included in the regressions re?ects the di?erent explanations that have been
suggested for the changes in the wage distribution over our sample period. The key set of
covariates on which we focus are education (six education groups), potential experience (nine
groups), union coverage, and the ?ve measures of occupational task requirements introduced
below. We also include controls for marital status and race in all the estimated models.
29
Before showing the decomposition results, it is useful to discuss some features of the estimated
RIF-coe?cients across the di?erent wage quantiles.
30
For example, the e?ect of the union status
across the di?erent quantiles is highly non-monotonic. In both 1988-90 and 2000-2002, the
e?ect ?rst increases up to 0.4 around the median, and then declines (Appendix Figure A2).
This indicates that unions increase inequality in the lower end of the distribution, but decrease
inequality even more in the higher end of the distribution. The results for unions illustrate
an important feature of RIF-regressions for quantiles, namely that they capture the e?ect of
covariates on both the between- and within-group components of wage dispersion. The between-
group e?ect dominates at the bottom end of the distribution, which explains why unions tend to
increase inequality in that part of the distribution. The opposite happens, however, in the upper
end of the wage distribution where the within-group e?ect dominates the between-group e?ect.
As in the case of unions, we ?nd that three of our ?ve task measures have non-monotonic impact
across the di?erent percentiles of the wage distribution. Both “information” and “no face-to-face”
have an inverse U-shaped impact, while “automation” has a largely negative U-shaped impact.
Furthermore, changes over time in the e?ect of these ?rst two task measures shows a declining
e?ect in the lower middle of the distribution, but an increasing e?ect in the upper middle of
the distribution. Changes over time in the wage e?ect of “automation” indicate a large negative
impact in the middle of the wage distribution, with a much smaller impact at the two ends of the
distribution. This is consistent with Autor, Levy and Murnane (2003) who show that workers
in the middle of the distribution are more likely to experience negative wage changes as the
“routine” tasks they used to perform can now be executed by computer technologies. Changes
29
The sample means for all these variables are provided in Appendix Table A1.
30
The RIF-regression coe?cients for the 10
th
, 50
th
, and 90
th
quantiles in 1988-90 and 2000-02, along with their (robust)
standard errors are reported in Appendix Table A4. The RIF-regression coe?cients for the variance and the Gini are
reported in Appendix Table A5. We also plot in Appendix Figure A2 (standard covariates) and Appendix Figure A3 (?ve
task measures) the estimated coe?cients from RIF-regressions for 19 di?erent wage quantiles (from the 5
th
to the 95
th
quantile) equally spread over the whole wage distribution.
21
over time in the impact of the other tasks measures appear less important.
The results of the decomposition are presented in Figures 3-5. Tables 3 and 4 also summarize
the results for the standard measures of top-end (90-50 gap) and low-end (50-10) wage inequality,
as well as for the variance of log wages and the Gini coe?cient. Note that the base group used in
the RIF-regression models consists of non-union, white, and married men with some college, 15
to 19 years of potential experience, and occupational task measures at half a standard deviation
below their sample averages.
31
A richer speci?cation with additional interaction terms is used to
estimate the logit models used in the computation of the reweighting factor.
32
The reweighting
approach performs well in the sense that the reweighted means of the covariates for the base
period are very close to those for the end period.
33
As is well known (e.g. Oaxaca and Ransom, 1999), the detailed wage structure part of the
decomposition (equation (8)) depends arbitrarily on the choice of the base group. This problem
has mostly been discussed in the case of categorical variables, but it also applies in the case of
continuous variables such as our task content measures.
34
Here, we normalize the task measure
variables such that the average di?erence between the end and beginning period is equal to half
a standard deviation of the raw measure. The wage structure e?ect for each task measure can be
interpreted as the change over time in the wage impact of a half a standard deviation increase in
the measure.
35
We also note that any “composition” e?ect associated with the task measures are
linked to changes in the shares of occupations over time, as our measures of task requirements
for each occupation are invariant over time.
31
We use “some college” as the base group as it represents the modal education group in the 1990s and 2000s. For the
1976-78 to 1988-90 period, we use high schol graduates as the base group as it was still the modal education group during
that period.
32
The logit speci?cation also includes a full set of interaction between experience and education, union status and educa-
tion, union status and experience, and education and occupation task measures.
33
The reweighting error is the second term in equation (8). If the reweighting was replicating the means perfectly, we
would have X
1
= X
01
and the reweighting error would be equal to zero. In Appendix Figure A5, the reweighting error
corresponds to the di?erence between the total composition e?ect obtained by reweighing and with the RIF-regressions and
is found to be very small and not signi?cant.
34
As discussed in Fortin, Lemieux and Firpo (2011), automatic normalization solutions to this issue are not satisfactory,
rather the choice of a reasonable and interpretable base group is preferred.
35
The choice of half of a standard deviation is based on the following reasoning. In Table 1, the di?erence between the
mean value of task measures for all occupations and the mean for the major group with lowest mean ranges from 45 percent
to 101 percent of the standard deviation. For example, the mean for automation in Panel A is 0.6871, which is 0.1014 (or 0.77
standard deviations) above the mean for professional, managerial, and technical occupations. This suggest that occupations
at half a standard deviation below the mean are reasonably representative of a large group of occupations with relatively
low values of the task measures. Thus, we use this criteria as a uniform way of choosing the base group for all ?ve tasks
measures.
22
A. Overall Decomposition Results
Figure 3 shows the overall change in (real log) wages at each percentile ?, (?
?
O
), and decomposes
this overall change into a composition (?
?
X
) and wage structure (?
?
S
) e?ect.
36
Consistent with
Autor, Katz and Kearney (2006), Figure 3b shows that the overall change between 1988-90 and
2000-02 is U-shaped as wage dispersion increases in the top end but declines in the lower end
of the distribution. This stands in sharp contrast with the situation that prevailed in the early
1980s. Figure 3a shows that the corresponding curve is positively sloped for all quantiles as wage
dispersion increases at all points of the distribution (as in Juhn, Murphy, and Pierce, 1993).
Figure 3c shows that although the wage distribution has been much more stable in recent years,
there is still a modest increase in inequality during the 2003-04 to 2009-10 period. On the one
hand, this is not surprising since the period under consideration is half as long as the two other
periods considered in Figure 3. On the other hand, one could have expected a more dramatic
drop in wages at the bottom end of the distribution given the adverse macroeconomic conditions
of the last few years.
Table 3 summarizes the changes reported in Figure 3 using a few standard measures of wage
dispersion. There is a large increase in inequality measures, such as the variance and the 90-10
gap, that capture wage changes over the entire distribution in the 1980s, and a more modest
increase in later periods. Consistent with Figure 3, inequality at the top end of the distribution
(the 90-50 gap) increases in all time periods. By contrast, the 50-10 gap increases before 1990
and after 2003, but declines substantially during the 1990s.
Figure 3 and Table 3 also show that, consistent with Lemieux (2006b), composition e?ects have
contributed to a substantial increase in inequality since the late 1970s. For instance, composition
e?ects account for between 20 percent and 45 percent of the growth in the 90-50 gap in each of
the three time periods. Looking at cumulative changes over all time periods, composition e?ects
account for all of the change in the 50-10 gap, and about a third of the change in the 90-50 gap.
37
But while composition e?ects account for a sizable part of the growth in overall inequality, it fails
to explain the U-shape pattern observed during the 1990s. As a result, all of the 1990s U-shape
feature in the change in the wage distribution is captured by the wage structure e?ect.
36
The composition e?ect reported in Figure 3 only captures the component,

?
?
X,p
from equation (8). The speci?cation
error,

?
?
X,e
, corresponds to the di?erence between the total composition e?ect obtained by reweighting and RIF-regression
methods illustrated in Appendix Figure A4. The ?gure shows that RIF-regressions capture quite accurately the overall trend
in composition e?ects, though there are a number of small discrepancies at various points along the wage distribution, likely
re?ecting spikes in the wage distribution.
37
The total change in the 50-10 and 90-50 gap between 1976-78 and 2009-10 is 0.0363 and 0.2210, respectively. The
corresponding composition e?ect is 0.0353 and 0.0770, respectively.
23
B. Detailed Decomposition Results
Figure 4 moves to the next step of the decomposition using RIF-regressions to apportion the
composition e?ect to the contribution of each set of covariates. Figure 5 does the same for the
wage structure e?ect. To simplify the presentation of the results, Figure 4 reports the composition
e?ect for ?ve set of explanatory factors: union status, education, experience, o?shorability and
technological change.
38
The e?ect of the other covariates used in the RIF-regressions (race and
marital status) is generally small. We report it in Panel A of Table 4 under the “other” category.
For the sake of simplicity, we focus the discussion on the impact of each factor in the lower and
upper part of the distribution. Those are also summarized in terms of the 50-10 and 90-50 gaps
for the main analysis period (1988-90 to 2000-02) in Table 4.
First consider composition e?ects for the 1988-90 to 2000-02 period. With the notable exception
of unions, all factors have a larger impact on the 50-10 than on the 90-50 gap. The total
contribution of all factors other than unionization is 0.033 and -0.002 for the 50-10 and 90-50
gaps, respectively. Composition e?ects linked to factors other than unions thus go in the “wrong
direction” as they account for rising inequality at the bottom end while inequality is actually
rising at the top end of the distribution.
In contrast, composition e?ects linked to unions (the impact of de-unionization) reduce in-
equality at the low end (e?ect of -0.013 on the 50-10 gap) and increase inequality at the top end
(e?ect of 0.027 on the 90-50). Note that, as in a Oaxaca-Blinder decomposition, these e?ects on
the 50-10 and the 90-50 gap can be obtained directly by multiplying the 5.3 percent decline in the
unionization rate (Appendix Table A1) by the RIF-regression estimates of the union e?ects for
1988-90 (Appendix Table A4). The resulting e?ect of de-unionization accounts for 24 percent of
the total change in the 50-10 gap, and 30 percent of the change in the 90-50 gap. The magnitude
of these estimates is comparable to the relative contribution of de-unionization to the growth
in inequality estimated for the 1980s (see Freeman, 1993, Card, 1992, and DiNardo, Fortin and
Lemieux, 1996).
The results for the 1976-78 to 1988-90 period are reported in Figure 4a. Since unionization
declined more dramatically during in the 1980s (9.3 percentage point decline) than in the 1990s
(5.3 percentage point decline), the estimated contribution of de-unionization to inequality changes
is also larger during the earlier period. As in the 1990s, de-unionization has a larger and positive
38
The e?ect of each set of factors is obtained by summing up the contribution of the relevant covariates. For example,
the e?ect for “education” is the sum of the e?ect of each of the ?ve education categories shown in Table A1.
24
e?ect on inequality growth at the top end, and a smaller negative impact at the low end for the
distribution. Interestingly, the results reported in Figure 4a are very similar to those obtained by
DiNardo, Fortin, and Lemieux (1996) using a di?erent method.
39
The e?ect of the other factors
is relatively modest and does not account for much of the large increase in inequality observed
during that period.
The rate of unionization only declined by 0.5 percentage points after 2002 (see Appendix Table
A1). As a result, composition e?ects linked to de-unionization are negligible for the 2003-04 to
2009-10 period. Changes in the distribution of educational attainment has a small impact on
inequality growth, while the e?ect of the other factors is negligible.
Figure 5 reports the corresponding estimates for the wage structure e?ect. As in the case
of composition e?ects, the contribution of each set of covariates to the wage structure e?ect
for 1988-90 to 2000-02 is reported in Panel B of Table 4. Table 4 (and Appendix Figure A6)
also reports the change in the intercept (constant) in the RIF-regressions. As in a standard
Oaxaca-Blinder decomposition, the change in intercepts captures the part of the wage structure
e?ect that cannot be accounted for by the covariates.
40
By de?nition, the change in intercepts
represents the change in the wage distribution for the base group used in the RIF-regression
analysis. One can therefore interpret that component of the decomposition as the residual (or
within-group) change for the base group.
As in the case of the composition e?ects, it is easier to discuss the results by focusing on
the 90-50 and 50-10 gaps presented in Table 4 for the 1988-90 to 2000-02 periods. The results
indicate that -0.050 of the -0.080 change (decline) in the 50-10 gap due to wage structure e?ects
remains unexplained (the e?ect of the “constant” in Table 4). By contrast, changes in the return
to covariates account for all (and even more) of the 0.057 change in the 90-50 gap linked to the
wage structure, as the residual term (the constant) is now negative. Taken at face value, these
results suggest a notable decline in residual wage inequality at most points of the distribution
(see also Appendix Figure 6b). This ?nding is consistent with Lemieux (2006b) who also ?nds
that the (composition adjusted) residual variance declined over that period.
Focusing on the contribution of the di?erent covariates, Table 4 shows that changes in the wage
structure linked to education play a substantial role at the top end of the distribution, but do not
39
Using a conditional reweighting approach, DiNardo, Fortin, and Lemieux ?nd that de-unionization reduced the 50-10
gap by 0.019 and increased the 90-50 gap by 0.040 between 1979 and 1988. The corresponding numbers from Figure 5a are
0.015 and 0.034, respectively.
40
More formally, the total wage structure e?ect,

?
?
S,p
, is the sum of the component explained by the RIF-regression
models,

M
k=2
X
1
(?
?
1
? ?
?
01
), and the residual component ?
?
1,1
? ?
?
01,1
captured by the change in the intercepts.
25
have much impact at the lower end. These ?ndings con?rm Lemieux (2006a)’s conjecture that
the large increase in the return to post-secondary education has contributed to a convexi?cation
of the wage distribution. Changes in the wage structure linked to experience go in the other
direction, re?ecting a decline in the returns to experience since the mid-1980s.
More importantly, the results show that changes in the wage structure linked to the technology
and o?shorability task measures have contributed to the U-shape change in the wage distribution
over this period. Table 4 shows that both factors make a large and positive contribution to the
increase in the 90-50 gap, and a sizable contribution to the decline in the 50-10 gap. This can
also be seen in Figure 5b where the wage structure e?ects linked to technology and o?shoring
both follow a distinct U-shape that closely mirrors the shape of the overall change in the wage
distribution (Figure 4b). The important ?nding here is that technological change and o?shora-
bility, as captured by the occupations task measures included in the RIF-regression, go a long
way towards explaining the polarization of wages observed in the 1990s.
This ?nding also raises an interesting question. If technological change and o?shorability are
indeed contributors to the polarization of wages during the 1990s, should they not also matter
in other time periods? Figure 5a shows that, as in the 1990s, technological change had a large
inequality enhancing e?ect at the top end of the distribution during the 1980s. In the 1980s,
however, technological change also had a large impact at the bottom end of the distribution.
This is consistent with the view that technological change was skill-biased during the 1980s (e.g.
Berman, Bound, and Griliches, 1994), but “routine-biased” during the 1990s (Autor, Levy, and
Murnane, 2003). By contrast, o?shorability has little impact during the 1980s, which is consistent
with service o?shoring being a relatively recent phenomenon, made possible by the development
of the internet and related technologies.
The other elements of the wage structure decomposition for 1976-78 to 1988-90 are generally
consistent with the previous literature. For instance, Figure 5a shows that the growth in returns
to education and experience contribute to the increase in inequality over that period. Interest-
ingly, little residual growth in inequality (the “e?ect” of the constant) is left after all the other
factors have been accounted for (Appendix Figure 6a). This may sound surprising since Juhn,
Murphy, and Pierce (1993) and others show that residual inequality increased substantially dur-
ing the 1980s. The di?erence here is that we add occupational task measures in the decomposition
exercise. This suggests that technological change, as captured by the changing returns to the
task measures, captures most of the residual change left after controlling for standard variables
26
like experience and education.
Finally, Figure 5c shows that, as in the 1990s, o?shorability has contributed to the polarization
of wages since the early 2000s. The fact that o?shorability has a substantial e?ect on wages in
recent years is consistent with the view of many labor market observers who have stressed the
importance of o?shoring, as opposed to technological change, in recent changes in the U.S. labor
market.
41
Interestingly, Figure 5c also shows that technological change only has a modest e?ect
on wage changes between 2003-04 to 2009-10, suggesting that the computer/internet revolution
may have run its course in terms of labor market impacts.
While the detailed decompositions presented in this paper capture most of the explanatory
factors suggested in the inequality literature, they do not account for the minimum wage which
played an important role at the bottom end of the wage distribution during the 1980s (DiNardo,
Lemieux, and Fortin, 1996, and Lee, 1999). As a crude way of capturing the impact of the
minimum wage, we include in the RIF-regressions the fraction of workers potentially a?ected by
changes in the minimum wage for each age and education group.
42
Since the real value of the
minimum wage was relatively stable from 1988-90 and the later periods considered here, we only
report the results of this exercise for the 1976-78 to 1988-90 when the minimum wage declined
dramatically in real terms. The results (reported in Appendix Figure A6) show that the decline
in the minimum wage had a large impact on the 5th and 10th percentiles of the wage distribution,
but little e?ect for higher quantiles. The e?ect at the bottom end is substantial and accounts
for 0.043 of the 0.070 total increase in the 50-10 gap during this period. Thus, except for the
very bottom of the distribution, introducing the minimum wage does not change the substantive
?ndings for the 1976-78 to 1988-90 period discussed above.
A number of interesting conclusions emerge from these detailed wage decompositions. First,
the composition e?ect linked to de-unionization accounts for a substantial part of the change
in inequality both at the lower (50-10) and upper (90-50) end of the distribution during the
1990s. Second, the changing wage structure e?ects linked to unionization, education, and the
occupational task measures of technology and o?shorability all help account for the changing
wage distribution during the 1980s and 1990s. One important contribution of the paper is
to show that occupational task measures substantially enhance the explanatory power of our
41
See Blinder (2007) and the refererences therein.
42
For the period 1976-78 to 1988-90 (the only one considered here), we compute the fraction of workers in 1988-90 who
earn more than the minimum wage in those years, but less than the (average) real value of the minimum wage for 1976-78.
We de?ne workers in this wage range as those potentially a?ected by a change of the minimum wage since their wage would
have likely been higher if the minimum wage had remained constant in real terms.
27
decomposition exercises. Furthermore, the pattern of results is consistent with the view that
technological change was skill-biased during the 1980s, “routine-biased” during the 1990s, but no
longer played much of a role in the years 2000. By contrast, o?shorability only started playing an
important role in the 1990s, and has contributed to the polarization of wages in both the 1990s
and 2000s.
VI. Conclusion
In this paper, we look at the contribution of occupations to changes in the distribution of
wages. We ?rst present a simple Roy-type skill pricing model, and use this as a motivation for
estimating models of changes in within-occupation wage percentiles between 1988-90 and 2000-
02. The ?ndings from this ?rst part of the empirical analysis suggest that changes in occupational
wage pro?les help explain the U-shape in changes in the wage distribution over this period. We
also ?nd that measures of technological change and o?shorability at the occupation level help
predict the changes in the occupational wage pro?les.
We then explicitly quantify the contribution of these factors (technological change and o?-
shorability) to changes in wage inequality relative to other explanations such as de-unionization
and changes in the returns to education. We do so using a decomposition based on the in?uence
function regression approach of Firpo, Fortin, and Lemieux (2009). The results indicate that
technological change and o?shorability are two factors that help enhance our ability to account
for the observed changes in the distribution of wages over the last three decades.
More generally, our results suggest that even after controlling for standard skill measures,
changes in both the level and dispersion of wages across occupations, as captured by our task
measures, have played an important role in changes in the wage distribution. Our interpretation
of this general ?nding is that returns to di?erent dimensions of skill are di?erent in di?erent
occupations, and have also changed di?erently over time. Like Acemoglu and Autor (2011),
we conclude that it is essential to go beyond general skills and formally introduce tasks and
occupations in our standard models of the labor market to adequately understand why the wage
distribution has changed so much over the last few decades.
28
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32
O*NET Indexes Information Automation Not On-Site
No Face-to-
Face
No Decision
Making
Panel A: using 1980-1990 Standard Occupation Codes
Overall Mean 0.6845 0.6871 0.4072 0.3171 0.3105
Standard Deviation 0.1519 0.1313 0.2089 0.1062 0.1057

Professional, Managerial,
Technical
0.8274 0.5857 0.5560 0.2498 0.2244
Clerical, Sales 0.7067 0.7177 0.6095 0.3037 0.3692
Production, Operators 0.6020 0.8205 0.2430 0.4197 0.3608
Primary, Construction,
Transport
0.6075 0.6993 0.2029 0.3395 0.3149
Service 0.5549 0.6437 0.4724 0.2762 0.3747
Panel B: using 2002 Census Codes
Overall Mean 0.6786 0.6310 0.4386 0.3155 0.3074
Standard Deviation 0.1188 0.1477 0.2084 0.1094 0.1083

Professional, Managerial,
Technical
0.8126 0.5644 0.5729 0.2661 0.2285
Clerical, Sales 0.7166 0.6825 0.6363 0.3047 0.3601
Production, Operators 0.5892 0.7630 0.2752 0.4299 0.3709
Primary, Construction,
Transport
0.5908 0.6469 0.2271 0.3394 0.3205
Service 0.5844 0.5843 0.4699 0.2566 0.3343
Technology Offshorability
Table 1. Average O*NET Indexes by Major Occupation Group
Note: The overall means are based on 510 basic occupations in Panel A and on 505 basic occaptions in Panel B.
33

O*NET Indexes
(1) (2) (3) (4) (5) (6) (7) (8)
Information content 0.004 0.035 0.059 0.031 0.005 0.030 0.020 -0.008
(0.007) (0.009) (0.009) (0.013) (0.011) (0.011) (0.012) (0.013)
Automation -0.023 -0.034 -0.070 -0.045 -0.016 -0.030 -0.028 -0.013
/routine (0.009) (0.008) (0.014) (0.010) (0.011) (0.010) (0.013) (0.012)
No on-site work 0.012 0.015 0.034 0.026 0.003 0.002 0.019 0.021
(0.010) (0.004) (0.007) (0.004) (0.006) (0.005) (0.007) (0.006)
No face-to-face -0.030 -0.035 -0.067 -0.051 -0.036 0.002 0.027 -0.014
(0.010) (0.009) (0.018) (0.011) (0.015) (0.015) (0.017) (0.018)
No decision making -0.003 -0.035 -0.078 -0.051 0.032 0.001 -0.045 -0.012
(0.009) (0.012) (0.012) (0.015) (0.017) (0.015) (0.019) (0.018)
Base wage No Yes No Yes No Yes No Yes
Adj. R-square --- --- --- --- 0.27 0.51 0.73 0.81
Notes: All models are estimated by running regressions of the 40 occupation-specific intercepts and slopes
(estimated in specification (5) of Table 2) on the task measures. The models reported in all columns are
weighted using the fraction of observations in each occupation in the base period.
Table 2. Estimated Effect of Task Requirements on Intercept and Slope of Wage
Change Regressions by 2-digit Occupation
Tasks Entered Together
Intercept Slope Intercept
Tasks Entered Separately
Slope
34

Inequality Measure: 90-10 50-10 90-50 Variance Gini
A: 1976/78 to 1988/90
Total Change 0.1742 0.0700 0.1043 0.0697 0.0310
(0.0077) (0.007) (0.0046) (0.002) (0.0006)
Wage Structure 0.1215 0.0620 0.0595 0.0441 0.0248
(0.0078) (0.006) (0.0057) (0.0022) (0.0006)
Composition 0.0565 0.0092 0.0474 0.0239 0.0054
(0.003) (0.0018) (0.0025) (0.001) (0.0003)
Specification Error -0.0007 0.0011 -0.0018 0.0027 0.0009
(0.006) (0.0051) (0.0039) (0.0008) (0.0002)
B: 1988/90 to 2000/02
Total Change 0.0349 -0.0561 0.0911 0.0164 -0.0023
(0.0053) (0.0042) (0.0046) (0.0019) (0.0005)
Wage Structure -0.0232 -0.0802 0.0570 -0.0122 -0.0050
(0.0047) (0.0039) (0.0044) (0.0019) (0.0005)
Composition 0.0443 0.0195 0.0248 0.0203 0.0005
(0.0017) (0.0012) (0.0016) (0.0006) (0.0003)
Specification Error 0.0156 0.0059 0.0097 0.0091 0.0023
(0.0024) (0.0022) (0.0018) (0.0005) (0.0001)
C: 2003/04 to 2009/10
Total Change 0.0480 0.0224 0.0256 0.0156 0.0042
(0.0065) (0.0041) (0.0063) (0.0024) (0.0006)
Table 3. Aggregate Decomposition Results
) ˆ ˆ (
ˆ
01 1 1 ,
? ? ?
? ? ? = ? X
p S
? ?
?
0 0 01 ,
ˆ ) (
ˆ
X X
p X
? = ? ) ˆ ˆ (
ˆ
0 01 01 ,
? ? ?
? ? ? = ? X
e X
(0.0065) (0.0041) (0.0063) (0.0024) (0.0006)
Wage Structure 0.0519 0.0342 0.0177 0.0121 0.0047
(0.0072) (0.0061) (0.0078) (0.0022) (0.0006)
Composition 0.0117 0.0066 0.0050 0.0051 -0.0001
(0.0023) (0.0016) (0.0017) (0.0009) (0.0003)
Specification Error -0.0153 -0.0182 0.0029 -0.0016 -0.0004
(0.0038) (0.0041) (0.0034) (0.0006) (0.0002)

Total Change: Wage Structure:
Composition : Specification Error:
Note: Bootstrapped standard errors are in parentheses (100 replications of the entire procedure).
The formulas for the different components are the following and the difference between the total
change and the sum of the three components shown is the reweighting error (not shown).
) , F(Y I
ˆ
R ) , F(Y I
ˆ
R
ˆ
0 1
? ?
?
? = ?
O
) ˆ ˆ (
ˆ
01 1 1 ,
? ? ?
? ? ? = ? X
p S
? ?
?
0 0 01 ,
ˆ ) (
ˆ
X X
p X
? = ? ) ˆ ˆ (
ˆ
0 01 01 ,
? ? ?
? ? ? = ? X
e X
35
Inequality Measure: 90-10 50-10 90-50 Variance Gini
A: Detailed Composition Effects:
Union 0.0140 -0.0132 0.0272 0.0062 0.0034
(0.0005) (0.0004) (0.0008) (0.0002) (0.0001)
Education -0.0012 0.0077 -0.0089 0.0009 -0.0034
(0.0013) (0.0009) (0.0009) (0.0004) (0.0001)
Experience 0.0154 0.0120 0.0034 0.0071 -0.0003
(0.0008) (0.0006) (0.0007) (0.0003) (0.0001)
Technology 0.0022 0.0070 -0.0048 -0.0004 -0.0009
(0.0006) (0.0005) (0.0005) (0.0002) (0.0001)
Offshorability 0.0109 0.0063 0.0046 0.0053 0.0008
(0.0007) (0.0006) (0.0005) (0.0003) (0.0001)
Other 0.0030 -0.0003 0.0033 0.0014 0.0009
(0.0003) (0.0002) (0.0003) (0.0001) (0.0001)
Total 0.0443 0.0195 0.0248 0.0203 0.0005
(0.0017) (0.0012) (0.0016) (0.0006) (0.0003)
B: Detailed Wage Structure Effects
Union 0.0051 0.0018 0.0033 0.0029 0.0020
(0.0017) (0.0013) (0.0016) (0.0005) (0.0001)
Education 0.0621 0.0057 0.0563 0.0253 0.0049
(0.0076) (0.0063) (0.0073) (0.0028) (0.0007)
Experience -0.0183 -0.0045 -0.0144 -0.0060 -0.0040
(0.0124) (0.008) (0.0119) (0.005) (0.0012)
Technology 0.0331 0.0007 0.0326 0.0146 0.0049
(0.0045) (0.004) (0.0037) (0.0017) (0.0005)
Offshorability 0.0115 -0.0111 0.0226 0.0030 0.0017
(0.0048) (0.003) (0.0041) (0.0017) (0.0005)
Other -0.0272 -0.0214 -0.0058 -0.0105 -0.0037
(0.0043) (0.0037) (0.0042) (0.0018) (0.0005)
Constant -0.0895 -0.0514 -0.0377 -0.0416 -0.0109
(0.0167) (0.0135) (0.0158) (0.0066) (0.0017)
Total -0.0232 -0.0802 0.0570 -0.0122 -0.0050
(0.0047) (0.0039) (0.0044) (0.0019) (0.0005)

Note: Bootstrapped standard errors are in parentheses (100 replications of the entire
procedure).
Table 4. Detailed Decomposition Results 1988/90-2000/02
36
Figure 1. Changes in Real Wages ($1979) by Percentile, Men
-
.
2
-
.
1
0
.
1
.
2
L
o
g

W
a
g
e

D
i
f
f
e
r
e
n
t
i
a
l
0 .2 .4 .6 .8 1
Quantile
1976/78 to 1988/90
1988/90 to 2000/02
2003/04 to 2009/10

Figure 2. Fitted Changes in Wages from 1988/90 to 2000/02
in Top 30 2-Digit Occupations
Execu
Managers
Engineers
Teachers
Profes
EnginTech
OtherTech
Supervi
SalesFinan
SalesComm
Sales1
Mail
AdminS2
Serv_Protect
Serv_Food
Serv_Clean
Mechanics
Constr1
Produc1
Produc2
Produc3
Transp1
Transp2
Constr2
Hand1
Hand2
Farm2
-
.
1
0
.
1
.
2
W
a
g
e

c
h
a
n
g
e
.5 1 1.5 2 2.5 3
Base period wage
37

Figure 3. Decomposition of Total Change into Composition and Wage Structure Effects
-
.
2
-
.
1
5
-
.
1
-
.
0
5
0
.
0
5
L
o
g

W
a
g
e

C
h
a
n
g
e
0 .2 .4 .6 .8 1
Quantile
Total Change
Wage Structure
Composition
A.Change in Log Wages 1976/78 to 1988/90

-
.
1
-
.
0
5
0
.
0
5
.
1
.
1
5
L
o
g

W
a
g
e

C
h
a
n
g
e
0 .2 .4 .6 .8 1
Quantile
Total Change
Wage Structure
Composition
B. Change in Log Wages 1988/90 to 2000/02

-
.
1
5
-
.
1
-
.
0
5
0
.
0
5
.
1
L
o
g

W
a
g
e

C
h
a
n
g
e
0 .2 .4 .6 .8 1
Quantile
Total Change
Wage Structure
Composition
C. Change in Log Wages 2003/04 to 2009/10
38

Figure 4. Detailed Decomposition of Composition Effects
-
.
0
5
0
.
0
5
L
o
g

W
a
g
e

C
h
a
n
g
e
0 .2 .4 .6 .8 1
Quantile
Union
Education
Experience
Technology
Offshorability
A. Detailed Composition Effects 1976/78 to 1988/90

-
.
0
5
0
.
0
5
L
o
g

W
a
g
e

C
h
a
n
g
e
0 .2 .4 .6 .8 1
Quantile
Union
Education
Experience
Technology
Offshorability
B. Detailed Composition Effects 1988/90 to 2000/02

-
.
0
5
0
.
0
5
L
o
g

W
a
g
e

C
h
a
n
g
e
0 .2 .4 .6 .8 1
Quantile
Union
Education
Experience
Technology
Offshorability
C. Detailed Composition Effects 2003/04 to 2009/10
39

Figure 5. Detailed Decomposition of Wage Structure Effects
-
.
0
5
0
.
0
5
L
o
g

W
a
g
e

C
h
a
n
g
e
0 .2 .4 .6 .8 1
Quantile
Union
Education
Experience
Technology
Offshorability
A. Detailed Wage Structure Effects 1976/78 to 1988/90

-
.
0
5
0
.
0
5
L
o
g

W
a
g
e

C
h
a
n
g
e
0 .2 .4 .6 .8 1
Quantile
Union
Education
Experience
Technology
Offshorability
B. Detailed Wage Structure Effects 1988/90 to 2000/02

-
.
0
5
0
.
0
5
L
o
g

W
a
g
e

C
h
a
n
g
e
0 .2 .4 .6 .8 1
Quantile
Union
Education
Experience
Technology
Offshorability
C. Detailed Wage Structure Effects 2003/04 to 2009/10

40
NOT INTENDED FOR PUBLICATION
Empirical test of the occupational wage setting model - Technical Appendix
A. Wage setting model
We now explain the empirical approach used to test the two main predictions of the model.
It is useful to ?rst consider how our approach could be implemented if we had panel data on
individuals who stay in the same occupation over time. We could then look at how the wage of
worker i changes in response to changes in the skill pricing parameters, ?r
jk
:
?w
ij
= ??
j
+
K

k=1
?r
jk
S
ik
+ ?u
ijt
.
The wage change, ?w
ij
, can be linked to the wage in the base period (t = 0) using a simple
linear regression equation
?w
ij
= ¯a
j
+
¯
b
j
w
ij0
+ e
ij
.
Under the simplifying assumption that the di?erent skill components S
ik
are uncorrelated, the
slope parameter of the regression,
¯
b
j
, can be written as:
(A-1)
¯
b
j
=
cov(?w
ij
, w
ij0
)
var(w
ij0
)
=
K

k=1
(r
jk0
?r
jk
) · ?
2
kj
K

k=1
r
2
jk0
· ?
2
kj
+ ?
2
uj0
,
where ?
2
kj
is the variance of the skill component S
ik
for workers in occupation k, and where ?
2
ujt
is the variance of the idiosyncratic error term u
ijt
.
Even when the r
jkt
’s cannot be estimated for lack of precise measures of the skill components
S
ik
, it is still possible to learn something about changes in the r
jkt
’s from the estimates of the
slope coe?cients b
j
. While the denominator in equation (A-1) (a variance) is always positive,
the sign of the numerator depends on the correlation between returns to skills in the base period
(r
jk0
), and change in the return to skill (?r
jk
). For example, in manual occupations where the
return to manual dexterity used to be large (r
jk0
>> 0) but declined substantially (?r
jk
> 0) and does increase over time
(?r
jk
>> 0), we expect the slope coe?cient
¯
b
j
to be positive.
41
In our empirical analysis, we rely on large repeated cross-sections of the CPS instead of panel
data. While it is not feasible to directly estimate
¯
b
j
in that setting, we can still estimate a closely
related parameter b
j
using percentiles of the within-occupation distribution of wages.
To ?x ideas, let’s further simplify the model by assuming that both the skill components, S
ik
(for k = 1, ..., K), and the idiosyncratic error term, u
ijt
, follow a normal distribution. It follows
that wages are themselves normally distributed, and the q
th
percentile of the distribution of w
ijt
,
w
q
jt
, is given by
(A-2) w
q
jt
= w
jt
+ ?
jt
?
?1
(q),
where ?(·) is the standard normal distribution function, w
jt
is the mean of wages in occupation
j at time t, and ?
jt
is its standard deviation, where
?
2
jt
=
K

k=1
r
2
jkt
· ?
2
kj
+ ?
2
ujt
.
Now consider a regression of ?w
q
j
on w
q
j0
:
43
(A-3) ?w
q
j
= a
j
+ b
j
w
q
j0
+ e
q
j
.
The slope parameter, b
j
, is now given by
(A-4) b
j
=
cov(?w
q
j
, w
q
j0
)
var(w
q
j0
)
=
(??
j
· ?
j0
) · var(?
?1
(q))
?
2
j0
· var(?
?1
(q))
=
??
j
?
j0
.
Using the linear approximations ??
j
? ??
2
j
/2?
j0
and ?r
2
jk
? 2r
jk0
?r
jk
yields
(A-5) b
j
?
K

k=1
(r
jk0
?r
jk
) · ?
2
kj
?
2
j0
+
??
2
uj
2?
2
j0
.
The ?rst term in equation (A-5) is similar to the slope coe?cient obtained earlier in (A-1) and
has, therefore, a similar interpretation. The second term re?ects the fact that an increase in the
variance of the idiosyncratic error term widens the wage distribution, which results in a positive
43
Note that under the normality assumption, the error term e
q
j
is equal to zero. We introduce the error term in the
equation, nonetheless, to later allow for a more general case where the normality assumption fails.
42
relationship between changes in wages and base wage levels.
Using the fact that E(w
q
jt
) = w
jt
(expectation taken over q, for q = 0, .., 1), the intercept in
the regression model, a
j
, can be written as:
(A-6) a
j
= ?w
j
?
??
j
?
j0
w
j0
,
where
(A-7) ?w
j
= ??
j
+
K

k=1
?r
jk
S
jk
.
Without loss of generality, we can normalize the base period wage in each occupation to have
a mean zero. The intercept can then be written as:
(A-8) a
j
= ??
j
+
K

k=1
?r
jk
S
jk
.
Like the slope parameter b
j
, the intercept a
j
depends on changes in the return to skill com-
ponents, ?r
jk
. The intercept also depends on ??
j
, which re?ects changes in occupational wage
di?erentials unrelated to skills. This could re?ect occupational rents, compensating wage di?er-
entials, etc. Under the strong assumption that skills S
ik
and the error term u
ijt
are normally
distributed, the regression model in equation (A-3) fully describes the relationship between the
base wage and the change in wage at each percentile q of the within-occupation wage distribution.
This suggests a simple way of assessing the contribution of changes in the occupational wage
structure to changes in the distribution of wages. In a ?rst step, we can estimate equation (A-
3) separately for each occupation (or in a pooled regression with interactions) and see to what
extent the simple linear model helps explain the observed changes in wages. We can then run
“second step” regressions of the estimated a
j
and b
j
on measures of task content of work that
correlates with the r’s and with the change in the r’s at the occupational level.
While the normality assumption is convenient for illustrating the basic predictions of the linear
skill pricing model, it is also restrictive. As is well known, the normal distribution is fully
characterized by its location (w
jt
above) and scale parameter (?
jt
above). This can be generalized
to the case where the wage distribution is not normal, but only the location and scale changes
over time. Relative to equation (A-2), this means we can replace ?
?1
(q) by a more general and
occupation-speci?c inverse probability function F
?1
j
(q). Equation (A-2) is then replaced by
43
(A-9) w
q
jt
= w
jt
+ ?
jt
F
?1
j
(q).
We can then get the same regression equation since
(A-10) ?w
q
j
= ?w
j
+ ??
j
F
?1
j
(q).
Solving for F
?1
j
(q) in equation (A-9) at t = 0, and substituting into equation (A-10) yields
(A-11) ?w
q
j
= ?w
j
?
??
j
?
j0
w
j0
+
??
j
?
j0
w
q
j0
,
which is identical to equation (A-3) since a
j
= ?w
j
?
??
j
?
j0
w
j0
and b
j
=
??
j
?
j0
.
In general, however, changes in the returns to skill r
jkt
are expected to change the shape of
the wage distribution above and beyond the scale and location; F
?1
j
(q) is no longer a constant
over time. As a result, equation (A-10) becomes
?w
q
j
= ?w
j
+
_
?
j1
F
?1
j1
(q) ? ?
j0
F
?1
j0
(q)
_
(A-12)
= ?w
j
+ ??
j
F
?1
j0
(q) + e
q
j
(A-13)
where e
q
j
= ?
j1
_
F
?1
j1
(q) ?F
?1
j0
(q)
_
. Substituting in F
?1
j0
(q) = (w
q
j0
? w
j0
)/?
j0
and using the
de?nitions of a
j
and b
j
then yields
(A-14) ?w
q
j
= a
j
+ b
j
w
q
j0
+ e
q
j
.
It is generally not possible to ?nd a close form expression for e
q
j
. If changes in the F
?1
jt
(q)
functions are similar across occupation, however, this will generate a percentile speci?c component
in the error term. For instance, Autor, Katz and Kearney (2008) show that the distribution of
wage residuals has become more skewed over time (convexi?cation of the distribution). This is
inconsistent with the normality assumption, but can be captured by allowing for a percentile-
speci?c component ?
q
in e
q
j
:
(A-15) e
q
j
= ?
q
+ ?
q
j
.
44
This leads to the main regression equation to be estimated in the ?rst step of the empirical
analysis:
(A-16) ?w
q
j
= a
j
+ b
j
w
q
j0
+ ?
q
+ ?
q
j
.
A more economically intuitive interpretation of the percentile-speci?c error components ?
q
is
that it represents a generic change in the return to unobservable skills of the type considered by
Juhn, Murphy, and Pierce (1993). For example, if unobservable skills in a standard Mincer type
regression re?ect unmeasured school quality, and that school quality is equally distributed and
rewarded in all occupations, then changes in the return to school quality will be captured by the
error component ?
q
.
B. Estimation results
The estimates of equation (3) are reported in Appendix Table A3. We use two di?erent
measures of ?t to evaluate how the model performs empirically. The adjusted R-square of the
model is ?rst used to assess whether model in equation (3) is the true wage determination model.
We note that because of the residual sampling error in the estimated wage changes, the regressions
would not explain all of the variation in the data.
44
The second measure of ?t consists of looking
at whether the model is able to explain the U-shaped feature of the raw data presented in Figure
1. For each estimated model, we run a simple regression of the estimated residuals on a linear
and quadratic term in the base wage
(A-17) ´?
q
j
= ?
0
+ ?
1
w
q
j0
+ ?
2
(w
q
j0
)
2
+ ?
q
j
,
to see whether there is any curvature left in the residuals that the model is unable to explain.
As a reference, the coe?cient on the quadratic term, ´ ?
2
, in the ?tted regression on the raw data
is equal to 0.136.
We ?nd that when equation (3) is estimated with the base wage as only explanatory variable
(column 1), essentially none of the variation in the data is explained as the adjusted R-square is
only equal to 0.0218. Since a linear regression cannot explain any of the curvature of the changes
in wages, the curvature parameter in the residuals (0.136) is exactly the same as in the simple
44
The average sampling variance of wage changes is 0.0002, which represents about 3 percent of the total variation in
wage changes by occupation and decile. This means that one cannot reject the null hypothesis that sampling error is the
only source of residual error (i.e. the model is “true”) whenever the R-square exceeds 0.97.
45
quadratic regression discussed above. When we only include the set of occupation dummies (the
a
j
’s) in the regression in column 2, we explain more than half of the raw variation in the data,
and about a third of the curvature. The curvature parameter declines from 0.136 to 0.087 but
remains strongly signi?cant. The restriction imbedded in this model is that all the wage deciles
within a given occupation increase at the same rate, i.e. there is no change in within-occupation
wage dispersion.
When we include only the decile dummies (the ?
q
’s) in column 3, essentially none of the
variation or curvature in the data is explained. This is a strong result as it indicates that
using a common within-occupation change in wage dispersion cannot account for any of the
observed change in wages. Adding the decile dummies to the occupation dummies (column 4)
only marginally improves the ?t of the model compared to the model with occupation dummies.
This indicates that within-occupation changes in the wage distribution are highly occupation-
speci?c, and cannot simply be linked to a pervasive increase in returns to skill “`a la” Juhn,
Murphy and Pierce (1993).
By contrast, the ?t of the model improves drastically once we introduce occupation-speci?c
slopes (the b
j
’s) in column 5. The R-square of the model jumps to 0.9274, which is quite close
to the critical value for which we cannot reject the null hypothesis that the model is correctly
speci?ed, and that all the residual variation is due to sampling error. The curvature parameter
´ ?
2
now drops to 0.002 and is no longer statistically signi?cant. In other words, we are able to
account for all the curvature in the data using occupation-speci?c slopes. Note also that once the
occupation-speci?c slopes are included, decile dummies play a more substantial role as we see a
drop in the adjusted R-square from 0.9274 (decile dummies included) to 0.8602 (decile dummies
excluded).
Finally, Panel B of Appendix Table A3 shows the results of similar speci?cations using a
reweighting approach to control for standard covariates. In that case, we also ?nd that the
model with decile dummies and occupation-speci?c slopes explains most of the variation in the
data and all of the curvature, although the R-square is generally lower since the covariates reduce
the explanatory power of occupations.
46
Difference Difference
Means
Standard
Deviation
Means
Standard
Deviation
in Means (88/90-
76/78)
Means
Standard
Deviation
in Means
(00/02-88/90)
Log wages 1.851 0.520 1.753 0.583 -0.098 1.812 0.597 0.059
Union covered 0.295 0.456 0.202 0.401 -0.093 0.149 0.356 -0.053
Non-white 0.101 0.302 0.127 0.333 0.026 0.140 0.347 0.013
Non-Married 0.295 0.456 0.386 0.487 0.091 0.415 0.493 0.028
Education
Primary 0.103 0.303 0.060 0.237 -0.043 0.042 0.200 -0.018
Some HS 0.174 0.379 0.121 0.326 -0.053 0.089 0.285 -0.032
High School 0.369 0.483 0.379 0.485 0.009 0.312 0.463 -0.067
Some College 0.168 0.374 0.203 0.402 0.035 0.274 0.446 0.071
College 0.106 0.307 0.137 0.344 0.032 0.188 0.391 0.051
Post-grad 0.080 0.272 0.100 0.301 0.020 0.095 0.294 -0.005
Age 35.708 12.854 35.766 11.738 0.058 37.569 11.824 1.803
Difference
Means
Standard
Deviation
Means
Standard
Deviation
in Means
Log wages 1.819 0.606 1.820 0.616 0.001
Union covered 0.141 0.348 0.136 0.343 -0.005
Non-white 0.133 0.340 0.144 0.351 0.011
Non-Married 0.406 0.491 0.423 0.494 0.017
Education
Primary 0.045 0.207 0.039 0.193 -0.006
Some HS 0.083 0.277 0.071 0.257 -0.013
High School 0.309 0.462 0.302 0.459 -0.007
Some College 0.270 0.444 0.276 0.447 0.006
College 0.194 0.396 0.207 0.405 0.012
Post-grad 0.099 0.298 0.106 0.308 0.008
Age 38.166 11.956 39.150 12.299 0.984
1988/90 2000/02 1976/78
Appendix Table A1. Descriptive Statistics
2003/04 2009/10
47
Appendix Table A2. O*NET 13.0 — Work Activities & Work Context

A. Characteristics linked to Technological Change/Offshorability
1

Information Content
4.A.1.a.1 Getting Information (J K)
4.A.2.a.2 Processing Information (J K)
4.A.2.a.4 Analyzing Data or Information (J K)
4.A.3.b.1 Interacting With Computers (J K)
4.A.3.b.6 Documenting/Recording Information (J K)

Automation/Routinization
4.C.3.b.2 Degree of Automation
4.C.3.b.7 Importance of Repeating Same Tasks
4.C.3.b.8 Structured versus Unstructured Work (reverse)
4.C.3.d.3 Pace Determined by Speed of Equipment
4.C.2.d.1.i Spend Time Making Repetitive Motions

B. Characteristics linked to Non-Offshorability

Face-to-Face
4.C.1.a.2.l Face-to-Face Discussions
4.A.4.a.4 Establishing and Maintaining Interpersonal Relationships (J K,B)
4.A.4.a.5 Assisting and Caring for Others (J K,B)
4.A.4.a.8 Performing for or Working Directly with the Public (J K,B)
4.A.4.b.5 Coaching and Developing Others (B)

On-Site J ob
4.A.1.b.2 Inspecting Equipment, Structures, or Material (J K)
4.A.3.a.2 Handling and Moving Objects
4.A.3.a.3 Controlling Machines and Processes
4.A.3.a.4 Operating Vehicles, Mechanized Devices, or Equipment
4.A.3.b.4 Repairing and Maintaining Mechanical Equipment (*0.5)
4.A.3.b.5 Repairing and Maintaining Electronic Equipment (*0.5)

Decision-Making
4.A.2.b.1 Making Decisions and Solving Problems (J K)
4.A.2.b.2 Thinking Creatively (J K)
4.A.2.b.4 Developing Objectives and Strategies
4.C.1.c.2 Responsibility for Outcomes and Results
4.C.3.a.2.b Frequency of Decision Making

1
Note: (JK) indicates a work activity used in J ensen and Kletzer (2007), (B) a work activity used or suggested in
Blinder (2007).
48
(1) (2) (3) (4) (5) (6)
A. Models without controls for observables
Adj. R-square 0.0218 0.5535 0.0284 0.5996 0.9274 0.8602
Curvature 0.136 0.087 0.122 0.073 0.002 0.020
in residuals (?
2
) (0.009) (0.005) (0.009) (0.006) (0.003) (0.004)
B. Models with controls for observables
Adj. R-square 0.0730 0.3982 0.0498 0.4644 0.8743 0.7711
Curvature 0.131 0.116 0.084 0.068 0.002 0.052
in residuals (?
2
) (0.015) (0.011) (0.015) (0.011) (0.005) (0.007)
Occupation dummies
(Intercept) Yes Yes Yes Yes
Decile dummies Yes Yes Yes
Base wage Yes Yes Yes
Occ * base wage
(Slope) Yes Yes
Notes: Regression models estimated for each decile (10th, 20th,., 90th) of each 2-digit occupation.
360 observations used in all models (40 occupations, 9 observations per occupation). Models are
weighted using the fraction of observations in the 2-digit occupation in the base period. Panel A
shows the results when regressions are estimated without any controls for observabable. Panel B
shows the results when the distribution of observables (age, education, race and marital status)
in each occupation is reweighted to be the same as the overall distribution over all occupations.
Appendix Table A3: Regression Fit of Models for 1988/90 to 2000/02 Changes in Wages
at each Decile, by 2-Digit Occupation
49

Years: 1988/90 2000/02
Explanatory Variables Quantiles: 10 50 90 10 50 90
Union covered 0.218 0.454 -0.048 0.161 0.414 -0.091
(0.003) (0.005) (0.005) (0.004) (0.006) (0.007)
Non-white -0.070 -0.136 -0.080 -0.037 -0.126 -0.045
(0.008) (0.005) (0.005) (0.006) (0.005) (0.008)
Non-Married -0.152 -0.127 -0.036 -0.095 -0.142 -0.089
(0.005) (0.004) (0.005) (0.004) (0.005) (0.006)
Education ( Some College omitted)
Primary -0.443 -0.504 -0.220 -0.496 -0.519 -0.134
(0.014) (0.008) (0.006) (0.018) (0.01) (0.007)
Some HS -0.431 -0.271 -0.089 -0.443 -0.300 -0.015
(0.011) (0.006) (0.005) (0.01) (0.006) (0.005)
High School -0.051 -0.134 -0.106 -0.047 -0.157 -0.072
(0.006) (0.005) (0.005) (0.005) (0.005) (0.006)
College 0.103 0.220 0.338 0.063 0.248 0.449
(0.005) (0.006) (0.009) (0.005) (0.006) (0.01)
Post-grad 0.042 0.230 0.665 0.022 0.278 1.006
(0.005) (0.006) (0.014) (0.006) (0.007) (0.022)
Potential Experience (15