Global COE Hi-Stat Discussion Paper Series 275

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

Changes in Returns to
Task-Specific Skills and Gender Wage Gap

Hi-Stat Discussion Paper

Shintaro Yamaguchi

January 2013

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

Changes in Returns to Task-Specific Skills andGender Wage Gap
Shintaro Yamaguchi∗
January 1, 2013

Abstract
How did skilled-biased technological change affect wage inequality, particularly between men and women? To answer that question this paper constructs a task-based Roy model in which workers possess a bundle of basic
skills, and occupations are characterized as a bundle of basic tasks. The modelis structurally estimated using the task data from the Dictionary of Occupational Titles and the PSID. The main empirical finding is that men have more
motor skills than women, but the returns to motor skills have dropped significantly, accounting for more than 40% of the narrowing gender wage gap.

Keywords: Roy model, task-based approach, occupational choice, skill-biased
technological change, soft skills.
JEL Codes: J24, J31∗ Department of Economics, McMaster University, 1280 Main St.

W., Hamilton, ON. Canada
L8S 4M4. Email: yamtaro@mcmaster.ca. Website: socserv.mcmaster.ca/yamtaro. I am grateful
to comments from John Jones, John Kennan, Ronni Pavan, Craig Riddell, Chris Robinson, Paul
Sullivan, and other participants of the seminars and conferences at ASSA, Calgary, Montreal, Ryerson, SOLE, Toronto, Washington Univ. in St. Louis, Western Ontario, and Wisconsin. The use of
SHARCNET computational facilities is gratefully acknowledged.

1

1

Introduction

This paper studies the contribution of the technological change induced by a broad
adoption of computers in 1980’s and 90’s to the narrowing gender wage gap using
the task data from the Dictionary of Occupational Titles (DOT) and the Panel Studyof Income Dynamics (PSID). Male wage inequality rapidly rose in the 1980’s andcontinued to through the 1990’s. Labor economists consider that the technologicalchange since the early 1980’s has raised the return to skills, which contributed to increased wage inequality. On the other hand, gender wage gap was stable until 1980
and dramatically decreased afterwards. Despite the fact that the rise of male wage
inequality and the fall of gender wage inequality occurred at the same time, many
papers, including Blau and Kahn (1997) and Card and DiNardo (2002), do not consider the role that technological change played in narrowing the gender wage gap.
They argue that, since men were more educated and experienced than women during
this period, the rise in returns to skills caused by the technological change shouldhave widened the gender wage gap. They consider that, despite the technologicalchange being unfavorable to women, the gender wage gap narrowed due to an increase in the measured and unmeasured human capital possessed by women, andpossibly a reduction in gender discrimination.
However, when one takes a closer look at the workplace, the technologicalchange seems to have reduced women’s disadvantages. Autor, Levy, and Murnane(2003) find that computers replaced routine manual tasks and lowered returns tomanual skills relative to nonroutine cognitive skills. Given that manual task intensive jobs (i.e. blue-collar jobs) are typically male-dominated, the technologicalchange was unfavorable to men, not women. Borghans, ter Weel, and Weinberg(2006) show that technological and organizational changes have increased the importance of people skills in the workplace, and that these changes help explain theincrease in women’s wages relative to men’s. Weinberg (2000) provides empirical evidence that the de-emphasis in physical skills following computerization has
increased the demand for female workers. Black and Spitz-Oener (2010) and Bacolod and Blum (2010) also find evidence that the shift in demand from manualtasks to analytical tasks plays an important role in the change of the gender wage2

gap. While these previous contributions provide suggestive evidence for the role oftasks in influencing the gender wage gap, the literature lacks an explicit economic
model to interpret the empirical findings. How and why are workers sorted acrosstasks? How are wages determined according to the workers’ skills and tasks? Howshould skills be measured? These basic questions remain unanswered.
The objective of this paper is twofold. First, I construct and estimate a structuralmodel of occupational choice in which workers possess a bundle of basic skills
and occupations are characterized as a bundle of basic tasks. The proposed model
demonstrates that heterogeneity in returns to skills across occupations is the key
mechanism by which workers with different skill endowments self-select into different occupations. Second, using the estimated model, I quantitatively evaluate theeffects of the technological change on the gender wage gap by comparing the actual
gender wage gap and the counterfactual gender wage gap under the scenario thatthe technological change did not occur.
I begin by showing a set of facts about the U.S. labor market from 1979 to 1996
to motivate the structural model. Using the data from the DOT and Current Population Survey (CPS), I show that during that period, motor-task intensive jobs suchas craft occupations experienced a large wage loss of around 18%, while cognitivetask intensive jobs such as professionals enjoyed a positive wage growth of 6%.
These wage growth patterns are consistent with the predictions of the nuanced-viewof technological change proposed by Autor, Levy, and Murnane (2003). Anotherrelevant fact is that the motor-task intensive jobs are male-dominated. For example,
craft occupations are the most motor-task intensive jobs and 95% of craft workers
are men. This gender difference in occupational distribution implies that the technological change adversely affected men relative to women. These stylized facts
suggest that examining workers’ tasks is a promising way to understand the sourceof the narrowing gender wage gap.
The model developed in this paper makes a clear distinction between tasks andskills. I define a task as a unit of work activity that produces output, and a skill
is a worker’s endowment of capabilities for performing tasks.1 An occupation isviewed as a bundle of cognitive and motor tasks, and thus, characterized in a two1 These definitions of a task and a skill follow Acemoglu and Autor (2011).

3

dimensional space of task complexity, using continuous indices of cognitive andmotor task complexity constructed from the DOT. Workers have two different typesof task-specific skills: cognitive and motor skills.2 To produce output workers apply
their skills to tasks. Skilled workers are always more productive than unskilledworkers at any level of task complexity, and the productivity difference between
the two increases with task complexity because skills are intensely used in complex
tasks. In other words, skilled workers have an absolute advantage in all tasks andcomparative advantage in complex tasks. This heterogeneity in returns to skills
across tasks is the main mechanism at which workers with different skills choose
different tasks.3
The distinction between tasks and skills are relevant not only for understanding
a worker-task assignment mechanism, but also for measuring skills. To estimate
workers’ endowments of task-specific skills, I rely not on the current task, but on thehistory of past tasks, the information of which is available from the PSID. Namely,
I use the sum of the task complexity indices from the previous jobs. This measurecan be interpreted as task-complexity-adjusted work experience and, justified byskill acquisition through learning-by-doing. A worker which experienced complex
cognitive tasks for many years, is likely to have developed more cognitive skills,
Taking further advantage of the panel structure of the PSID, I take the correlated
random effect approach (see Wooldridge (2009)) to address an endogeneity biasthat arises from the selection into occupations based on unobserved skills. The
basic idea of this approach is to put restrictions on the conditional distribution ofunobserved heterogeneity given the entire occupational history. This extensive useof occupational history is an important departure from the previous contributions
such as Black and Spitz-Oener (2010) and Bacolod and Blum (2010), as they do not
explicitly distinguish tasks and skills and measure skills by the current tasks. The
empirical evidence indicates that variables constructed from occupational history
2 The contributions to the empirical literature on task-specific skills include, but not limited to,
Poletaev and Robinson (2008), Gathmann and Schönberg (2010), and Yamaguchi (2012).
3 Teulings (1995) and Gibbons, Katz, Lemieux, and Parent (2005) consider similar wage structures that sort workers across different jobs. Assuming an occupation as a bundle of tasks and using
task complexity measures from the DOT, this paper develops a method to include about 500 occupations at the 3-digit classification level.

4are strongly correlated with wages, suggesting that omitting these variable resultsin biased estimates.
The results from structural estimation show that, during the period of 19791996, men had substantially more motor skills than women, and the returns to motor
skills decreased dramatically. This fall of returns to motor skills suggests that thetechnological change helped women catch up to men in labor market outcomes. The
estimated model is then used to conduct counterfactual simulations to decompose
the change in the gender wage gap during the period. The results indicate that morethan 40% of the reduced gender wage gap can be explained by the fall of returns tomotor skills and the rest is largely explained by an increase in women’s cognitiveand general skills. This main result holds even when I take into account a change
in women’s labor force participation pattern that is pointed out by Mulligan and
Rubinstein (2008).
Related Literature
There are a few papers that attempt to explain gender wage gap based on a multidimensional skill model. Galor and Weil (1996) argue that gender differences inbrains and brawn are important to explain the narrowing gender gap in the labormarket. Welch (2000) also develops a brains-and-brawn model of earnings to explain the narrowing gender wage gap, as well as the rising male wage inequality
in a single framework. These papers consider that men’s skills are relatively morebrawn intensive than brain, while women’s skills are more brain intensive relative
to brawn. Consequently, a rise in the price of brains relative to brawn explains simultaneously the rise in male wage inequality and the narrowing gender wage gap.
Rendall (2010) constructs a one sector general equilibrium model in which workers possess brains and brawn, and calibrate it to the U.S. economy to examine thesources of the narrowing gender wage gap. Their models are based on the GormanLancaster characteristics model of earnings, and its key feature is that the return toskills is uniform across economy.
However, Heckman and Scheinkman (1987) study conditions under which skills
are uniformly priced across subsectors when worker skills cannot be unbundled andreject the hypothesis of uniform pricing of skills in the U.S. data. Their finding im5

plies that the Gorman-Lancaster model is not the correct vehicle to study how workers are sorted across different subsectors of economy. This is an important limitation
when one wishes to take a task-based approach in modeling wages or earnings, because different tasks naturally imply different subsectors. Building on Heckman
and Sedlacek (1985), I overcome this limitation by constructing a task-based Roymodel to explain worker assignment and wage determination when workers’ skills
cannot be unbundled. Unlike the Gorman-Lancaster model, returns to skills are heterogeneous across occupations, and this heterogeneity is the key mechanism thatsorts workers based on their skills endowment.4
Recently, Beaudry and Lewis (2012) examined if computerization has reduced
the gender wage gap at the city level using the census in 1980 and 2000. Theyfind that cities that experienced faster growth in the college vs. high school graduates wage gap saw a bigger drop in the male-female wage gap. This is suggestivethat computerization could be a factor that affected both wage gaps simultaneously.
Beaudry and Lewis (2012)’s approach is unique in the identification strategy which
relies on cross-city variations, rather than aggregate time-series variation. Because
the time-series evidence could easily be spurious, their findings add more credibility to the hypothesis that computerization reduced the gender wage gap. This paper
differs from Beaudry and Lewis (2012) in two respects. First, the present paper
develops a model of worker assignment to tasks, which is missing from their single
sector model. Second, although the identification strategy here relies on time-series
variation, by taking advantage of the panel structure of the PSID this paper uses arich set of control variables for skills in order to avoid endogeneity biases.
The rest of the paper is structured as follows. Section 2 documents the factsof the U.S. labor market from 1979 to 1996, in order to motivate the economic
model. Section 3 lays out the structural model of occupational choice. Section
4 discusses the estimation strategy. Section 5 describes the data. The estimation
results are presented in Section 6. Section 7 discusses robustness of the main result
as well as the issues of endogenous female labor force participation decision, gender
4 In a recent paper, Firpo, Fortin, and Lemieux (2011) develop an argument in favor of the Roymodel against the Gorman-Lancaster model. Firpo, Fortin, and Lemieux (2011) find that heterogeneity in returns to skills is an important feature to understand the sources of the recent labor market
polarization in the U.S.

6

discrimination, and international trade. Section 8 concludes.

2

U.S. Labor Market Facts in 1979-1996

In this section I show that motor-task intensive occupations suffered a large wage
loss, while cognitive-task intensive occupations experienced no wage loss or evenpositive wage growth for the 1979-1996 period in the U.S. This difference in thewage growth pattern across occupations has the potential to explain the narrowing
gender wage gap considering that the motor-task intensive occupations are maledominated while the cognitive-task intensive occupations are not. Moreover, thiscan also account for the rising wage inequality among men, because majority ofthe male workers in the motor-task intensive occupations have less than a college
education, while majority of the male workers in the cognitive-task intensive occupations are college educated. This simple descriptive analysis then motivates the
structural model in the following section and clarifies the main driving force behindthe estimation results for the structural model.

2.1

Data

2.1.1

Current Population Survey

In this section, I use the 1980 and 1997 CPS for the descriptive analysis becauseof its representativeness and large sample size. Then, I use the PSID to estimate
the structural model to take advantage of its panel structure. The CPS survey years
were selected to match the sample period of the PSID data used. The CPS sample
consists of civilian male and female non self-employed full-time workers in the
non-agricultural sector between the ages of 18 and 65. Full-time work is defined
as 1,500 hours of work per year or more. Hourly wages are deflated by the 1983
PCE deflator. I exclude wages less than $1 per hour and more than $250 per hourfrom the sample. Note that wages and hours reported in the CPS, as well as in the
PSID, are previous years’ wages. Thus, the 1980 and 1997 surveys report wages
and hours worked in 1979 and 1996, respectively. The sample restrictions imposedin this paper are comparable to Blau and Kahn (1997).
7

2.1.2

Dictionary of Occupational Titles

The DOT contains information on 12,099 occupations defined by worker performed
tasks in each individual occupation. The U.S. Department of Labor compiled thedata to provide standardized occupational information for an employment service
matching job applicants with job openings. The information included in the DOT
is based on the on-site observation of jobs as they are performed in diverse businessestablishments and, for jobs that are difficult to observe, on information obtained
from professional and trade associations. On this basis, in the fourth edition of the
DOT, analysts rate each occupation with respect to about 50 characteristics including aptitudes, temperaments, and interests necessary for adequate performance.
In light of the previous papers using the DOT data, this paper assumes that tasks
are broadly categorized into either cognitive or motor tasks. By examining the textual definitions of the DOT variables, I select a few variables to measure each type oftasks. The DOT variables which measure cognitive task complexity consist of twoworker function variables for data and people, three variables from General Educational Development for reasoning, mathematical, and language skills, three aptitude
variables for intelligence, verbal, and numerical skills, and two temperament variables for influencing people and dealing with people. Motor task complexity ismeasured by one worker function variable for things and seven aptitude variables
for motor coordination, manual dexterity, finger dexterity, eye-hand-foot coordination, spatial, form perception, and color discrimination. I summarize each set ofvariables into a single index of cognitive or motor task complexity by a dimension
reduction technique. 5 The constructed indices are normalized such that the meanis 0.5 and the standard deviation is 0.1. As a robustness check, I also constructed
the indices using a subset of the variables to more sharply define tasks, but that does
not change any of the main results of the paper. Details of variable construction areavailable in the online appendix.
Although my task complexity measures are not identical to the routine and nonroutine measures as in Autor, Levy, and Murnane (2003), complex motor tasks
5 Multiple Correspondence Analysis is used. This method is similar to Principal Component
Analysis, but can handle ordinal variables. See Greenacre (2007) for an excellent introduction to themethod.

8

largely correspond to routine manual tasks, and complex cognitive tasks largely correspond to nonroutine analytical/interactive tasks in their measures. My motor task
index does not include a physical strength measure, which might seem problematicfor those who interpret the brains-and-brawn story literally, but the nuanced view oftechnological change emphasizes that computers replaced routine tasks while someof physically demanding tasks cannot be replaced by computers. Indeed, the physical strength measure seems to pick up nonroutine physical tasks. This is suggestedby the wage regression results in Bacolod and Blum (2010) who indicate that returns to physical tasks did not decrease over time, while those to motor tasks did.
These two variables are positively correlated, but need to be carefully distinguishedin an empirical analysis that studies the relationship between tasks and wages.
Figure 1 plots the levels of cognitive and motor task complexity for each 1-digit
occupation. Cognitive tasks of professionals and managers are the most complex,
and are followed by sales, clerical, and craft workers. Cognitive task complexity islowest for service workers, operators, and laborers. The complexity of motor tasksof craft workers is the highest among all occupations, followed by professionals,
clerical workers, and operators. Service and sales workers, and laborers are involved
in simple motor tasks. Managers report the lowest level of motor task complexity.

2.2

Wage Growth by Occupation and Gender Gaps

The nuanced view of technological change argues that strong complementarities exist between computers and complex cognitive tasks, while substantial substitution
exists between computers and complex motor tasks. We can deduce from Figure
1, that occupations in the bottom and right regions (craft workers, operators, andlaborers) should have been harmed by computerization, because they are relatively
motor-task intensive occupations. Occupations in the top left region (professionals, managers, and sales) should have benefited from computerization, because they
are relatively cognitive-task intensive occupations. Occupations near the diagonal(clerical and service) should have been less affected by computerization.
To examine if this prediction is consistent with the data, I calculate the changes
in the composition-adjusted mean wages from 1979 to 1996 for each 1-digit oc-

9

0.65
0.60
0.55

●

●

Sales
●

Clerical
0.50

Craft

0.45
0.40

Cognitive Task

Professional
Managers

Service
Operators
Laborers

0.45

0.50

0.55

0.60

Motor Task

Figure 1: Occupations in the Task Space
Note: The data source is the 1971 CPS augmented by the fourth edition of the DOT. The taskcomplexity indexes are normalized so that the mean and standard deviation for the 1971 CPS are 0.5
and 0.1, respectively.

cupation.6 The conditional mean logwage function for 1996 is estimated by anonparametric regression spline method using the CPS data.7 Covariates include
age, gender, five education levels (high school dropouts, high school graduates,
some college, college graduates, and advanced degree), and 1-digit occupations.
The composition-adjusted mean wage is calculated by applying the estimated wage
equation to the 1979 CPS data.
As reported in Table 1, operators, laborers, and craft workers suffered large
wage losses of 18% during this period. Clerical and service workers had modest
wage losses from 8% to 5%. Wages of sales workers and managers remained almost
constant, and professionals enjoyed 6% wage growth. Note that wage growth during
this period did not monotonically change with the occupations’ skill level. For
6 The 1950 census occupation classification is used.

Although the 1990 coding scheme is alsoavailable, the 1950 coding scheme is much more similar to the 1970 coding scheme, which is usedin the PSID.
7 See Ma, Racine, and Yang (2011).

10

example, craft workers experienced a large wage loss of 18%, but their average wage
in 1979 is the third highest among 1-digit occupations, and immediately follows
those of professionals and managers. Clerical and service workers had modest wage
losses, and their wages are the first and second lowest, respectively. The wage
growth patterns presented here cannot be explained by a simple model in which
workers possess a single dimensional skill and its return increases over time.
These wage changes result in different consequences between men and women,
and for men between high school and college graduates. First, the occupations
which suffered the largest wage losses are male-dominated. In 1979, only 10%of laborers and 5% of craft workers were female. Female operators were also uncommon; their employment share was 28%. In contrast to men, the majority ofwomen were in occupations that did not experience a significant wage loss, which
resulted in a smaller wage gap between men and women. Second, majority of maleworkers in occupations that suffered the largest wage losses have less than a 4-yearcollege degree. Specifically, only 3-5% of male laborers, operators, and craftsmen
posses a 4-year college education. (not in the table). They are mostly concentrated
in managerial, sales, and professional occupations. Hence, less educated workers
tend to suffer a large wage loss, while many educated workers enjoyed a positive
wage growth, resulting in a greater wage inequality between education levels. The
descriptive analysis here strongly suggests that changes in returns to cognitive andmotor skills are the key to understanding the driving forces behind the narrowing
gender wage gap and widening education wage gap.
Another notable change during the period is that the share of female workers has
increased significantly among professional, manager, and sales workers: from 41%
to 53% in professionals, from 24% to 40% in managers, and from 32% to 41% insales workers. Because these occupations are cognitive-task intensive, this change
may reflect an increase in women’s cognitive skills.

3

A Roy Model of Occupational Choice

The descriptive statistics in the last section suggest that occupational task is the key
to understanding the relationship between the technological change and the gender11

Table 1: Composition-Adjusted Wages and Share of Female Workers

Operatives
Laborer
Craftsmen
Service
ClericalManagers
Sales
Professional

1979
1.99
1.93
2.25
1.70
1.89
2.36
2.11
2.31

Logwage1996
Diff
1.81 −0.18
1.75 −0.18
2.07 −0.18
1.62 −0.08
1.84 −0.06
2.35 −0.01
2.10 −0.01
2.36
0.06

Fraction of Women
1979 1996
Diff
0.28 0.27 −0.02
0.10 0.14
0.04
0.05 0.07
0.02
0.49 0.52
0.03
0.77 0.77
0.00
0.24 0.40
0.16
0.32 0.41
0.09
0.41 0.54
0.12

Note: The data source is CPS 1980 and 1997. The worker composition is fixed at the 1980 level.
The variables controlled include age, gender, five education levels (high school dropouts, high school
graduates, some college, college graduates, and advanced degree), and 1-digit occupations.

wage gap. Applying the task-based approach, this section develops a model ofoccupational choice that helps interpret the stylized facts above.

3.1

Environment

Workers have a set of skills that consists of cognitive, motor, and general skills. The
skill vector of worker i in year t is denoted by sit = (sC,it , sM,it , sG,it ) where sC,it ,sM,it , and sG,it are cognitive, motor, and general skills, respectively, and take nonnegative values. An occupation is defined as a bundle of tasks. Let x j = (xC, j , xM, j )be a vector of the cognitive and motor task complexity indices that characterize thetask of occupation j. The indices take non-negative values, and greater values of
xC, j (xM, j ) imply that the cognitive (motor) task of occupation j is more complex.
Labor is the only factor of production. When occupation j is filled by a worker,
she produces q j (sit ) units of type j goods. Assume, for simplicity, that technology isconstant over time in this section. The aggregate output produced by all workers in
occupation j is denoted by Q jt = ∑i∈I q j (sit ), where I j is the set of workers whosejoccupation is j. This is used as an intermediate input in the production of final
consumption goods and it is priced Pjt in the intermediate input market.

12

3.2

Wage Structure

Wages are paid according to the value of marginal product of laborwi jt = Pjt q j (sit ).

(1)

Assuming that the output of worker i in occupation j is given by a Cobb-Douglas
production function, I specify the logwage of worker i in occupation j at time t asln wi jt = ln Pjt + ln α j + βC, j ln sC,it + βM, j ln sM,it + ln sG,it(2)≡ Π jt + βC, j ln sC,it + βM, j ln sM,it + ln sG,it .

(3)Note that the intercept Π jt and returns to skills (βC, j and βM, j ) vary across occupations and that occupations are characterized by tasks. Hence, these occupationspecific parameters can be replaced by functions of tasks,
Π jt = pt (x j )(4)βC, j = bC (xC, j )(5)βM, j = bM (xM, j ).

(6)

Cognitive and motor skills (sC and sM ) are referred to as task-specific skills, because
log of their marginal product of labor varies across occupations depending on thecomplexity of the task performed. In contrast, the general skill sG is general in thesense that its log-marginal product of labor is constant across all occupations. This
heterogeneity in returns to skills is an important feature of a Roy model. Depending on the workers’ skill endowment, best-paying jobs are different for different
workers, which gives rise to self-selection into occupations. This is the key difference from the Gorman-Lancaster characteristics type of model in which returns toskills are uniform across subsectors of the economy. With uniform returns to skills,
workers are indifferent between jobs, and no occupational choice problem exists.
In the standard Roy model, an occupation is treated as a distinct category, andthe occupation-specific parameters vary arbitrarily across occupations. A major limitation with this standard approach is that the number of variables and parameters13

increase with the number of occupations in the model. This is particularly problematic when a researcher wishes to use a list of finely defined 3-digit occupations in
the U.S. census classification system, which covers about 500 occupations. Even
though estimation itself is straightforward in a linear model, it may be hard to learn
from so many parameter estimates how and why returns to skills are different acrossoccupations. Even worse, when hundreds of free parameters exist in the model, theprecision of estimates may be too low to make any definitive conclusions. For anonlinear model (e.g. a structural dynamic programming model), computationalburden for estimation may be enormous with hundreds of free parameters. Many
empirical researchers avoid this problem by aggregating occupations into a small
number of broadly defined occupation groups (e.g. the 1-digit classification system). The drawback of the aggregation is the loss of rich information available atthe narrowly defined occupation level.
This limitation of the standard Roy model approach can be overcome in thetask-based approach. Any differences across occupations such as return to skills are
explained by the differences in tasks. In addition, computation is greatly simplified
because the number of variables does not change with the number of occupationsin the model, but with the number of tasks that characterize occupations. As longas the dimension of the task vector that characterizes occupations stays low, model
estimation is tractable even when millions of different occupations are in the model.
How should the occupation-specific parameters vary across occupations? Consider a simple task. It can be properly done regardless of worker skills, althoughskilled workers may produce more. In contrast, for a complex task, worker’s skills
matter very much: bad workers will likely fail and good workers succeed. Skills are
more used and contribute to productivity, when the corresponding tasks are complex. Assuming differentiability, I can formulate this idea as
∂ pt
< 0
∂ xk
∂ bk
> 0
∂ xk

(7)
(8)

for k ∈ {C, M}. Figure 2 illustrates how logwage changes with a worker’s task-

14specific skill between simple and complex tasks. In both simple and complex tasks,
logwage increases with skills, but the slope of the logwage schedule is steeper forthe complex task. Also note that the intercept of the logwage schedule is lower
for the complex task. What the figure indicates is that when the task is simple, theproductivity difference between skilled and unskilled workers is small. In contrast,
when the task is complex, output is sensitive to worker skills and the productivity
difference between skilled and unskilled workers is amplified. Hence, in Figure 2,
all workers with skills less than s∗ earn more in the simple task than in the complex
task, while workers with skills more than s∗ earn more in the complex task than in
the simple task.8
LogwageComplex Task

Simple Task

Low-Skill Workerss*Task-Specific
SkillsHigh-Skill Workers

Figure 2: Occupational Sorting Based on Task-Specific Skill

3.3

Skill GrowthWorkers enter the labor market with a vector of initial skills endowment siti where ti
is the year when worker i entered the labor market. Task-specific and general skills
8 Yamaguchi (2012) takes the approach to approximate occupation-specific parameters by func-

tions of tasks, but does not show how heterogeneity in returns to skills sort workers across tasks. A
technical, but important difference between the present model and that in Yamaguchi (2012) is thatthe present model incorporates general skills. Without general skills, the estimated model does notpresent the trade-off between the intercept and the slope, which is the key driving force of worker
sorting.

15

grow over time according to the following skill growth equations,ln sk,it − ln sk,it−1 = gk, j (eit ) = gk (eit , xk, j ) for k ∈ {C, M}(9)ln sG,it − ln sG,it−1 = gG (eit )(10)

where eit is general work experience and occupation-specific function gk, j is replaced by a function of tasks gk (xk, j ), like the wage equation parameters in Equations (4)-(6). Assume that skills remain unchanged when one does not work.
The skill growth rates decrease with experience, which generates a concave
experience-skill profile, and ultimately, a concave experience-wage profile. The
growth rates of task-specific skills vary across tasks, which allows for heterogeneous profiles of skill and wage over time. In the estimated model, the task-specificskill growth rates increase with task complexity, suggesting skill acquisition throughlearning-by-doing. In other words, by doing a complex task, a worker can develop
relevant skills more quickly than when she does a simple task.

3.4

Individual Utility Maximization

Workers supply labor inelastically and do not borrow or lend money, implying consumption equals wages cit = wi jt . I further assume that the utility for consumption is
given by the logarithmic function. In each period while in the labor market, a worker
chooses an occupation to maximize her present value of lifetime utility. This is the
only choice made by workers in this model. The decision horizon is infinite and no
uncertainty exists. These last assumptions are for expositional purpose only and are
not essential for the substance of the argument below.
The value function of a worker with skill sit isVt (sit ) = max ln wt (x j , sit ) + ρVt+1 (sit+1 )
xj

(11)

where ρ is a discount factor. The constraints for the worker’s maximization problem are given by the skill growth equations (9) and (10). Note that choosing an
occupation is equivalent to choosing a bundle of tasks.
16

To characterize a worker’s optimal occupational choice easily, I assume that
there is a continuum of occupations so that workers can choose any task vector x j
in a continuous space. Assuming an interior solution, the first order condition for
optimality is given by differentiating the value function with respect to the index fortask k,∂ ln wi jt∂Vt+1 (sit+1 )
+ρ
∂ xk
∂ xk
∂Vt+1 (sit+1 ) ∂ sk,it+1∂ pt ∂ bk+
ln sk,it + ρ= 0.
=∂ xk ∂ xk∂ sk,it+1
∂ xk

(12)

The first two terms capture the marginal wage return to the task, and the third term
captures the marginal effect of the task on the future utility generated through skill
growth. When conditions (7) and (8) are satisfied, a worker faces a trade-off between the intercept and the slope as illustrated in Figure 2. In addition, she also
takes into account the skill learning opportunities, as captured by the last term ofEquation (12).

4

Estimation Strategy

4.1

Model Specification

4.1.1

Wage Equation

The model laid out in the previous section captures the relationship between tasks,
skills, and wages. Although the main focus of the paper is the role of tasks and taskspecific skills in changing the gender wage gap, other factors, particularly a declineof union coverage rates, might have played an important role as well. Blanchflower
and Bryson (2004) finds that workers make at least 15% higher wages when theirjobs are covered by a union contract. In the PSID, 34.3% of men were covered bya union contract in 1979, but the rate decreased to 20.4% by 1996 (Table 2). On
the other hand, the union coverage rate for women has been around 18% in both
years. Given that many blue collar jobs are motor-task intensive and covered by aunion contract, the large wage decline of motor-task intensive jobs in Section 2.2
17might reflect the decline of union coverage rates, rather than the decline in returns
to motor skills. To address this concern, I include the union coverage in the wage
equation and specify it asln wi jt = Π jt + βC, j ln sC,it + βM, j ln sM,it + ln sG,it + βU,t uit ,(13)

where uit is an indicator variable that takes one if individual i’s job is covered by aunion contract and takes zero otherwise. The parameter βU,t is union wage premium
and it varies with time. While it is technically feasible to allow for the time-varying
parameter to change arbitrarily across years, I cannot estimate it precisely due to thesample size being small. As an accommodation, the time-varying wage premium isapproximated by a piecewise-linear function
βU,t = βU,0 + βU,1t79 + βU,2t89 ,(14)

where t79 = (t − 1979), t89 = (t − 1989) · I(t ≥ 1989). I(·) is an indicator function that takes the value one if the condition in the parenthesis is satisfied and zerootherwise.
As discussed above, occupation-specific parameters are replaced by functionsof tasks (see Equations 4-6). The intercept Π jt is specified as a quadratic function
for tasks

Π jt = pt (x)22= π0,t + π1,t xC, j + π2,t xM, j + π3,t xC,
j + π4,t xM, j + π5,t xC, j xM, j .

(15)

Because the function pt (x) is time-varying, so are the parameters π. These timevarying parameters π are approximated by a piecewise-linear function. For example, the parameter π0,t is given by
π0,t = π0 + π0,79t79 + π0,89t89 .

(16)

In Section 3, technology is assumed to be constant over time so that the returns

18

to skills (βC, j and βM, j ) are time-invariant. When estimating the model, however,I allow for them to change over time, in order to observe the effect of technological change. Assuming that technological change has a secular trend, I specify thefunctions for returns to skills as
βk, j,t = bk,t (xk, j )= (βk,0 + βk,1t79 ) + (βk,2 + βk,3t79 )xk, j .

(17)Modeling the technological change by a linear trend term is a common approach in
the literature (see Katz and Murphy (1992), for example).
4.1.2

Skill Equation

The initial skill endowment is specified as0
di + σk,i + εk,iti ),sk,iti = exp(γk,0(18)

where ti is the year when worker i enters the labor market. di is a vector of worker’s
characteristics that are invariant after the entry into the labor market, such as education, race, and gender.9 σk,i is a time-invariant unobserved component, and εk,iti isa time-varying unobserved component.
The skill growth Equations (9) and (10) together with Equation (18) imply thatlog skills in year t can be written ast−10
ln sk,it = γk,0di + γk,1 eit + γk,2 e2it + γk,3 ∑ xk,i jτ + σk,i + εk,it k ∈ {C, M} (19)τ=ti0ln sG,it = γG,0di + γG,1 eit + γG,2 e2it + σG,i + εG,it .

(20)

Note that none of the parameters in the skill equations are time-varying. This restriction implies that workers in different years are comparable if their observed
characteristics and occupational histories are the same. The fourth term in Equa9 Many papers on gender wage gap do not include a gender dummy in their wage equations, but

doing so raises concern over omitted variable bias. Fortin (2008) extensively discusses this issue andsupports the use of a gender dummy variable.

19tion (19) is the sum of the task indices of the previous jobs. This term captures the
skill component acquired through learning-by-doing. Because this term gives rise
to a heterogeneous skill growth profile conditional on occupational experiences, thisspecification allows for heterogeneous wage growth profiles.
Notice that neither demeaning nor first-differencing eliminates the time-invariant
unobserved skills σk,i , because they are interacted with the task index x. The quasidifferencing method used by Gibbons, Katz, Lemieux, and Parent (2005) does notwork either, because there is more than one time-invariant unobserved variable.
I take the correlated random effect approach (see Wooldridge (2009)) to address
the endogeneity bias caused by the correlation between unobserved skills σ andtasks x. The basic idea of the correlated random effect approach is to put restrictions
on the conditional distribution of unobserved heterogeneity given the entire historyof the covariates. Specifically, the time-invariant components of the unobservedtask-specific skills are modeled as
σk,i = γk,4 x̄k,i + γk,5 ūi + γk,6 x̄k,i ūi + θk,i for k ∈ {C, M}(21)σG,i = γG,3 ūi + θG,i
E(θk,i |xi jt , x̄i , ūi , eit , di ) = 0 for k ∈ {C, M, G},

(22)
(23)

where x̄i and ūi are time-averages of the task indices and union coverage over years
observed in the data, respectively.
Motivated by the worker assignment mechanism outlined in Section 3.4, I include the variable x̄i to control for the time-invariant unobserved skills σk,i . In themodel, workers who have high time-invariant unobserved cognitive (motor) skills
choose complex cognitive (motor) tasks persistently throughout their careers, whichis captured by the time-average of the task indices x̄k,i . As well, workers with highmotor skills tend to take jobs that are covered by a union contract. To allow for thecorrelation between union coverage and worker skills, I include the variable ūi as
an additional control for the time-invariant skills.
Finally, the time-varying components of the unobserved skills satisfy the condi-

20

tional mean independence assumption,E(εk,it |xi jt , x̄i , ūi , eit , di ) = 0 for k ∈ {C, M, G}.

4.2

(24)

Estimation by Nonlinear Least Squares

The parameters of the wage equation (13) and the skill equations (19)-(20) in Section 4.1 are estimated by the nonlinear least squares. Estimation involves a singleequation because the wage equation incorporates the skill equations. Nonlinearity
arises from the restriction that parameters of the skill equations are time-invariant,while those of the wage equation are time-varying. Because skills do not have anatural unit, a normalization restriction must be imposed on either the return-toskill equation (17) or skill equation (19). Without loss of generality, I impose that
βk,2 = 1 in equation (17). Under the assumptions (23) and (24) the parameters are
consistently identified.
Note that there are no restrictions imposed as implied by the optimal occupational choice (e.g. Equation (12)). Such restrictions improve efficiency of the estimator if correct, but they bias estimates if incorrect. In fact, the true occupational
choice may be more complicated than that characterized by the first order condition (12). This is true, for example, when preference for tasks and uncertainty affectworkers’ decisions. Similarly, this approach allows me to estimate the parameters of
the wage and skill equations without modeling a labor force participation process,which can be very complicated for women. The approach taken in this paper isrobust to different models of occupational choice and labor force participation. Another benefit of this less complex approach is that it makes the estimation process
and the driving force of the result relatively transparent.10
10 Yamaguchi (2012) structurally estimates both the wage and occupational choice equations de-

rived from his task-based Roy model by the Kalman filter using the data from NLSY79. The estimation strategy taken in this paper differs from this previous work in three ways. First, the present paper
estimates only the wage equation for robustness. Second, this paper does not assume a parametric
distribution for unobserved skills, while the previous work assumes normality to apply the Kalmanfilter. Third, the econometric model in Yamaguchi (2012) allows for serially correlated unobserved
skills, but not for the permanent unobserved skills.

21

4.3

Identification

The key identifying assumption is selection on observables: a broader set of control
variables captures the heterogeneity amongst workers sufficiently well and takes
care of the endogeneity bias effectively. I consider two components of unobserved
skills: time-invariant and time-varying. The time-invariant component is largely
controlled by the correlated random effect approach detailed in Section 4.1.2. The
control variable, the time-average of task indices x̄, is motivated by the theoreticalargument over worker assignment to tasks in Section 3.4. I also argue that the
time-varying component of unobserved skills is controlled for by including a rich
set of observed variables in the skill equation (19). In particular, the key variable
is the sum of the task indices of the past jobs, which allows me to account forheterogeneity in wage growth profiles.
A possible alternative approach to the selection bias is the instrumental variable
method. For example, Gould (2002) and Fletcher and Sindelar (2009) instrument
occupations using the occupations of the worker’s father, because fathers affect occupational preference of children. Fletcher and Sindelar (2009) in their study of thecausal effect of occupations on health use the fractions of blue-collar workers in agiven state to measure availability of blue-collar and white-collar jobs. The fact thata substantial proportion of jobs in Michigan are blue collar increases the likelihoodthat a new entrant will start working in a blue collar job.
However, I do not instrument the task indices for occupations by these variables
for two reasons. First, these instruments may not satisfy an exclusion restrictionin the present context. Second, my control variables for skills seem to work well,and father’s occupation and local labor market conditions do not provide much additional identification power. I run the instrumental variable first-stage regressions
to see how strongly the instruments are correlated with the task indices. Without
my key control variables constructed from workers’ occupational history, the instruments are strongly correlated with task indices. Once the control variables areincluded, the instruments are no longer strong. This exercise suggests, but by nomeans proves, that the additional skill control variables effectively take care of theendogeneity problem at least to the extent that the previous papers do using instrumental variables approach. Details of this exercise are available in the online
22

appendix.
Another important issue on identification is what features of the data allow one
to identify how an observed characteristic such as education can be associated withthree different types of skills. That can be identified by variations of the wage return to the worker characteristic (e.g. education) across different tasks. Suppose that
education increases cognitive skills. Then, the wage gap between high school andcollege educated workers increases with cognitive task complexity, because returns
to cognitive skills increase with task complexity. Similarly, if men possess more
motor skills than women, the gender wage gap increases with motor task complexity. The component of the wage gap invariant to tasks is associated with generalskills. This argument is elaborated in the online appendix.

5

Data: PSID

5.1

Sample Restrictions and Variable Definitions

The PSID is a nationally representative household panel survey that began in 1968.
To study the evolutions of tasks, skills, and wages, I draw a sample of household
heads and wives11 who worked full-time (1,500 hours a year or more) from 1979
to 1996. I select these survey years, because all the variables are available, andmore importantly, we observe that the wage inequality increased and the genderwage gap narrowed rapidly during this period. I restrict the sample of individuals
to be between 18 and 65 years old. The sample does not include self-employed andagricultural workers. The sample restrictions are comparable to those used in theliterature such as in Blau and Kahn (1997).12
Hourly wages are calculated by dividing labor income by hours of work, and are
deflated by the 1983 PCE Index. Note that hours of work and labor income indicatedare for the previous year of the survey, similar to the CPS. The number on the years
11 In the PSID, a man is by construction a household head for a married or cohabiting couple. A
women can be a household head in a single household.
12 Blau and Kahn (1997) also extensively examine the issue of sample attrition in the PSID bycomparing various statistics with the CPS. They find that the reported hourly wages in the PSID tend
to be higher than the CPS, but do not find evidence of a significant attrition bias in other statistics.
Most importantly, they find that changes in gender wage gap are very similar in the two data sets.

23

of experience is not available for every survey year. For years when experience is
not recorded, it is imputed using hours of work observation. Occupations in the
PSID are coded using the 1970 census scheme. This coding is used to merge the
PSID sample with the task indices from DOT. Details of variable definitions are
outlined in the online appendix.

5.2

Summary Statistics of the Sample

Table 2 reports the means of selected labor market outcomes for men and womenin 1979 and 1996. The mean log hourly wage exhibits well-known patterns. Men’s
wages were higher than women’s by 48.1% in 1979 and 29.0% in 1996. From1996 to 1979, the gender wage gap decreased by 19.1 percentage points. Bothmen’s and women’s cognitive task complexity indices grew over the period, while
their motor task complexity indices decreased. These patterns exhibit the shift frommotor to cognitive tasks, and are consistent with the nuanced view of technologicalchange. Furthermore, both men and women became better educated over time andachieved that at about the same rate in the sample period. The gender gap in thework experience has significantly decreased from 6.5 years to 4 years. The union
coverage rate for men was 34.3% in 1979, but dropped to 20.4% by 1996. Women’s
union coverage rates remained stable around 18% in both years.
Table 2: Differences Between Men and Women in 1979 and 1996

Logwage
Cognitive Task
Motor Task
White
Education
Experience
Union Coverage

Men
2.405
0.518
0.511
0.896
12.63318.294
0.343

1979
Women
1.924
0.514
0.499
0.861
12.456
11.836
0.182

Diff
0.481
0.005
0.013
0.034
0.177
6.458
0.161

Men
2.400
0.529
0.501
0.896
13.63419.092
0.204

1996
Women
2.109
0.543
0.482
0.863
13.52015.223
0.177

Diff
0.290
−0.014
0.020
0.033
0.114
3.869
0.027

D-in-D−0.191−0.0180.007−0.002−0.063−2.589−0.134

Note: The source is the PSID in 1979-1996. Wages are deflated by 1983 PCE Index. The sample
includes household heads and wives who worked full-time (1,500 hours a year or more). Those whoare younger than 18 or older than 65 are excluded from the sample. Self-employed and agricultural
workers are also not in the sample. The PSID sample weights are applied.

24

6

Empirical Results

This section presents the main result of the paper. In Subsection 6.1, I show thatthe skill measures based on occupational history are strongly correlated with wages.
Subsection 6.2 shows how returns to skills vary across occupations and change from1979 to 1996. Subsection 6.3 presents estimated differences in skill endowments
between men and women. In Subsection 6.4, I decompose the changes in the genderwage gap using a version of the Oaxaca-Blinder decomposition method.

6.1

Parameter Estimates

In this subsection I restrict the discussion to a few parameter estimates concernedwith skills. All the parameter estimates are reported in the online appendix.
To control for worker skills, I take a correlated random effect approach and include in the skill equations the averages of task complexity indices x̄ and union
dummies ū and their interaction (See Equations 21 and 22). I test the null hypothesis that these variables are uncorrelated with unobserved skills σk for each typeof skill. The test statistics and p-values are reported in rows 1-3 of Table 3. The
null hypotheses are soundly rejected for cognitive and general skills, while it ismarginally rejected for motor skills at the 10% significance level (p-value is 0.082).
I also test the null hypothesis that all of the additional variables used to control forthe correlated random effects are zero. This is soundly rejected as well. Therefore,
the test results here indicate that these additional variables are useful in controlling
for time-invariant worker skills.
Another set of key variables used to estimate task-specific skills are sums oftask complexity indices for the past jobs. They are included in the skill equations toaccount for differences in time-varying components of task-specific skills across individuals. They are statistically significant at 1% level for both cognitive and motor
skills, and the asymptotic t-values are 6.714 and 2.833, respectively (see Table 12 in
the online appendix). Omitting these variables results in biased parameter estimateseven if a correlated random effect approach is taken, because it does not take careof time-varying components of worker skills.
All the variables discussed in this subsection are not included in the wage re25

gressions in the previous papers. The significance test results, however, indicatethat omitting them produces biased estimates of a wage regression with occupation
dummies and/or task indices.

Table 3: Testing Correlated Random Effects
Wald Statistic p-Value(1) Cognitive Skill
85.3860.000(2) Motor Skill
6.705
0.082
(3) General Skill
75.7930.000(4) All Skills
686.904
0.000
Note: The null hypothesis for row (1) is that γC,4 = γC,5 = γC,6 = 0 in Equation (21). The null
hypothesis for row (2) is that γM,4 = γM,5 = γM,6 = 0 in Equation (21). The null hypothesis for row(3) is that γG,4 = 0 in Equation (22). The null hypothesis for row (4) is that all of these parameters
are jointly zero.

6.2

Wage Structure

6.2.1

Heterogeneity in Returns to Skills Across Tasks

Heterogeneity in returns to skills across tasks is the main driver of worker-task assignment, as discussed in Section 3. The key feature of the assignment mechanismis the trade-off between the intercept and the slope of the wage schedule in Figure 2.
On the one hand, a simple task offers a high guaranteed wage, but the wage changes
little with skills. On the other hand, a complex task offers a low guaranteed wage,
but the wage quickly increases with skills. Given these wage schedules, and workers’ self-selection, low skill workers take a simple task and high skill workers takea complex task. In estimating the model, I do not impose a restriction that generates such a trade-off. Nevertheless, in the estimated model a trade-off between theintercept and the slope emerges.
Figure 3 illustrates the estimated wage schedules for 1979.13 The horizontal
axes show normalized task-specific skills. They are normalized so that mean andstandard deviation of the skills are zero and one for all male and female workers in
1979. The vertical axes show normalized logwage. It is normalized so that mean is
13 A figure for the estimated wage schedule for 1996 is available upon request.

26

zero for those whose skills and occupations are average, i.e. the skill is zero and task
is 0.5 in the graphs. The top panel of Figure 3 displays the wage schedule along thedimension of cognitive tasks and skills, while the bottom panel represents the wageschedule for the motor tasks and skills. For both dimensions, a trade-off between
the intercept and the slope is evident.
Identical workers are paid differently depending on tasks. For example, a worker
with cognitive skills one standard deviation higher than the average earns 18%
higher wage by taking a complex task (x = 0.6) than by taking a simple task (x =0.4).14 Similarly, a worker with cognitive skills one standard deviation lower than
the average earns 11% higher wage by taking a simple task than by taking a complex task. Wage differences are also found across different motor tasks, although
they are smaller than those across cognitive tasks. For example, a worker with motor skills one standard deviation higher than the average earns 6% higher wage bytaking a complex task than by taking a simple task. A worker with motor skills one
standard deviation lower than the average earns 1% higher wage by taking a simple
task than by taking a complex task.
6.2.2

Changes in Average Returns to Skills

To provide a general picture of the evolution of returns to skills, I calculate theaverage of the returns to skills over all workers in a given year using the PSID sampling weights. The average returns to skills change over time for two reasons. First,
workers undertake different tasks over time. If workers complete more complex
tasks over time, the returns to skills increase over time, because complex tasks utilize their skills more intensely, resulting in a higher rate of return. This effect ofoccupational composition can be obtained by fixing the parameters for the returns
to skills at the 1979 level. Then, the difference in the returns to skills between 1979
and 1996 under this restriction reflects the effect of changes in occupational composition. Second, technological change directly affects the returns to skills, whichis captured by changes in the parameters over time. I calculate this effect by fixing
the occupational composition in 1979 with parameters being allowed to change over
14 Remember that the task index is normalized such that mean is 0.5 and standard deviation is 0.1.

27

0.6
0.0
−0.6 −0.4 −0.2

Logwage

0.2

0.4

x=0.4
x=0.5
x=0.6

−2

−1

0

1

2

1

2

0.2

Cognitive Skill

0.0
−0.2

−0.1

Logwage

0.1

x=0.4
x=0.5
x=0.6

−2

−1

0
Motor Skill

Figure 3: Estimated Wage Schedules in 1979
Note: Estimated wage schedules in 1979 are presented for three different tasks. The horizontal axis
shows skills normalized so that the mean is zero and the standard deviation is one. The verticalaxis shows logwage normalized so that the average worker (her skill level is zero) earns zero at the
average job (x = 0.5).

28

time, which isolates the effect of the technological change.
Table 4 summarizes the estimates for the changes in returns to skills. From 1979
to 1996, the return to cognitive skills increased by 13.5%, while those to motor
skills decreased by 68.3%. It was the technological change during this period thatwas largely responsible for these changes in returns to skills. The technologicalchange increased the returns to cognitive skills by 7.8% and decreased the returns
to motor skills by 66.7%. Changes in occupational composition also contributed tothe changes in returns to skills, but to a lesser extent. They increased the returns
to cognitive skills by 5.7% and decreased the returns to motor skills by only 1.6%.
These patterns are consistent with the theory by Autor, Levy, and Murnane (2003)
and descriptive statistics shown in Section 2.2.
Table 4: Changes in Returns to Skills

Tech Change%∆ Returns to Cognitive Skill%∆ Returns to Motor Skill
Occ. Composition%∆ Returns to Cognitive Skill%∆ Returns to Motor Skill
Total%∆ Returns to Cognitive Skill%∆ Returns to Motor Skill

6.3

Estimates

Std. Error

7.8
−66.7

5.3
9.9

5.7
−1.6

0.6
0.6

13.5
−68.3

5.4
10.0

Skill Endowments

Table 5 reports estimated skill gaps between men and women. Because no natural
metric for skills exists, the skill gaps for both years are measured in logwage bymultiplying the skill gaps and the returns to skills for an average task (x = 0.5)
in 1979. The gaps are calculated by subtracting the average women’s skills fromthe average men’s skills. Hence, positive numbers indicate that men have moreskills than women, and vice versa. Relative to the motor skill gap, the cognitive
skill gap between men and women was small. In 1979, men had more cognitive
skills than women, and the difference was equivalent to 1.2% higher wage. In 1996,29

women’s cognitive skills exceeded men’s, and the gap was worth 2.6% higher wage
for women. The difference in each year is neither statistically nor economicallysignificant. A significant gap in motor skills, however, existed between men andwomen: men have more motor skills than women, which resulted in a 12.4-13.0%
higher wage for men between 1979 and 1996. Lastly, I find a large gender gap ingeneral skills, worth around 25-29% higher wage for men.
In the previous literature, no gender difference in cognitive skills and a significant gender difference in motor skills are often assumed, but not estimated.(SeeGalor and Weil (1996) and Rendall (2010)). Black and Spitz-Oener (2010) and Bacolod and Blum (2010) measure the gender difference in these skills by the task
indices alone. However, they do not find a difference large enough to lead to asignificant gender wage gap. This paper takes one step further and estimates thegender gap in skill endowments. I find the estimates are intuitive, and confirm theassumptions made by Galor and Weil (1996) and Rendall (2010).
Table 5: Skill Gaps Between Men and Women

Cognitive Skill
Motor Skill
General Skill

1979
Estimates Std. Error
0.012
0.015
0.130
0.023
0.285
0.027

1996
Estimates Std. Error−0.026
0.015
0.124
0.022
0.245
0.026

Note: Measured in logwage by multiplying the skill gaps and the returns to skills for an average task
(x = 0.5) in 1979. Positive numbers indicate that men have more skills than women, and vice versa.

6.4

Wage Gap Decomposition

One of the key findings so far is that men have more motor skills than women,
and the technological change reduced returns to motor skills. This implies that thetechnological change is responsible for the reduced gender wage gap from 1979 to
1996. In this subsection I estimate the effect of the technological change on thegender wage gap, along with contributions of the other factors.
I decompose changes in the gender wage gap using a method similar to OaxacaBlinder decomposition. Namely, changes in the gap are decomposed into (1) the30

wage structure effect that reflects changes in parameter values and (2) the composition effect that reflects the changes in tasks and skills. To derive the composition
effect, I fix the parameters (i.e., the wage structure) at either the 1979 or 1996 level
and calculate counterfactual wage gaps. The difference between the predicted wage
gap of the estimated model and the composition effect identifies the wage structure
effect. The decomposition exercise is carried out as follows. The gender wage gap
in year t ,Gt , is measured by mean logwage difference between men and womenand given by
Gt = G(Θt , Ft )where Θt is a set of parameters in year t, and Ft is a distribution function in yeart for task, skill, and gender. The change in the gender wage gap from 1979 and1996 is ∆G = G(Θ96 , F96 ) − G(Θ79 , F79 ), which can be decomposed into the twocomponents in two different ways:∆G = [G(Θ96 , F96 ) − G(Θ79 , F96 )] + [G(Θ79 , F96 ) − G(Θ79 , F79 )]"Wage Structure Effect""Composition Effect"(25)∆G = [G(Θ96 , F96 ) − G(Θ96 , F79 )] + [G(Θ96 , F79 ) − G(Θ79 , F79 )].
"Composition Effect""Wage Structure Effect"

(26)

or

Notice that the logwage is linearly separable in the cognitive, motor, and generalskill components. Hence, composition and wage structure effects are further decomposed into these different skill components.15
Table 6 presents the results for the gender logwage gap decomposition using
Equations (25) and (26). From 1979 to 1996, the observed gender logwage gap has
decreased by 0.187 log points. Out of 0.187 log points, changes in returns to skills
and tasks, and the union premium (wage structure effects) account for 0.080-0.086
15 Although it is technically feasible, I do not decompose into the effects of skills and those oftasks, because tasks are endogenously determined. Given the theoretical model, changes of tasks areinterpreted as consequences of changes in skills.

31

Table 6: Decomposition of Changes in Gender Logwage Gap
Base Year: 1979
Estimate Std. Error

Base Year: 1996
Estimate Std. Error

Wage Structure EffectOutput Price
Returns to Cognitive Skill
Returns to Motor Skill
Union Premium
Composition EffectCognitive Task & Skill
Motor Task & Skill
Interaction of Cognitive & Motor Tasks
General Skill
Union Coverage

0.003−0.006−0.084
0.001

0.009
0.007
0.010
0.000

−0.001
0.003−0.087
0.005

0.005
0.005
0.010
0.003

−0.0580.002
0.010−0.041−0.014

0.006
0.004
0.003
0.004
0.001

−0.035−0.007−0.006−0.041−0.018

0.007
0.003
0.003
0.004
0.002

Residuals−0.0040.009−0.004

0.009

Total

−0.191

0.027−0.1910.027

Note: Base year refers to the year in which the parameters are fixed in calculating the composition
effect. Namely, the first two columns use Equation (25), and the second two columns use Equation(26).

change in skill endowments, while tasks and union coverages (composition effects)
account for 0.101-0.107 of the change. The remaining 0.004 stay as unexplained by
the model.
The most notable feature in the table is that the drop in returns to motor skills
accounts for about half of the narrowing gender wage gap: 0.084-0.087 log points.
This result is along the same line as the empirical analysis in Section 2.2 in which
motor-task intensive jobs suffer a large wage loss and are male-dominated. Devaluation of motor skills hurt men, but not women, resulting in a narrowing gender wage
gap. Changes in returns to cognitive skills and tasks affected the gender wage gap
little, because the gender gap in cognitive skills was modest in the first place.
Another important point is that women’s growth in general and cognitive skills
greatly narrowed the gender wage gap: women’s cognitive skills growth accounts
for 0.035-0.058 log points, and their general skills growth accounts for 0.041 log
points. During the period examined, women became more educated and experienced, and undertook more complex cognitive tasks than they used to, resulting in32

larger cognitive and general skill endowments. Again, this result is along the line ofthe observed increase in the share of female workers in managerial and professional
occupations, as seen in Section 2.2.
De-unionization does not appear to have a large effect on gender wage gap.
Union premium was 0.106 and fairly stable over time (see Table 9), and its change
had very little effect on the gender wage gap. The decrease in men’s union coveragerate from 34% to 20% from 1979 to 1996 (see Table 2) accounts for only 0.014 log
points.
Previous papers find that the wage structure effect is small or leads to a widening
gender wage gap. Blau and Kahn (1997) find that changes in the wage structure
should have widened the gender wage gap, because they measure skills by educationand experience, and the returns to those variables have increased. Bacolod andBlum (2010) include occupational task variables in their wage regression and findthat the wage structure effect narrowed the gender wage gap by only 0.02 log points.
Their results indicate that the composition effect is the major factor in explaining
the narrowing gender wage gap. In contrast, this paper finds a large wage structure
effect: the decrease in the rate of return to motor skills has narrowed the genderwage gap significantly. The main methodological difference of this paper from theprevious contributions is in taking the estimation one step further by allowing forheterogeneous returns to skills across tasks and including a broader set of control
variables for task-specific skills.
Although the main focus of this paper is the gender wage gap, the theory also
predicts a rise in male wage inequality across education categories. To see if thetechnological change also accounts for the wage gap among males, I examine skill
gaps between men with high school education only and and college graduates andthen decompose the change of their wage gap during the same period in a similar
fashion as above. The following summarizes the results for men. Details of thisexercise are available in the online appendix.
The estimates show that college educated men have more cognitive skills thantheir high school educated counterparts. The gap translates into 36% and 42%
higher wages in 1979 and 1996, respectively. High school educated men haveslightly more motor skills than college educated men, reflecting the fact that the33former tend to occupy motor-task intensive jobs. The motor skill gap is worth only
6% higher wage. No significant difference in general skills exists.
From 1979 to 1996, the observed logwage gap between high school and college
educated men has decreased by 0.237 log points. Out of 0.237 log points, changes in
returns to skills and tasks, and the union premium (wage structure effects) accountfor 0.100-0.107, while changes in skill endowments, tasks and the union coverage(composition effects) account for 0.123-0.131. The remaining 0.007 log points are
unexplained by the model. Most of the wage structure effect comes from changes
in returns to task-specific skills, and the effects of changes in output price and theunion premium have a modest effect. Faster growth of cognitive and general skills
for college educated men than high school educated men also significantly widened
the wage gap.

7

Discussion

7.1

Selection into Labor Force

Mulligan and Rubinstein (2008) find that the rise in returns to skills, which changed
the labor force participation patterns of women, ultimately changed the observed
gender wage gap. During the 1970’s, unskilled women participated in the labormarket, while skilled women remained at home. In the 1980’s and 90’s, returns toskills rose, increasing the opportunity cost of staying at home for skilled women.
Consequently, more and more skilled women started participating in the labor market. They claim that this compositional change of female labor force accounts forthe change in the observed gender wage gap even if no change in the wage structure
exists.
Although this paper does not model labor force participation, it addresses thecomposition change in female labor force by including a rich set of variables tomeasure skills. In the CPS data used by Mulligan and Rubinstein (2008), actual
work experience, and more importantly, workers’ occupational history are not available. These are key variables to measure women’s skills, and the estimation results
reported in Table 5 indicate that the model indeed captures women’s skill upgrading34

over time. To further check if women’s skill upgrading not captured by the current
model exists, I estimate the model allowing for cohort effects. This change does
not affect the main result.16 The decomposition exercise in Section 6.4 shows thatthe composition change is an important source of the narrowing gender wage gap,
but it is far from the whole explanation. The decrease in returns to motor skills also
played an important role in reducing the gender wage gap.

7.2

Gender Discrimination

In the model, wages are equal to the value of the marginal product of labor, and thegender wage gap is due to differences in skills and tasks. Gender discrimination
may potentially be picked up by a female dummy variable in the skill functions (19)and (20). However, the estimates of task-specific skill endowments do not sufferfrom a bias arising from potential gender discrimination, unless the level of discrimination is correlated with task complexity. Discussions in Section 4.3 and in
the online appendix explain how the gender difference in task-specific skills is identified. In the data, the gender wage gap increases with motor task complexity, andthis positive correlation between motor task complexity and the gender wage gap isthe identification source of the gender gap in motor skills. If gender discrimination
exists but it is not correlated with task complexity, discrimination is absorbed bygeneral skills.
Most theories of gender discrimination do not suggest a correlation between
tasks and discrimination. An exception is the “glass ceiling” theory - that women
are kept from rising to the upper rungs of the corporate ladder - which implies thatwomen are more strongly discriminated against as the cognitive tasks become more
complex (e.g. managerial positions). This effect may bias women’s cognitive skill
endowments downward, which implies women had more cognitive skills than men
during the period examined. If this is the case, there may be a stronger role for thetechnological change in accounting for the change in the gender wage gap, because
returns to cognitive skills increased during the period. However, the “glass ceiling”
theory may not be as relevant in the present context, because it is about executive
16 See the online appendix for details of this exercise.

35

positions.
Note that women’s growth of general skills is driven by better education andmore experience. This is true even if the estimates of the general skill endowments
are biased due to gender discrimination, because the coefficient for a female dummy
is time-invariant in the skill production function. Hence, once a broad set of worker
characteristics is controlled for, a change in gender discrimination does not appear
as an important source of the narrowing gender wage gap.17

7.3

International Trade

This paper argues that the technological change is the source of the changes in returns to skills. However, trade with developing countries may also hurt unskilledworkers. In the Heckscher-Ohlin model, trade with developing countries raises thedemand for skill-intensive goods made in the U.S. This change in demand ultimately increases returns to skills in the U.S. through a price increase of the skillintensive goods, the effect known as the Stolper-Samuelson theorem. However,Lawrence and Slaughter (1993) and Sachs and Shatz (1994) find that the relative
price of skill-intensive goods did not increase over the period of increasing inequality. Another evidence in conflict with the trade theory’s is that returns to skills indeveloping countries also increased. This is opposite to the theoretical predictions.
Furthermore, another evidence in support of the technology view and against thetrade view is that the share of skilled workers increased within industries, while thetrade theory predicts it would have remained intact. Moreover, Berman, Bound, andGriliches (1994) find that the skill-biased technological change is pervasive acrossdeveloped countries, implying that the technological change increases returns toskills even in an open economy.18
17 Of course, it is possible that the changes in worker characteristics are results of a change in

gender discrimination.
18 There is an on-going debate about how off-shoring affects the U.S. labor market. Among others,
Firpo, Fortin, and Lemieux (2011) find that off-shoring contributes to wage inequality in the U.S,
but that occurred since 2000s. Because the period of study of this paper is from 1979 to 1996,
international trade and off-shoring seem to have little effect on the changes in returns to skills.

36

8Conclusion

Based on the task-based approach, this paper constructs a Roy model of occupational choice in which workers possess cognitive and motor skills and occupations
are characterized by cognitive and motor tasks. The key feature of the model is theheterogeneity in returns to skills across occupations that gives rise to self-selection
into occupations. The model is used as a guide to how a wage equation should beformulated and motivates the way to measure skills.
The empirical results indicate that men have significantly more motor skills than
women, while only a small difference in cognitive skills between genders exists.
Between 1979 and 1996, the returns to motor skills dropped dramatically, while
those to cognitive skills increased modestly. This suggests that technological change
is responsible for the narrowing gender wage gap. In particular, the significant dropin returns to motor skills accounts for more than 40% of the narrowing in the gap.
Increases in women’s cognitive and general skills also significantly narrowed thegender wage gap. This technological change also accounts for the large portion of
the rise in male wage inequality across education categories.
Although I provide evidence that taking occupational choice and labor force participation as exogenous, conditional on the broad set of control variables, does notlargely bias the main results, incorporating these features in the model is a promising direction for future research. Changes in returns to skills should have affected
workers’ skill investment as well as occupational choice and labor force participation decisions. Studying these changes in worker behavior is an important step
toward a thorough understanding of how technological change has reshaped the labor market.

References
ACEMOGLU , D., AND D. AUTOR (2011): Skills, Tasks and Technologies: Implications for Employment and EarningsElsevier, vol. 4 of Handbook of Labor
Economics, chap. 12, pp. 1043–1171.
AUTOR , D. H., F. L EVY, AND R. J. M URNANE (2003): “The Skill Content of37

Recent Technological Change: An Empirical Exploration,” Quarterly Journal of
Economics, 118(4), 1279–1333.
BACOLOD , M., AND B. S. B LUM (2010): “Two Sides of the Same Coin: U.S.
“Residual" Inequality and the Gender Gap,” Journal of Human Resources, 45(1),197–242.
B EAUDRY, P., AND E. L EWIS (2012): “Do Male-Female Wage Differentials Reflect Differences in the Return to Skill? Cross-City Evidence From 1980-2000,”
Dartmouth College.
B ERMAN , E., J. B OUND , AND Z. G RILICHES (1994): “Changes in the Demandfor Skilled Labor within U.S. Manufacturing: Evidence from the Annual Surveyof Manufactures,” The Quarterly Journal of Economics, 109(2), 367–97.
B LACK , S. E., AND A. S PITZ -O ENER (2010): “Explaining Women’s Success:Technological Change and the Skill Content of Women’s Work,” The Review of
Economics and Statistics, 92(1), 187–194.
B LANCHFLOWER , D. G., AND A. B RYSON (2004): “What Effect Do Unions Haveon Wages Now and Would Freeman and Medoff Be Surprised?,” Journal of Labor
Research, 25(3), 383–414.
B LAU , F. D., AND L. M. K AHN (1997): “Swimming Upstream: Trends in the
Gender Wage Differential in the 1980s,” Journal of Labor Economics, 15(1), 1–42.
B ORGHANS , L., B. TER W EEL , AND B. A. W EINBERG (2006): “People People:
Social Capital and The Labor-Market Outcomes of Underrepresented Groups,”
NBER Working Paper 11985.
C ARD , D., AND J. E. D I NARDO (2002): “Skill-Biased Technological Change andRising Wage Inequality: Some Problems and Puzzles,” Journal of Labor Economics, 20(4), 733–783.
F IRPO , S., N. F ORTIN , AND T. L EMIEUX (2011): “Occupational Tasks andChanges in the Wage Structure,” University of British Columbia.
38

F LETCHER , J., AND J. L. S INDELAR (2009): “Estimating Causal Effects of Early
Occupational Choice on Later Health: Evidence Using the PSID,” NBER Working Paper no. 15256.
F ORTIN , N. (2008): “The Gender Wage Gap among Young Adults in the UnitedStates: The Importance of Money versus People,” Journal of Human Resources,
43(4), 884–918.
G ALOR , O., AND D. N. W EIL (1996): “The Gender Gap, Fertility, and Growth,”
American Economic Review, 86(3), 374–87.
G ATHMANN , C., AND U. S CHÖNBERG (2010): “How General is Specific Human
Capital? A Task-Based Approach,” Journal of Labor Economics, 28(1), 1–50.
G IBBONS , R., L. F. K ATZ , T. L EMIEUX , AND D. PARENT (2005): “Comparative Advantage, Learning and Sectoral Wage Determination,” Journal of Labor
Economics, 23(4), 681–724.
G OULD , E. D. (2002): “Rising Wage Inequality, Comparative Advantage, and theGrowing Importance of General Skills in the United States,” Journal of Labor
Economics, 20(1), 105–47.
G REENACRE , M. (2007): Correspondence Analysis in Practice. Chapman &Hall/CRC.
H ECKMAN , J., AND J. S CHEINKMAN (1987): “The Importance of Bundling in a
Gorman-Lancaster Model of Earnings,” Review of Economic Studies, 54(2), 243–
55.
H ECKMAN , J. J., AND G. S EDLACEK (1985): “Heterogeneity, Aggregation, andMarket Wage Functions: An Empirical Model of Self-Selection in the Labor Market,” Journal of Political Economy, 93(6), 1077–1125.
K ATZ , L. F., AND K. M. M URPHY (1992): “Changes in Relative Wages, 19631987: Supply and Demand Factors,” The Quarterly Journal of Economics,
107(1), 35–78.
39

L AWRENCE , R. Z., AND M. J. S LAUGHTER (1993): “International Trade andAmerican Wages in the 1980s: Giant Sucking Sound or Small Hiccup?,” Brookings Papers on Economic Activity. Microeconomics, (2), 161–226.
M A , S., J. S. R ACINE , AND L. YANG (2011): “Spline Regression in the Presenceof Categorical Predictors,” McMaster University.
M ULLIGAN , C. B., AND Y. RUBINSTEIN (2008): “Selection, Investment, and
Women’s Relative Wages Over Time,” Quarterly Journal of Economics, 123(3),1061–110.
P OLETAEV, M., AND C. ROBINSON (2008): “Human Capital Specificity: Evidence
from the Dictionary of Occupational Titles and Displaced Worker Surveys 19842000,” Journal of Labor Economics, 26(4), 387–420.
R ENDALL , M. (2010): “Brain versus Brawn: The Realization of Women’s Comparative Advantage,” University of Zurich.
S ACHS , J. D., AND H. J. S HATZ (1994): “Trade and Jobs in U.S. Manufacturing,”
Brookings Papers on Economic Activity, (1), 1–94.
S TAIGER , D., AND J. H. S TOCK (1997): “Instrumental Variables Regression with
Weak Instruments,” Econometrica, 65(3), 557–586.
T EULINGS , C. (1995): “The wage distribution in a model of the assignment ofskills to jobs,” Journal of Political Economy, 103(2), 180–215.
W EINBERG , B. A. (2000): “Computer Use and the Demand for Female Workers,”
Industrial and Labor Relations Review, 53(2), 290–308.
W ELCH , F. (2000): “Growth in Women’s Relative Wages and in Inequality among
Men: One Phenomenon or Two?,” American Economic Review, 90(2), 444–49.
W OOLDRIDGE , J. M. (2009): “Correlated Random Effects Models With Unbalanced Panels,” Michigan State University.
YAMAGUCHI , S. (2012): “Tasks and Heterogeneous Human Capital,” Journal ofLabor Economics, 30(1), 1 – 53.
40

A

Details on the Data (For Online Publication)

A.1

DOT

In the DOT, many characteristics are measured by a multi-point scale and have detailed definitions. For example, the variable DATA measures by integers from 0 to
6 the complexity of tasks in relation to information, knowledge, and conceptions.
Tasks at the lowest level of complexity involve judging the readily observable characteristics of data. Examples include sorting hats according to color and size specified, comparing invoices of incoming articles with the actual number and weight ofarticles, and so on. Tasks at the intermediate level of complexity involve compiling information. Examples include summarizing details of transactions, collecting,classifying, and recording data, and receiving customer complaints to record and filethem for future processing. Tasks at the highest level of complexity involve integrating analysis of data to discover facts and developing the knowledge of concepts
for interpretations. Examples include formulating hypotheses and experimental designs, writing critical reviews of art for publication, and conducting research. Other
tasks such as operating machines or equipment are also evaluated in a similar manner. Some tasks are measured by a binary variable that takes the value one if theoccupation involves the task and zero otherwise.
Table 7: DOT Variables for Cognitive Task Complexity Index
Variable
Worker Function
DATA
PEOPLE
General Educational Development
reasoningmathematics
language
Aptitudeintelligence
verbalnumerical
Temperament
influencing people
dealing with people

41

No of Categories/Levels
7
9
6
6
6
4
5
5
2
2

Table 8: DOT Variables for Motor Task Complexity Index
Variable
Worker Function
THINGS
Aptitude
motor coordination
finger dexterity
manual dexterity
eye-hand-foot coordination
spatialform perception
color discrimination

No of Categories/Levels
8
5
5
5
5
5
5
5

Tables 7 and 8 show variables that measure cognitive and motor task complexity. They are highly correlated within the task group, and thus the information canbe summarized by a single index using Multiple Correspondence Analysis (MCA).
Correspondence analysis is a generalized principal component analysis tailored forthe analysis of qualitative data. MCA is an extension of correspondence analysis
which allows one to analyze the pattern of relationships of several categorical dependent variables. In short, MCA is a dimension reduction technique for categoricalvariables. There are 10 categorical variables for the cognitive task complexity index
and 8 categorical variables for the motor task complexity index. These variables areconverted into 52 and 43 indicator variables, respectively. In MCA, variation of thedata is called inertia, which is the sum of chi-square distances to the centroid. In
calculating inertia, I account for off-diagonal subtables of the Burt matrix only.
I apply the MCA to the April 1971 CPS, augmented by the fourth edition of
the DOT.19 This is the only data that contains the 1970 census occupation code, theDOT occupation code, and the DOT variables, which allows for linking the DOT
variables and the census occupation code. The task complexity indices constructedby MCA account for 50% and 39% of the inertia of the 1971 CPS sample, respectively. The resulting indices at the individual level are aggregated into the level ofthe 1970 census occupation by taking the mean for each of the 1970 census 3-digit
occupations using the sampling weights so that they can be merged with the PSID.
The indices are normalized so that the mean is 0.5 and the standard deviation is 0.1
19 The data file is available at the ICPSR website (http://dx.doi.org/10.3886/ICPSR07845.v2).

42

for the working individuals in the 1971 augmented CPS.

A.2

PSID

The following is the definitions of the variables taken from the PSID.
Education Education is reported in the PSID in 1968, 1975, and 1985 for existingheads20 of households, and every year for the new entrants into the sample only.
When education is missing, I first use education reported in the survey prior to theyear when education is missing. Then, if necessary, I use the education reported in
the survey after the year when education is missing.
Demographic Variables Age, gender, and race are used in this paper. Wife’s race
is not reported between 1968 and 1984. I assume wife’s race is the same as that ofher husband during this period. If more than one race is reported throughout thesurvey years, the most often reported answer is used.
Wages Hourly wages are calculated by dividing total labor earnings by hours
worked. They are then deflated by the1983 PCE Index. Hourly wages less than
$1 or more than $250 are treated as missing.
Hours Worked When missing, I impute hours of work by taking an average of
those in the previous and next years. The imputed values are used to determine
whether one works full-time or not. A full-time work consists of 1,500 hours ofwork in a year. This variable is subsequently used to construct experience and task
indices. The imputed values are not used to calculate hourly wages.
Experience Experience is reported for 1974, 1975, 1976, 1985, and years whena household is interviewed for the first time. For all other years, experience is imputed, using the indicators for full-time work and experience reported in the earlier
20 In the PSID, a man is by construction a household head for a married or cohabiting couple. A

women can be a household head in a single household.

43

survey closest to the year when experience is missing. For example, to impute experience in 1980, I add years of full-time work from 1976 to 1979 to experience
reported in 1976. Similarly, experience in 1990 is calculated by adding years offull-time work from 1985 to 1989 to experience reported in 1990.
Occupation and Industry For years between 1968 and 1980, I use the occupationand industry codes from the retrospective supplemental data files. From 1981 on,the code reported in each survey year is used.
Union Coverage An indicator for whether the job is covered by a union contract
is available in all years from 1979 to 1996 for both household heads and wives.
Task Index The task indices constructed from the DOT are merged with the PSID
sample using the 1970 Census 3-digit occupation code. When occupation is missing, but those in the previous and next years are available, the task index is imputedby taking an average of those. When occupation is missing, but that in the previous(next) year is available and the individual does not work full-time in the next (previous) year, the task index in the current year is assumed to be the same as that in
the previous (next) year. No imputation is conducted in all other cases.
Cumulated Task Index Because the PSID does not include the whole occupational history since the entry into the labor market, the cumulative task index is
imputed as follows. I first run a fixed-effect regression of the task index on experience and its square. Here, I assume that individuals have a common slope for the
profile of task index and experience, but they have different intercepts. The individual intercept is given by an average of residuals from the fixed-effect regression.
The missing values are imputed using the estimated task-experience profile withheterogeneous intercepts.

B

Parameter Estimates (For Online Publication)

The following tables report the estimates of the structural parameters of the model.
44

Table 9: Effect of Union Coverage
Estimate
0.106
0.002
−0.001

Union Coverage
Union Coverage × t79
Union Coverage × t89

Std. Error
0.011
0.001
0.002

Note: The parameter estimates for Equation (14) are reported. t79 = (t − 1979) and t89 = (t −1989) · I(t ≥ 1989) where I(·) is an indicator function that takes the value one if the condition in theparenthesis is satisfied and zero otherwise.

Table 10: Output Price Function
Intercept
t79
t89
COG
COG × t79
COG × t89
COG-sq
COG-sq × t79
COG-sq × t89
MTR
MTR × t79
MTR × t89
MTR-sq
MTR-sq × t79
MTR-sq × t89
COG × MTR
COG × MTR × t79
COG × MTR × t89

Estimate
0.879
0.028
0.084
−1.7650.002−0.197−1.796−0.0860.147
2.734−0.142−0.046−1.7300.035
0.052−2.1400.217−0.024

Std. Error
0.212
0.026
0.053
0.532
0.070
0.149
0.690
0.077
0.128
0.500
0.065
0.134
0.482
0.061
0.119
0.586
0.077
0.167

Note: The parameter estimates for Equations (15) and (16) are reported. COG and MTR are abbreviations for cognitive and motor, respectively. t79 = (t − 1979) and t89 = (t − 1989) · I(t ≥ 1989) whereI(·) is an indicator function that takes the value one if the condition in the parenthesis is satisfied andzero otherwise.

45

Table 11: Returns to Skills
Cognitive Skill
Intercept
t79
COG
COG × t79
Motor Skill
Intercept
t79
MTR
MTR × t79

Estimate

Std. Error−0.1840.004
1.000−0.001

0.037
0.008

0.388
−0.0091.000−0.031

0.309
0.029

0.004

0.025

Note: The parameter estimates for Equation (17) are reported. COG and MTR are abbreviations forcognitive and motor skills, respectively. t79 = (t − 1979) and t89 = (t − 1989) · I(t ≥ 1989) whereI(·) is an indicator function that takes the value one if the condition in the parenthesis is satisfied andzero otherwise.

46

Table 12: Skill Equations
Cognitive Skill
Woman
White
Education
Experience
Experience2 /100
Sum of COG
Ave. of COG
Ave. of Union
Ave. of COG × Ave. of Union
Motor Skill
Woman
White
Education
Experience
Experience2 /100
Sum of MTR
Ave. of MTR
Ave. of Union
Ave. of MTR × Ave. of Union
General Skill
Woman
White
Education
Experience
Experience2 /100
Ave. of Union

Estimate

Std. Error

0.089−0.0690.070
0.034−0.114
0.047
6.780
1.575
−3.532

0.047
0.049
0.012
0.007
0.016
0.007
0.752
0.289
0.527

−0.116−0.009−0.0090.013−0.050
0.017
0.487
0.091
−0.149

0.041
0.016
0.006
0.006
0.017
0.006
0.192
0.114
0.198

−0.197
0.104
0.017
0.002
0.014
0.295

0.027
0.020
0.006
0.004
0.010
0.034

Note: The parameter estimates for Equations (19)-(22) are reported. COG and MTR are abbreviations for cognitive and motor skills, respectively.

C

Comparison Between High School andCollege Educated Men (For Online Publication)

The following tables report statistics and estimates for high school and college educated men. See the footnotes for details.

47

Table 13: Differences Between High School and College Educated Men in 1979
and 1996

Logwage
Cognitive Task
Motor Task
White
Education
Experience
Union Coverage

College
2.655
0.611
0.483
0.956
15.95015.752
0.140

1979
HS
2.360
0.489
0.529
0.877
12.00018.039
0.428

Diff
0.295
0.122
−0.0460.079
3.950−2.288−0.288

College
2.750
0.604
0.471
0.945
16.28118.977
0.115

1996
HS
2.218
0.482
0.522
0.874
12.00018.998
0.281

Diff
0.532
0.122
−0.0510.071
4.281−0.021−0.166

D-in-D
0.237
0.000−0.005−0.008
0.331
2.267
0.121

Note: The source is the PSID 1979-1996. Wages are deflated by 1983 PCE Index. The sample
includes household heads and wives who worked full-time (1,500 hours a year or more). Selfemployed workers and those who are younger than 18 or older than 65 are excluded from the sample.
Sample weights are applied.

Table 14: Skill Gap Between High School and College Educated Men

Cognitive Skill
Motor Skill
General Skill

1979
Estimates Std. Error
0.358
0.022
−0.0600.021−0.0180.026

1996
Estimates Std. Error
0.415
0.025
−0.062
0.022
0.029
0.027

Note: Measured in logwage by multiplying the skill gaps and the returns to skills for an average task
(x = 0.5) in 1979. Positive numbers indicate that college educated men have more skills than highschool educated men, and vice versa.

48

Table 15: Decomposition of Changes in Male Logwage Gap
Base Year: 1979
Estimate Std. Error

Base Year: 1996
Estimate Std. Error−0.0100.079
0.043−0.005

0.084
0.090
0.015
0.003

−0.0070.075
0.041−0.009

0.086
0.089
0.014
0.005

0.064
−0.008
0.007
0.047
0.013

0.005
0.004
0.002
0.004
0.001

0.070
0.002
−0.005
0.047
0.017

0.005
0.002
0.002
0.004
0.001

Residuals

0.007

0.010

0.007

0.010

Total

0.237

0.046

0.237

0.046

Wage Structure EffectOutput Price
Returns to Cognitive Skill
Returns to Motor Skill
Union Premium
Composition EffectCognitive Task & Skill
Motor Task & Skill
Interaction of Cognitive & Motor Tasks
General Skill
Union Coverage

Note: Base year refers to the year in which the parameters are fixed in calculating the composition
effect. Namely, the first two columns use Equation (25), and the second two columns use Equation
(26).

D

Identification Strategy (For Online Publication)

D.1

First Stage Regression for Instrumental Variables

I run the instrumental variable first-stage regressions to see how strongly instruments used in previous papers are correlated with the task indices. The dependent
variables are the cognitive and motor task indices, and the instruments used include 9 dummies for father’s occupation, the state-level employment shares for 8
occupations (1-digit), and the state-level unemployment rate. Along with these instruments, I include two sets of covariates. In model 1, I include variables that areroutinely used in wage regressions: education, experience, experience-squared, anddummies for whites and females. In model 2, in addition to the covariates in model
1, I include the sum of the task indices for the past jobs, the time-average of thetask indices, the time-average of the union status, and the interaction of the last
two. These additional variables in model 2 are not used by previous papers, and I
49

expect them to control for worker heterogeneity in this model regression. I run thefirst-stage regressions for models 1 and 2 by pooling the PSID sample, eliminating
observations with missing variables.
Table 16 reports F-statistics. Staiger and Stock (1997) suggest a rule-of-thumbthat the F-statistic must be greater than 10 to reject the null hypothesis of weak instruments in cross-section data with homoskedastic error terms when one instrument
exists in the model. In model 1, the instrumental variables are strongly correlatedwith the cognitive task index with the F-statistic being 67.245. The F-statistic for the
motor task index is at 10.221. However, in model 2 with the skill control variables,
the instruments are no longer as strong. For the cognitive task index, the F-statistic
is only 9.393, and it is 2.633 for the motor task index.
Table 16: Significance Test for Instruments for Task Indices

Model 1
Cognitive Task
Motor Task
Model 2
Cognitive Task
Motor Task

DF

F-statistic

18
18

67.24510.221

18
18

9.393
2.633

Source: PSID 1979-1996. Sample size is 61,311.
Note: IVs include 9 dummies for father’s occupation, the state-level employment shares for 8 occupations (1-digit), and the state-level unemployment rate. In model 1, I also include education,
experience, experience-squared, and dummies for whites and females. In model 2, in addition to thecovariates in model 1, I include the sum of the task indexes for the past jobs, the time-average of thetask indexes, and its squared.

D.2

Identifying Source for Skill Endowments

The model allows me to estimate how an observed characteristic such as education
can be associated with three different types of skills: cognitive, motor, and general. This subsection explains which features of the data allow me to identify the
relationship between a single variable and three different types of skills.
To simplify the discussion, consider t = 1979 and drop the time subscript. De50

note conditioning variables by Xi . The conditional mean logwage is given byE(ln wi j |Xi )2
2= π0 + π1 xC, j + π2 xM, j + π3 xC,
j + π4 xM, j + πt xC, j xM, j +t−10(βC,0 + βC,2 xC, j ) · (γC,0di + γC,1 ei + γC,2 e2i + γC,3 ∑ xC,i jτ + γC,4 x̄C,i + γC,5 ūi + γC,6 x̄C,i ūi )
τ=ti
t−1

0
di + γM,1 eit + γM,2 e2it + γM,3 ∑ xM,i jτ + γM,4 x̄M,i + γM,5 ūi + γM,6 x̄M,i ūi )(βM,0 + βM,2 xC, j ) · (γM,0τ=ti
0+(γG,0di + γG,1 eit + γG,2 e2it + γG,3 ūi ) + βU ui ,(27)

where the second line corresponds to Π j (the intercept of the production function),
the third line is the product of returns to cognitive skill and the skill endowments,
the fourth line is the product of those of motor skills, and the fifth line includes
general skills and union coverage.
Identification of the parameters for the occupation-specific intercept, generalskills, and union coverage (π, γG , and βU , respectively) is straightforward. The
parameters in the function for returns to skills β and those in the skill equations γ
are identified up to scale. One of the parameters for the returns to skills or the skill
function must be fixed for each of the task-specific skills. Without loss of generality,
I normalize the parameters by setting βk,2 = 1.
The parameters for the task-specific skill production function (γk for k ∈ {C, M})
are identified using the variation of the product of the current task complexity index
and the worker characteristics d, because
βk,2 γk,0 =∂ E(ln wi j |Xi )∂ xk, j ∂ di(28)

and βk,2 = 1. Hence, variation in returns to worker characteristics di across tasks x
allows me to identify how a single characteristic such as education can be associatedwith three different types of skills.
To understand the intuition behind this result, consider the identification of taskspecific skill differences across education. In the data, the wage gap between highschool graduates and college graduates increases with the cognitive task complexity,51

conditional on the set of the control variables. Note that the worker assignment totasks can be considered exogenous given the set of the control variables under theidentification assumptions discussed in the previous section. This varying wage
gap between the education levels across tasks implies that college graduates possess
more cognitive skills than high school graduates, all else being equal. At any levelof complexity of the cognitive task, college graduates earn more than high school
graduates because they possess more cognitive skills. Moreover, their advantage incognitive skills is more strongly pronounced in a complex cognitive task, because
cognitive skills are intensely utilized in a complex task. Similarly, I need to examine
how the education wage gap changes with the motor task complexity, in order to
identify how education is associated with motor skills. The education wage gap that
does not vary across tasks identifies how education is associated with general skills.

E

Selection into Labor Force(For Online Publication)

I attempt to account for changes in the skill composition of workers and so allow
for cohort effects in the general skills function by including a birth year variable andits interaction with a female dummy. These additional variables capture changes in
conditional mean unobserved skills, given full-time labor force participation, which
may include the selection effect pointed out by Mulligan and Rubinstein (2008) andthe pure cohort effects. Note that these effects are identified separately for men andwomen. Cohort effects could be included in the task-specific skill functions as well,
but the standard errors are too large to interpret the result in a meaningful way.
Table 17 reports the Oaxaca-Blinder decomposition result under the augmented
specification. There is no significant difference from the results for the preferred
specification in Table 6. In the augmented model, changes in cognitive and general skills account for 0.063-0.090 out of 0.191, which is not very different to theestimates in the preferred specification of 0.076-0.099. The results indicate thatchanges in selection and cohort effects are largely taken care of by including theadditional skill measures.

52

Table 17: Decomposition of Changes in Gender Logwage Gap (Accounting for
Cohort Effects)
Base Year: 1979
Estimate Std. Error

Base Year: 1996
Estimate Std. Error

Wage Structure EffectOutput Price
Returns to Cognitive Skill
Returns to Motor Skill
Union Premium
Composition EffectCognitive Task & Skill
Motor Task & Skill
Interaction of Cognitive & Motor Tasks
General Skill
Union Coverage

0.014−0.018−0.092
0.001

0.007
0.006
0.010
0.000

−0.011
0.012−0.097
0.005

0.004
0.004
0.010
0.003

−0.0580.000
0.009−0.032−0.014

0.007
0.006
0.003
0.011
0.001

−0.031−0.010−0.007−0.032−0.018

0.007
0.004
0.003
0.011
0.002

Residuals−0.0020.011−0.002

0.011

Total

−0.191

0.027−0.1910.027

Note: Base year refers to the year in which the parameters are fixed in calculating the composition
effect. Namely, the first two columns use Equation (25), and the second two columns use Equation(26).

53